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  • 251.
    Kopriva, David A
    et al.
    Department of Mathematics, The Florida State University, Tallahassee, USA.
    Winters, Andrew Ross
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Bohm, Marvin
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Gassner, Gregor J
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    A provably stable discontinuous Galerkin spectral element approximation for moving hexahedral meshes2016Inngår i: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 139, s. 148-160Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We design a novel provably stable discontinuous Galerkin spectral element (DGSEM) approximation to solve systems of conservation laws on moving domains. To incorporate the motion of the domain, we use an arbitrary Lagrangian-Eulerian formulation to map the governing equations to a fixed reference domain. The approximation is made stable by a discretization of a skew-symmetric formulation of the problem. We prove that the discrete approximation is stable, conservative and, for constant coefficient problems, maintains the free- stream preservation property. We also provide details on how to add the new skew-symmetric ALE approximation to an existing discontinuous Galerkin spectral element code. Lastly, we provide numerical support of the theoretical results.

    Fulltekst (pdf)
    A provably stable discontinuous Galerkin spectral element approximation for moving hexahedral meshes
  • 252. Kozdon, Jeremy E.
    et al.
    Dunham, Eric M.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Interaction of waves with frictional interfaces using summation-by-parts difference operators I: Weak enforcement of nonlinear boundary conditions2010Rapport (Annet vitenskapelig)
  • 253.
    Kozdon, Jeremy E.
    et al.
    Department of Geophysics, Stanford University, Stanford, USA.
    Dunham, Eric M.
    Department of Geophysics, Stanford University, Stanford, USA.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Interaction of waves with frictional interfaces using summation-by-parts difference operators II: Extension to full elastodynamics2010Rapport (Annet vitenskapelig)
    Abstract [en]

    Problems in elastodynamics with nonlinear boundary conditions, such as those arising when modeling earthquake rupture propagation along internal interfaces (faults) governed by nonlinear friction laws, are inherently boundary driven. For such problems, stable and accurate enforcement of boundary conditions is essential for obtaining globally accurate numerical solutions (and predictions of ground motion in earthquake simulations). High-order finite difference methods are a natural choice for problems like these involving wave propagation, but enforcement of boundary conditions is complicated by the fact that the stencil must transition to one-sided near the boundary.

    In this work we develop a high-order method for tensor elasticity with faults whose strength is a nonlinear function of sliding velocity and a set of internal state variables obeying differential evolution equations (a mathematical framework known as rate-and-state friction). The method is based on summation-by-parts finite difference operators and weak enforcement of boundary conditions using the simultaneous approximation term method. We prove that the method is strictly stable and dissipates energy at a slightly faster rate than the continuous solution (with the difference in energy dissipation rates vanishing as the mesh is refined)

  • 254.
    Kozdon, Jeremy E.
    et al.
    Department of Geophysics, Stanford, CA, USA.
    Dunham, Eric M.
    Department of Geophysics, Stanford, CA, USA.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap.
    Interaction of waves with frictional interfaces using summation-by-parts difference operators: Weak enforcement of nonlinear boundary conditions2011Rapport (Fagfellevurdert)
    Abstract [en]

    We present a high-order difference method for problems in elastodynamics involving the interaction of waves with highly nonlinear frictional interfaces. We restrict our attention to two-dimensional antiplane problems involving deformation in only one direction. Jump conditions that relate tractions on the interface, or fault, to the relative sliding velocity across it are of a form closely related to those used in earthquake rupture models and other frictional sliding problems. By using summation-by-parts (SBP) finite difference operators and weak enforcement of boundary and interface conditions, a strictly stable method is developed. Furthermore, it is shown that unless the nonlinear interface conditions are formulated in terms of characteristic variables, as opposed to the physical variables in terms of which they are more naturally stated, the semi-discretized system of equations can become extremely stiff, preventing efficient solution using explicit time integrators.

    The use of SBP operators also provides a rigorously defined energy balance for the discretized problem that, as the mesh is refined, approaches the exact energy balance in the continuous problem. This enables one to investigate earthquake energetics, for example the efficiency with which elastic strain energy released during rupture is converted to radiated energy carried by seismic waves, rather than dissipated by frictional sliding of the fault. These theoretical results are confirmed by several numerical tests in both one and two dimensions demonstrating the computational efficiency, the high-order convergence rate of the method, the benefits of using strictly stable numerical methods for long time integration, and the accuracy of the energy balance.

  • 255.
    Kozdon, Jeremy E.
    et al.
    Department of Geophysics, Stanford University.
    Dunham, Eric M.
    Department of Geophysics, Stanford University.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap. Linköpings universitet, Tekniska högskolan.
    Interaction of Waves with Frictional Interfaces Using Summation-by-Parts Difference Operators: Weak Enforcement of Nonlinear Boundary Conditions2012Inngår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 50, nr 2, s. 341-367Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We present a high-order difference method for problems in elastodynamics involving

    the interaction of waves with highly nonlinear frictional interfaces. We restrict our

    attention to two-dimensional antiplane problems involving deformation in only one direction.

    Jump conditions that relate tractions on the interface, or fault, to the relative sliding velocity

    across it are of a form closely related to those used in earthquake rupture models and

    other frictional sliding problems. By using summation-by-parts (SBP) finite difference operators

    and weak enforcement of boundary and interface conditions, a strictly stable method

    is developed. Furthermore, it is shown that unless the nonlinear interface conditions are formulated

    in terms of characteristic variables, as opposed to the physical variables in terms of

    which they are more naturally stated, the semi-discretized system of equations can become

    extremely stiff, preventing efficient solution using explicit time integrators.

    The use of SBP operators also provides a rigorously defined energy balance for the discretized

    problem that, as the mesh is refined, approaches the exact energy balance in the

    continuous problem. This enables one to investigate earthquake energetics, for example the

    efficiency with which elastic strain energy released during rupture is converted to radiated

    energy carried by seismic waves, rather than dissipated by frictional sliding of the fault.

    These theoretical results are confirmed by several numerical tests in both one and two dimensions

    demonstrating the computational efficiency, the high-order convergence rate of

    the method, the benefits of using strictly stable numerical methods for long time integration,

    and the accuracy of the energy balance.

    Fulltekst (pdf)
    fulltext
  • 256.
    Kozdon, Jeremy E.
    et al.
    Department of Geophysics, Stanford University, USA.
    Dunham, Eric M.
    Department of Geophysics, Stanford University, USA.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    Simulation of Dynamic Earthquake Ruptures in Complex Geometries Using High-Order Finite Difference Methods2013Inngår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 55, nr 1, s. 92-124Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We develop a stable and high-order accurate finite difference method for problems in earthquake rupture dynamics in complex geometries with multiple faults. The bulk material is an isotropic elastic solid cut by pre-existing fault interfaces that accommodate relative motion of the material on the two sides. The fields across the interfaces are related through friction laws which depend on the sliding velocity, tractions acting on the interface, and state variables which evolve according to ordinary differential equations involving local fields. The method is based on summation-by-parts finite difference operators with irregular geometries handled through coordinate transforms and multi-block meshes. Boundary conditions as well as block interface conditions (whether frictional or otherwise) are enforced weakly through the simultaneous approximation term method, resulting in a provably stable discretization. The theoretical accuracy and stability results are confirmed with the method of manufactured solutions. The practical benefits of the new methodology are illustrated in a simulation of a subduction zone megathrust earthquake, a challenging application problem involving complex free-surface topography, nonplanar faults, and varying material properties.

    Fulltekst (pdf)
    fulltext
  • 257.
    Kozlov, Vladimir A
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Nazarov, Sergei A.
    St.Petersburg State University, Mathematics and Mechanics Faculty, St. Petersburg, Russia.
    A simple one-dimensional model of a false aneurysm in the femoral artery2016Inngår i: Journal of Mathematical Sciences, ISSN 1072-3374, E-ISSN 1573-8795, Vol. 214, nr 3, s. 287-301Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Using the dimension reduction procedure, a one-dimensional model of a periodic blood flow in the artery through a small hole in a thin elastic wall to a spindle-shaped hematoma, is constructed. This model is described by a system of two parabolic and one hyperbolic equations provided with mixed boundary and periodicity conditions. The blood exchange between the artery and the hematoma is expressed by the Kirchhoff transmission conditions. Despite the simplicity, the constructed model allows us to describe the damping of a pulsating blood flow by the hematoma and to determine the condition of its growth. In medicine, the biological object considered is called a false aneurysm.

  • 258.
    Kozlov, Vladimir A.
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Nazarov, Sergei A.
    St. Petersburg State University, St. Petersburg, Russia .
    Asymptotic Models of the Blood Flow in Arteries and Veins2013Inngår i: Journal of Mathematical Sciences, ISSN 1072-3374, E-ISSN 1573-8795, Vol. 194, nr 1, s. 44-57Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Asymptotic analysis is applied for obtaining one-dimensional models of the blood flow in narrow, thin-walled, elastic vessels. The models for arteries and veins essentially distinguish from each other, and the reason for this is the structure of their walls, as well as the operationing conditions. Although the obtained asymptotic models are simple, they explain various effects known in medical practice, in particular, describe the mechanism of vein-muscle pumping of blood.

  • 259.
    Kozlov, Vladimir
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Nazarov, Sergei A.
    St. Petersburg State University, St. Petersburg State Polytechnical University, Institute for Problems in Mechanical Engineering RAS, 61, Bolshoi pr. V.O., St. Petersburg, Russia.
    One-Dimensional Model of Viscoelastic Blood Flow Through a Thin Elastic Vessel2015Inngår i: Journal of Mathematical Sciences, ISSN 1072-3374, E-ISSN 1573-8795, Vol. 207, nr 2, s. 249-269Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Based on the three-dimensional Oldroyd viscoelastic fluid model, we develop a simple linear one-dimensional model of blood flow through a thin blood vessel with an elastic multilayer cylindrical wall. Unlike known models, the obtained system of integrodifferential equations with respect to the variables z and t (the longitudinal coordinate ant time) includes the Volterra operator in t, which takes into account the relaxation effect of stresses in a pulsating flow of blood regarded as a many-component viscoelastic fluid. We construct a simplified differential model corresponding to “short-term memory.” We study the effect of high-amplitude longitudinal oscillations of wall under a dissection (lamination). Bibliography: 24 titles. Illustrations: 1 figure.

  • 260.
    Kozlov, Vladimir
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Radosavljevic, Sonja
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Turesson, Bengt-Ove
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Wennergren, Uno
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Biologi. Linköpings universitet, Tekniska fakulteten.
    Estimating effective boundaries of population growth in a variable environment2016Inngår i: Boundary Value Problems, ISSN 1687-2762, E-ISSN 1687-2770, s. 1-28, artikkel-id 2016:172Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the impact of age-structure and temporal environmental variability on the persistence of populations. We use a linear age-structured model with time-dependent vital rates. It is the same as the one presented by Chipot in (Arch. Ration. Mech. Anal. 82(1):13-25, 1983), but the assumptions on the vital rates are slightly different. Our main interest is in describing the large-time behavior of a population provided that we know its initial distribution and transient vital rates. Using upper and lower solutions for the characteristic equation, we define time-dependent upper and lower boundaries for a solution in a constant environment. Moreover, we estimate solutions for the general time-dependent case and also for a special case when the environment is changing periodically.

    Fulltekst (pdf)
    fulltext
  • 261.
    Kozlov, Vladimir
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Rossmann, Juergen
    Univ Rostock, Germany.
    On the behavior of solutions of the nonstationary Stokes system near the vertex of a cone2019Inngår i: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, artikkel-id UNSP e201800305Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The paper deals with the Dirichlet problem for the nonstationary Stokes system in a threedimensional cone. The authors study the asymptotics of the solutions near the vertex of the cone. They show that the solutions are sums of singular functions and a regular remainder, where the singular functions depend on the eigenvalues of a certain operator pencil.

  • 262. Kreiss, Gunilla
    et al.
    Efraimsson, Gunilla
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Elimination of first order errors in shock calculations2001Inngår i: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 38, s. 1986-1998Artikkel i tidsskrift (Fagfellevurdert)
    Fulltekst (pdf)
    fulltext
  • 263.
    Kresin, Gershon
    et al.
    Ariel Univ, Israel.
    Mazya, Vladimir
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. Univ Liverpool, England.
    Sharp estimates for the gradient of the generalized Poisson integral for a half-space2018Inngår i: Georgian Mathematical Journal, ISSN 1072-947X, E-ISSN 1572-9176, Vol. 25, nr 2, s. 283-290Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A representation of the sharp coefficient in a pointwise estimate for the gradient of the generalized Poisson integral of a function f on R-n is obtained under the assumption that f belongs to L-p. The explicit value of the coefficient is found for the cases p = 1 and p = 2.

  • 264.
    Krig, Kåre
    Linköpings universitet, Matematiska institutionen.
    Methods for phylogenetic analysis2010Independent thesis Advanced level (degree of Master (One Year)), 20 poäng / 30 hpOppgave
    Abstract [en]

    In phylogenetic analysis one study the relationship between different species. By comparing DNA from two different species it is possible to get a numerical value representing the difference between the species. For a set of species, all pair-wise comparisons result in a dissimilarity matrix d.

    In this thesis I present a few methods for constructing a phylogenetic tree from d. The common denominator for these methods is that they do not generate a tree, but instead give a connected graph. The resulting graph will be a tree, in areas where the data perfectly matches a tree. When d does not perfectly match a tree, the resulting graph will instead show the different possible topologies, and how strong support they have from the data.

    Finally I have tested the methods both on real measured data and constructed test cases.

    Fulltekst (pdf)
    FULLTEXT01
  • 265.
    Krishnasamy, Ezhilmathi
    Linköpings universitet, Institutionen för konstruktions- och produktionsteknik, Hållfasthetslära.
    Hybrid CPU-GPU Parallel Simulations of 3D Front Propagation2014Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    This master thesis studies GPU-enabled parallel implementations of the 3D Parallel Marching Method (PMM). 3D PMM is aimed at solving the non-linear static Jacobi-Hamilton equations, which has real world applications such as in the study of geological foldings, where each layer of the Earth’s crust is considered as a front propagating over time. Using the parallel computer architectures, fast simulationscan be achieved, leading to less time consumption, quicker understanding of the inner Earth and enables early exploration of oil and gas reserves. Currently 3D PMM is implemented in shared memory architecture using OpenMP Application Programming Interface (API) and the MINT programming model, which translates C code into Compute Unified Device Architecture (CUDA) code for a single Graphical Process Unit (GPU). Parallel architectures have seen rapid growth in recent years, especially GPUs, allowing us to do faster simulations. In this thesis work, a new parallel implementation for 3D PMM has been done to exploit multicore CPU architectures as well as single and multiple GPUs. In a multiple GPU implementation, 3D data isdecomposed into 1D data for each GPU. CUDA streams are used to overlap the computation and communication within the single GPU. Part of the decomposed 3D volume data is kept in the respective GPU to avoid complete data transfer between the GPUs over a number of iterations. In total, there are two kinds of datatransfers that are involved while doing computation in the multiple GPUs: boundary value data transfer and decomposed 3D volume data transfer. The decomposed 3D volume data transfer is optimized between the multiple GPUs by using the peer to peer memory transfer in CUDA. The speedup is shown and compared between shared memory CPUs (E5-2660, 16cores), single GPU (GTX-590, C2050 and K20m) and multiple GPUs. Hand coded CUDA has shown slightly better performance than the Mint translated CUDA, and the multiple GPU implementation showed promising speedup compared to shared memory multicore CPUs and single GPU implementations.

    Fulltekst (pdf)
    fulltext
  • 266.
    Kronbäck, Susanna
    et al.
    Linköpings universitet, Institutionen för beteendevetenskap och lärande. Linköpings universitet, Utbildningsvetenskap.
    Hendsel, Jevgenia
    Linköpings universitet, Institutionen för beteendevetenskap och lärande. Linköpings universitet, Utbildningsvetenskap.
    Algebra på gymnasiet = Svårt?!: Förekomst av felsvar och feltyper vid åk 1-gymnasieelevers beräkningar inom algebra2019Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Innehållet i studien handlar om att kategorisera olika typer av fel som elever i åk 1 på gymnasiet gör i algebra. Data utgörs av 80 elevprov skrivna av elever på samhällsvetenskapsprogrammet och VVS- och fastighetsprogrammet läsåret 2017/2018 och 2018/2019. Uppgifterna som eleverna har fått göra är lösa ekvationer, förenkla uttryck, räkna värdet av ett uttryck samt problemlösning. Elevernas svar har analyserats och kategoriserats i sex feltyper: 1. Förståelsefel, 2. Procedurfel, 3. Modelleringsfel eller problemlösningsfel, 4. Resonemangsfel, 5. Redovisningsfel eller kommunikationsfel, 6. Övriga fel.

    I resultatet preseneteras varje feltyp illustrerad med elevexempel. Med tidigre forskning som utgångspunkt identifieras och diskuteras vilka missuppfattningar och svårigheter som kan vara den bakomliggande orsaken till att eleverna gjort dessa fel. 

    Några exempel på orsaker är att eleverna inte uppfattar variabelns (x) symboliska värde, förstår inte variablers generella beteckning (a och b), att variabeln kan representera en siffra, eleverna övergeneraliserar, förstår inte räkning med negativa tal, kan inte hantera aritmetik, förstår inte likhetstecknets betydelse, har oeffektiv resonemang (gissar, testar sig fram), samt skriver av uppgiften fel.

    Fulltekst (pdf)
    fulltext
  • 267.
    Krus, Kristofer
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Wave Model and Watercraft Model for Simulation of Sea State2014Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    The problem of real-time simulation of ocean surface waves, ship movement and the coupling in between is tackled, and a number of different methods are covered and discussed. Among these methods, the finite volume method has been implemented in an attempt to solve the problem, along with the compressible Euler equations, an octree based staggered grid which allows for easy adaptive mesh refinement, the volume of fluid method and a variant of the Hyper-C advection scheme for compressible flows for advection of the phase fraction field.

    The process of implementing the methods that were chosen proved to be tricky in many ways, as they involve a large number of advanced topics, and the implementation that was implemented in this thesis work suffered from numerous issues. There were for example problems with keeping the interface intact, as well as a harsh restriction on the time step size due to the CFL condition. Improvements required to make the method sustainable for real-time applications are discussed, and a few suggestions on alternative approaches that are already in use for similar purposes are also given and discussed.

    Furthermore, a method for compensating for gain/loss of mass when solving the incompressible flow equations with an inaccurately solved pressure Poisson equation is presented and discussed. A momentum conservative method for transporting the velocity field on staggered grids without introducing unnecessary smearing is also presented and implemented. A simple, physically based illumination model for sea surfaces is derived, discussed and compared to the Blinn–Phong shading model, although it is never implemented. Finally, a two-dimensional partial differential equation in the spatial domain for simulating water surface waves for mildly varying bottom topography is derived and discussed, although it is deemed to be too slow for real-time purposes and is therefore never implemented.

    Fulltekst (pdf)
    Wave Model and Watercraft Model for Simulation of Sea State
  • 268. Bestill onlineKjøp publikasjonen >>
    Kurujyibwami, Celestin
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Admissible transformations and the group classification of Schrödinger equations2017Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    We study admissible transformations and solve group classification problems for various classes of linear and nonlinear Schrödinger equations with an arbitrary number n of space variables.

    The aim of the thesis is twofold. The first is the construction of the new theory of uniform seminormalized classes of differential equations and its application to solving group classification problems for these classes. Point transformations connecting two equations (source and target) from the class under study may have special properties of semi-normalization. This makes the group classification of that class using the algebraic method more involved. To extend this method we introduce the new notion of uniformly semi-normalized classes. Various types of uniform semi-normalization are studied: with respect to the corresponding equivalence group, with respect to a proper subgroup of the equivalence group as well as the corresponding types of weak uniform semi-normalization. An important kind of uniform semi-normalization is given by classes of homogeneous linear differential equations, which we call uniform semi-normalization with respect to linear superposition of solutions.

    The class of linear Schrödinger equations with complex potentials is of this type and its group classification can be effectively carried out within the framework of the uniform semi-normalization. Computing the equivalence groupoid and the equivalence group of this class, we show that it is uniformly seminormalized with respect to linear superposition of solutions. This allow us to apply the version of the algebraic method for uniformly semi-normalized classes and to reduce the group classification of this class to the classification of appropriate subalgebras of its equivalence algebra. To single out the classification cases, integers that are invariant under equivalence transformations are introduced. The complete group classification of linear Schrödinger equations is carried out for the cases n = 1 and n = 2.

    The second aim is to study group classification problem for classes of generalized nonlinear Schrödinger equations which are not uniformly semi-normalized. We find their equivalence groupoids and their equivalence groups and then conclude whether these classes are normalized or not. The most appealing classes are the class of nonlinear Schrödinger equations with potentials and modular nonlinearities and the class of generalized Schrödinger equations with complex-valued and, in general, coefficients of Laplacian term. Both these classes are not normalized. The first is partitioned into an infinite number of disjoint normalized subclasses of three kinds: logarithmic nonlinearity, power nonlinearity and general modular nonlinearity. The properties of the Lie invariance algebras of equations from each subclass are studied for arbitrary space dimension n, and the complete group classification is carried out for each subclass in dimension (1+2). The second class is successively reduced into subclasses until we reach the subclass of (1+1)-dimensional linear Schrödinger equations with variable mass, which also turns out to be non-normalized. We prove that this class is mapped by a family of point transformations to the class of (1+1)-dimensional linear Schrödinger equations with unique constant mass.

    Delarbeid
    1. Equivalence groupoid for (1+2)-dimensional linear Schrodinger equations with complex potentials
    Åpne denne publikasjonen i ny fane eller vindu >>Equivalence groupoid for (1+2)-dimensional linear Schrodinger equations with complex potentials
    2015 (engelsk)Inngår i: SEVENTH INTERNATIONAL WORKSHOP: GROUP ANALYSIS OF DIFFERENTIAL EQUATIONS AND INTEGRABLE SYSTEMS (GADEISVII), IOP Publishing: Conference Series / Institute of Physics (IoP) , 2015, Vol. 621, nr UNSP 012008, s. UNSP 012008-Konferansepaper, Publicerat paper (Fagfellevurdert)
    Abstract [en]

    We describe admissible point transformations in the class of (1+2)-dimensional linear Schrodinger equations with complex potentials. We prove that any point transformation connecting two equations from this class is the composition of a linear superposition transformation of the corresponding initial equation and an equivalence transformation of the class. This shows that the class under study is semi-normalized.

    sted, utgiver, år, opplag, sider
    IOP Publishing: Conference Series / Institute of Physics (IoP), 2015
    Serie
    Journal of Physics Conference Series, ISSN 1742-6588 ; 621
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-120668 (URN)10.1088/1742-6596/621/1/012008 (DOI)000357939100008 ()
    Konferanse
    7th International Workshop on Group Analysis of Differential Equations and Integrable Systems (GADEIS)
    Tilgjengelig fra: 2015-08-20 Laget: 2015-08-20 Sist oppdatert: 2017-05-15
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  • 269. Bestill onlineKjøp publikasjonen >>
    La Cognata, Cristina
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    High order summation-by-parts based approximations for discontinuous and nonlinear problems2017Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Numerical approximations using high order finite differences on summation-byparts (SBP) form are investigated for discontinuous and fully nonlinear systems of partial differential equations. Stability and conservation properties of the approximations are obtained through a weak imposition of interface and boundary conditions with the simultaneous-approximation-term (SAT) technique. The SBP-SAT approximations replicate the continuous integration by parts rule. From this property, well-posedness and integral properties of the continuous problem are mimicked, and energy estimates leading to stability are obtained.

    The first part of the thesis focuses on the simulations of discontinuous linear advection problems. An artificial interface is introduced, separating parts of the spatial domain characterized by different wave speeds. A set of flexible stability conditions at the interface are derived, which can be adapted to yield conservative or non-conservative approximations. This model can be interpreted as a simplified version of nonlinear problems involving jumps at shocks, or as a prototypical of wave propagation through different materials.

    In the second part of the thesis, the vorticity/stream function formulation of the nonlinear momentum equation for an incompressible inviscid fluid is considered. SBP operators are used to derive a new Arakawa-like Jacobian with mimetic properties by combining different consistent approximations of the convection terms. Energy and enstrophy conservation is obtained for periodic problems using schemes with arbitrarily high order of accuracy. These properties are crucial for long-term numerical calculations in climate and weather forecasts or ocean circulation predictions.

    The third and final contribution of the thesis is dedicated to the incompressible Navier-Stokes problem. First, different completely general formulations of energy bounding boundary conditions are derived for the nonlinear equations. The boundary conditions can be used at both far field and solid wall boundaries. The discretisation in time and space with weakly imposed initial and boundary conditions using the SBP-SAT framework is proved to be stable and the divergence free condition is approximated with the design order of the scheme. Next, the same formulations are considered in a linearised setting, whereupon the spectra associated with the initial boundary value problem and its SBP-SAT discretisation are derived using the Laplace-Fourier technique. The influence of different boundary conditions on the spectrum and in particular the convergence to steady state is studied.

    Delarbeid
    1. Well-posedness, stability and conservation for a discontinuous interface problem
    Åpne denne publikasjonen i ny fane eller vindu >>Well-posedness, stability and conservation for a discontinuous interface problem
    2016 (engelsk)Inngår i: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 56, nr 2, s. 681-704Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    The advection equation is studied in a completely general two domain setting with different wave-speeds and a time-independent jump-condition at the interface separating the domains. Well-posedness and conservation criteria are derived for the initial-boundary-value problem. The equations are semi-discretized using a finite difference method on Summation-By-Part (SBP) form. The relation between the stability and conservation properties of the approximation are studied when the boundary and interface conditions are weakly imposed by the Simultaneous-Approximation-Term (SAT) procedure. Numerical simulations corroborate the theoretical findings.

    sted, utgiver, år, opplag, sider
    Springer, 2016
    Emneord
    Interface – Discontinuous coefficients problems – Initial boundary value problems – Well-posedness – Conservation – Stability – Interface conditions – High order accuracy – Summation-by-parts operators
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-121468 (URN)10.1007/s10543-015-0576-7 (DOI)000376580200016 ()
    Tilgjengelig fra: 2015-09-21 Laget: 2015-09-21 Sist oppdatert: 2017-12-04bibliografisk kontrollert
    2. A new high order energy and enstrophy conserving Arakawa-like Jacobian differential operator
    Åpne denne publikasjonen i ny fane eller vindu >>A new high order energy and enstrophy conserving Arakawa-like Jacobian differential operator
    2015 (engelsk)Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 301, s. 167-177Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    A new high order Arakawa-like method for the incompressible vorticity equation in two-dimensions has been developed. Mimetic properties such as skew-symmetry, energy and enstrophy conservations for the semi-discretization are proved for periodic problems using arbitrary high order summation-by-parts operators. Numerical simulations corroborate the theoretical findings.

    sted, utgiver, år, opplag, sider
    Elsevier, 2015
    Emneord
    Non-linear problems; Summation-by-parts operators; Jacobian; Mimetic schemes; High-order schemes; Stability; Finite difference
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-121469 (URN)10.1016/j.jcp.2015.08.028 (DOI)000362379300010 ()
    Tilgjengelig fra: 2015-09-21 Laget: 2015-09-21 Sist oppdatert: 2019-04-11bibliografisk kontrollert
    3. Energy Stable Boundary Conditions for the Nonlinear Incompressible Navier-Stokes Equations
    Åpne denne publikasjonen i ny fane eller vindu >>Energy Stable Boundary Conditions for the Nonlinear Incompressible Navier-Stokes Equations
    2017 (engelsk)Rapport (Annet vitenskapelig)
    Abstract [en]

    The nonlinear incompressible Navier-Stokes equations with boundary conditions at far fields and solid walls is considered. Two different formulations of boundary conditions are derived using the energy method. Both formulations are implemented in both strong and weak form and lead to an estimate of the velocity field. Equipped with energy bounding boundary conditions, the problem is approximated by using difference operators on summation-by-parts form and weak boundary and initial conditions. By mimicking the continuous analysis, the resulting semi-discrete as well as fully discrete scheme are shown to be provably stable, divergence free and high-order accurate.

    sted, utgiver, år, opplag, sider
    Linköping University Electronic Press, 2017. s. 31
    Serie
    LiTH-MAT-R, ISSN 0348-2960 ; 2017:9
    Emneord
    Navier-Stokes equations, incompressible, boundary conditions, energy estimate, stability, summation-by-parts, high-order accuracy, divergence free
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-139730 (URN)LiTH-MAT-R--2017/09--SE (ISRN)
    Tilgjengelig fra: 2017-08-14 Laget: 2017-08-14 Sist oppdatert: 2017-09-05bibliografisk kontrollert
    4. Spectral analysis of the incompressible Navier-Stokes equations with different boundary conditions
    Åpne denne publikasjonen i ny fane eller vindu >>Spectral analysis of the incompressible Navier-Stokes equations with different boundary conditions
    2017 (engelsk)Rapport (Annet vitenskapelig)
    Abstract [en]

    The influence of boundary conditions on the spectrum of the incompressible Navier-Stokes equations is studied. The spectra associated to different types of boundary conditions are derived using the Fourier-Laplace technique. In particular, the effect of various combinations of generalized in- and outgoing variables on the convergence to the steady state is investigated. The boundary conditions are analysed in both the continuous and semi-discrete problems. In the latter, high-order schemes in summation-by-parts form with weakly imposed boundary conditions are used to approximate the equations. Numerical calculations are performed and show that the discrete behaviour agrees with the theoretical analysis.

    sted, utgiver, år, opplag, sider
    Linköping: Linköping University Electronic Press, 2017. s. 34
    Serie
    LiTH-MAT-R, ISSN 0348-2960 ; 2017:10
    Emneord
    Incompressible flows, Navier-Stokes, Fourier-Laplace technique, summation-by-parts, weak boundary conditions
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-139729 (URN)LiTH-MAT-R--2017/10—SE (ISRN)
    Tilgjengelig fra: 2017-08-14 Laget: 2017-08-14 Sist oppdatert: 2017-09-05bibliografisk kontrollert
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    High order summation-by-parts based approximations for discontinuous and nonlinear problems
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  • 270.
    La Cognata, Cristina
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Spectral analysis of the incompressible Navier-Stokes equations with different boundary conditions2017Rapport (Annet vitenskapelig)
    Abstract [en]

    The influence of boundary conditions on the spectrum of the incompressible Navier-Stokes equations is studied. The spectra associated to different types of boundary conditions are derived using the Fourier-Laplace technique. In particular, the effect of various combinations of generalized in- and outgoing variables on the convergence to the steady state is investigated. The boundary conditions are analysed in both the continuous and semi-discrete problems. In the latter, high-order schemes in summation-by-parts form with weakly imposed boundary conditions are used to approximate the equations. Numerical calculations are performed and show that the discrete behaviour agrees with the theoretical analysis.

    Fulltekst (pdf)
    fulltext
  • 271.
    La Cognata, Cristina
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    Well-posedness, Stability and Conservation for a Discontinuous Interface Problem2015Rapport (Annet vitenskapelig)
    Abstract [en]

    The advection equation is studied in a completely general two domain setting with different wave-speeds and a time-independent jump-condition at the interface separating the domains. Well-posedness and conservation criteria are derived for the initial-boundary-value problem. The equations are semidiscretized using afinite dfference method on summation-by-parts (SBP) form. The stability and conservation properties of the approximation are studied when the boundary and interface conditions are weakly imposed by the simultaneous approximation term (SAT) procedure. Numerical simulations corroborate the theoretical finndings.

    Fulltekst (pdf)
    Well-posedness, Stability and Conservation for a Discontinuous Interface Problem
  • 272.
    La Cognata, Cristina
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Well-posedness, stability and conservation for a discontinuous interface problem2016Inngår i: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 56, nr 2, s. 681-704Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The advection equation is studied in a completely general two domain setting with different wave-speeds and a time-independent jump-condition at the interface separating the domains. Well-posedness and conservation criteria are derived for the initial-boundary-value problem. The equations are semi-discretized using a finite difference method on Summation-By-Part (SBP) form. The relation between the stability and conservation properties of the approximation are studied when the boundary and interface conditions are weakly imposed by the Simultaneous-Approximation-Term (SAT) procedure. Numerical simulations corroborate the theoretical findings.

    Fulltekst (pdf)
    Fulltext
  • 273.
    La Cognata, Cristina
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Well-Posedness, Stability and Conservation for a Discontinuous Interface Problem: An Initial Investigation2015Inngår i: Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014, Springer, 2015, s. 147-155Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    A robust interface treatment for the discontinuous coefficient advection equation satisfying time-independent jump conditions is presented. The aim of the investigation is to show how the different concepts like well-posedness, conservation and stability are related. The equations are discretized using high order finite difference methods on Summation By Parts (SBP) form. The interface conditions are weakly imposed using the Simultaneous Approximation Term (SAT) procedure. Spectral analysis and numerical simulations corroborate the theoretical findings.

    Fulltekst (pdf)
    Well-Posedness, Stability and Conservation for a Discontinuous Interface Problem: An Initial Investigation
  • 274.
    Lauer, Fabien
    et al.
    University of Lorraine, France.
    Ohlsson, Henrik
    Linköpings universitet, Institutionen för systemteknik. University of Calif Berkeley, CA 94720 USA.
    Finding sparse solutions of systems of polynomial equations via group-sparsity optimization2015Inngår i: Journal of Global Optimization, ISSN 0925-5001, E-ISSN 1573-2916, Vol. 62, nr 2, s. 319-349Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of linear equations. Then, two approaches are considered to find these group-sparse solutions. The first one is based on a convex relaxation resulting in a second-order cone programming formulation which can benefit from efficient reweighting techniques for sparsity enhancement. For this approach, sufficient conditions for the exact recovery of the sparsest solution to the polynomial system are derived in the noiseless setting, while stable recovery results are obtained for the noisy case. Though lacking a similar analysis, the second approach provides a more computationally efficient algorithm based on a greedy strategy adding the groups one-by-one. With respect to previous work, the proposed methods recover the sparsest solution in a very short computing time while remaining at least as accurate in terms of the probability of success. This probability is empirically analyzed to emphasize the relationship between the ability of the methods to solve the polynomial system and the sparsity of the solution.

  • 275.
    Laurén, Fredrik
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Practical Inlet Boundary Conditions for Internal Flow Calculations2018Inngår i: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 175, s. 159-166Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    To impose boundary conditions, data at the boundaries must be known, and consequently measurements of the imposed quantities must be available. In this paper, we consider the two most commonly used inflow boundary conditions with available data for internal flow calculations: the specification of the total temperature and total pressure. We use the energy method to prove that the specification of the total temperature and the total pressure together with the tangential velocity at an inflow boundary lead to well-posedness for the linearized compressible Euler equations. Next, these equations are discretized in space using high-order finite-difference operators on summation-by-parts form, and the boundary conditions are weakly imposed. The resulting numerical scheme is proven to be stable and the implementation of the corresponding nonlinear scheme is verified with the method of manufactured solutions. We also derive the spectrum for the continuous and discrete problems and show how to predict the convergence rate to steady state. Finally, nonlinear steady-state computations are performed, and they confirm the predicted convergence rates.

    Fulltekst tilgjengelig fra 2020-08-17 00:01
  • 276.
    Law, Craig
    et al.
    School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, Johannesburg, South Africa.
    Abbas, Qaisar
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Skews, Beric W.
    School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, Johannesburg, South Africa.
    The Effect of Reynolds Number in High Order Accurate Calculations with Shock Diffraction2010Inngår i: Proc. 7th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2010, s. 78:1-8Konferansepaper (Fagfellevurdert)
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  • 277. Bestill onlineKjøp publikasjonen >>
    Lei, Lei
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten.
    From Orthogonal to Non-orthogonal Multiple Access: Energy- and Spectrum-Efficient Resource Allocation2016Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    The rapid pace of innovations in information and communication technology (ICT) industry over the past decade has greatly improved people’s mobile communication experience. This, in turn, has escalated exponential growth in the number of connected mobile devices and data traffic volume in wireless networks. Researchers and network service providers have faced many challenges in providing seamless, ubiquitous, reliable, and high-speed data service to mobile users. Mathematical optimization, as a powerful tool, plays an important role in addressing such challenging issues.

    This dissertation addresses several radio resource allocation problems in 4G and 5G mobile communication systems, in order to improve network performance in terms of throughput, energy, or fairness. Mathematical optimization is applied as the main approach to analyze and solve the problems. Theoretical analysis and algorithmic solutions are derived. Numerical results are obtained to validate our theoretical findings and demonstrate the algorithms’ ability of attaining optimal or near-optimal solutions.

    Five research papers are included in the dissertation. In Paper I, we study a set of optimization problems of consecutive-channel allocation in single carrier-frequency division multiple access (SCFDMA) systems. We provide a unified algorithmic framework to optimize the channel allocation and improve system performance. The next three papers are devoted to studying energy-saving problems in orthogonal frequency division multiple access (OFDMA) systems. In Paper II, we investigate a problem of jointly minimizing energy consumption at both transmitter and receiver sides. An energy-efficient scheduling algorithm is developed to provide optimality bounds and near-optimal solutions. Next in Paper III, we derive fundamental properties for energy minimization in loadcoupled OFDMA networks. Our analytical results suggest that the maximal use of time-frequency resources can lead to the lowest network energy consumption. An iterative power adjustment algorithm is developed to obtain the optimal power solution with guaranteed convergence. In Paper IV, we study an energy minimization problem from the perspective of scheduling activation and deactivation of base station transmissions. We provide mathematical formulations and theoretical insights. For problem solution, a column generation approach, as well as a bounding scheme are developed. Finally, towards to 5G communication systems, joint power and channel allocation in non-orthogonal multiple access (NOMA) is investigated in Paper V in which an algorithmic solution is proposed to improve system throughput and fairness.

    Delarbeid
    1. A Unified Graph Labeling Algorithm for Consecutive-Block Channel Allocation in SC-FDMA
    Åpne denne publikasjonen i ny fane eller vindu >>A Unified Graph Labeling Algorithm for Consecutive-Block Channel Allocation in SC-FDMA
    2013 (engelsk)Inngår i: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 12, nr 11, s. 5767-5779Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    Optimal channel allocation is a key performance engineering aspect in single-carrier frequency-division multiple access (SC-FDMA). In SC-FDMA with localized channel assignment, the channels of each user must form a consecutive block. Subject to this constraint, various performance objectives, such as maximum utility, minimum power, and minimum number of channels, have been studied. We present a unified graph labeling algorithm for these problems, based on the structural insight that SC-FDMA channel allocation can be modeled as finding an optimal path in an acyclic graph. By this insight, our algorithm applies the concept of labeling and label domination that represent non-trivial extensions of finding a shortest or longest path. The key parameter in trading performance versus computation is the number of labels kept per node. Increasing the number ultimately enables global optimality. The algorithms approach is further justified by its global optimality guarantee with strong polynomial-time complexity for two specific scenarios, where the input is user-invariant and channel-invariant, respectively. For the general case, we provide numerical results demonstrating the algorithms ability of attaining near-optimal solutions.

    sted, utgiver, år, opplag, sider
    Institute of Electrical and Electronics Engineers (IEEE), 2013
    Emneord
    Algorithm, channel allocation, optimization, single carrier frequency division multiple access
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-102855 (URN)10.1109/TWC.2013.092313.130092 (DOI)000328058400034 ()
    Merknad

    R)||A*STAR, Singapore||Linkoping-Lund Excellence Center in Information Technology (ELLIIT), Sweden||

    Tilgjengelig fra: 2014-01-07 Laget: 2014-01-02 Sist oppdatert: 2017-12-06
    2. Resource Scheduling to Jointly Minimize Receiving and Transmitting Energy in OFDMA Systems
    Åpne denne publikasjonen i ny fane eller vindu >>Resource Scheduling to Jointly Minimize Receiving and Transmitting Energy in OFDMA Systems
    2014 (engelsk)Inngår i: 2014 11TH INTERNATIONAL SYMPOSIUM ON WIRELESS COMMUNICATIONS SYSTEMS (ISWCS), IEEE , 2014, s. 187-191Konferansepaper, Publicerat paper (Fagfellevurdert)
    Abstract [en]

    Resource scheduling in orthogonal frequency division multiple access (OFDMA) for energy saving has attracted extensive attention. Most current research considers the reduction of energy at the transmitter or the receiver separately. In this paper, we focus on minimizing the energy consumption in both sides concurrently by formulating the problem of joint receiving and transmitting energy-efficient scheduling (RTEES) in OFDMA downlink. We show that this problem can be cast as a binary integer programme. We solve the RTEES problem by a computationally efficient algorithm. We proposed a specialized solution approach, named time-slot-oriented column generation (TSOCG) algorithm, for approaching and bounding the global optimality. Numerical studies show that the proposed algorithm solution is competitive and time-efficient to provide a close-to-optimum solution and a tight bound.

    sted, utgiver, år, opplag, sider
    IEEE, 2014
    Emneord
    Energy saving; column generation; resource allocation; resource scheduling; OFDMA
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-123094 (URN)000363906500036 ()978-1-4799-5863-4 (ISBN)
    Konferanse
    11th International Symposium on Wireless Communications Systems (ISWCS)
    Tilgjengelig fra: 2015-12-03 Laget: 2015-12-03 Sist oppdatert: 2016-04-08
    3. Power and Load Coupling in Cellular Networks for Energy Optimization
    Åpne denne publikasjonen i ny fane eller vindu >>Power and Load Coupling in Cellular Networks for Energy Optimization
    2015 (engelsk)Inngår i: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, nr 1, s. 509-519Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    We consider the problem of minimization of sum transmission energy in cellular networks where coupling occurs between cells due to mutual interference. The coupling relation is characterized by the signal-to-interference-and-noise-ratio (SINR) coupling model. Both cell load and transmission power, where cell load measures the average level of resource usage in the cell, interact via the coupling model. The coupling is implicitly characterized with load and power as the variables of interest using two equivalent equations, namely, non-linear load coupling equation (NLCE) and non-linear power coupling equation (NPCE), respectively. By analyzing the NLCE and NPCE, we prove that operating at full load is optimal in minimizing sum energy, and provide an iterative power adjustment algorithm to obtain the corresponding optimal power solution with guaranteed convergence, where in each iteration a standard bisection search is employed. To obtain the algorithmic result, we use the properties of the so-called standard interference function; the proof is nonstandard because the NPCE cannot even be expressed as a closed-form expression with power as the implicit variable of interest. We present numerical results illustrating the theoretical findings for a real-life and large-scale cellular network, showing the advantage of our solution compared to the conventional solution of deploying uniform power for base stations.

    sted, utgiver, år, opplag, sider
    Institute of Electrical and Electronics Engineers (IEEE), 2015
    Emneord
    Cellular networks; energy minimization; load coupling; power coupling; power adjustment allocation; standard interference function
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-115830 (URN)10.1109/TWC.2014.2353043 (DOI)000349675400041 ()
    Merknad

    Funding Agencies|Linkoping-Lund Excellence Center in Information Technology (ELLIIT), Sweden; Chinese Scholarship Council (CSC); Institute for Infocomm Research (I2R), A*STAR, Singapore

    Tilgjengelig fra: 2015-03-20 Laget: 2015-03-20 Sist oppdatert: 2017-12-04
    4. Optimal Cell Clustering and Activation for Energy Saving in Load-Coupled Wireless Networks
    Åpne denne publikasjonen i ny fane eller vindu >>Optimal Cell Clustering and Activation for Energy Saving in Load-Coupled Wireless Networks
    2015 (engelsk)Inngår i: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 14, nr 11, s. 6150-6163Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    Optimizing activation and deactivation of base station transmissions provides an instrument for improving energy efficiency in cellular networks. In this paper, we study the problem of performing cell clustering and setting the activation time of each cluster, with the objective of minimizing the sum energy, subject to a time constraint of serving the users traffic demand. Our optimization framework accounts for inter-cell interference, and, thus, the users achievable rates depend on cluster formation. We provide mathematical formulations and analysis, and prove the problems NP hardness. For problem solution, we first apply an optimization method that successively augments the set of variables under consideration, with the capability of approaching global optimum. Then, we derive a second solution algorithm to deal with the trade-off between optimality and the combinatorial nature of cluster formation. Numerical results demonstrate that our solutions achieve more than 40% energy saving over existing schemes, and that the solutions we obtain are within a few percent of deviation from global optimum.

    sted, utgiver, år, opplag, sider
    IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2015
    Emneord
    Cell activation; cell clustering; energy minimization; load coupling; column generation
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-123331 (URN)10.1109/TWC.2015.2449295 (DOI)000365046100020 ()
    Merknad

    Funding Agencies|European Union FP7 Marie Curie Project MESH-WISE [434515]; European Union FP7 Marie Curie Project WiNDOW [318992]; Chinese Scholarship Council; Institute for Infocomm Research (I2R); A*STAR, Singapore, through overseas Ph.D. research internship scheme; Swedish Research Council; European Union FP7 Marie Curie IOF [329313]

    Tilgjengelig fra: 2015-12-14 Laget: 2015-12-11 Sist oppdatert: 2017-12-01
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  • 278.
    Leifsson, Patrik
    Linköpings universitet, Matematiska institutionen.
    Fractal sets and dimensions2006Independent thesis Basic level (professional degree), 20 poäng / 30 hpOppgave
    Abstract [en]

    Fractal analysis is an important tool when we need to study geometrical objects less regular than ordinary ones, e.g. a set with a non-integer dimension value. It has developed intensively over the last 30 years which gives a hint to its young age as a branch within mathematics.

    In this thesis we take a look at some basic measure theory needed to introduce certain definitions of fractal dimensions, which can be used to measure a set's fractal degree. Comparisons of these definitions are done and we investigate when they coincide. With these tools different fractals are studied and compared.

    A key idea in this thesis has been to sum up different names and definitions referring to similar concepts.

    Fulltekst (pdf)
    FULLTEXT01
  • 279.
    Lidén, Tomas
    et al.
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten.
    Joborn, Martin
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten.
    An optimization model for integrated planning of railway traffic and network maintenance2017Inngår i: Transportation Research Part C: Emerging Technologies, ISSN 0968-090X, E-ISSN 1879-2359, Vol. 74, s. 327-347Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Abstract Railway transportation systems are important for society and have many challenging and important planning problems. Train services as well as maintenance of a railway network need to be scheduled efficiently, but have mostly been treated as two separate planning problems. Since these activities are mutually exclusive they must be coordinated and should ideally be planned together. In this paper we present a mixed integer programming model for solving an integrated railway traffic and network maintenance problem. The aim is to find a long term tactical plan that optimally schedules train free windows sufficient for a given volume of regular maintenance together with the wanted train traffic. A spatial and temporal aggregation is used for controlling the available network capacity. The properties of the proposed model are analyzed and computational experiments on various synthetic problem instances are reported. Model extensions and possible modifications are discussed as well as future research directions.

    Fulltekst (pdf)
    An optimization model for integrated planning of railway traffic and network maintenance
  • 280.
    Lin, Ling
    Linköpings universitet, Institutionen för datavetenskap. Linköpings universitet, Tekniska högskolan.
    A value-based indexing technique for time sequences1997Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    A time sequence is a discrete sequence of values, e.g. temperature measure ments, varying over time. Conventional indexes for time sequences are built on the time domain and cannot deal with inverse queries on time sequences under some interpolation assumptions (i.e. computing the times when the values satisfy some conditions). To process an inverse query the entire time sequence has to be scanned.This thesis presents a dynamic indexing technique, termed the IP-index (Interpolation-index), on the value domain for large time sequences. This index can be implemented using regular ordered indexing techniques such as B-trees.Performance measurements show that this index dramatically improves the query processing time of inverse queries compared to linear scanning. For periodic time sequences that have a limited range and precision on their value domain (most time sequences have this property), the IP-index has an upper bound for insertion time and search time.The IP-index is useful in various applications such as scientific data analysis or medical symptom analysis. In this thesis we show how this index can be applied in the aeroplane navigation problem and dramatically improve the real-time performance.

  • 281.
    Lindberg, Rasmus
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    A heuristic approach for scheduling of electrical buses2020Independent thesis Basic level (degree of Bachelor), 14 hpOppgave
    Abstract [en]

    The planning process of public transit systems have for long been a subject treated in operations research. In recent years, research within the public transit area focus on adapting this planning process for electric vehicles. This thesis evaluates a heuristic approach to the vehicle scheduling problem for electrical buses without the use of any licensed software.

    Among the previous research is an article that presents a mathematical model for scheduling of electrical buses using AMPL and CPLEX. However, due to not finding optimal solutions for all instances of the problem, the question of a heuristic approach is raised. Literature studies indicate that large neighbourhood search (LNS)-based heuristics have shown previous success for scheduling of vehicles. Results from the implementation of a constructive heuristic combined with an LNS-heuristic are compared with the results from the mathematical model and CPLEX. We see some success using the heuristic approach. However, the method we compare against still provide better solutions for almost all instances. More specifically, the difference between the results (number of buses needed) increases with an increasing complexity of the problem. Finally, due to the lacking results, some recommendations are given for improving the performance of the heuristic.

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  • 282. Bestill onlineKjøp publikasjonen >>
    Linders, Viktor
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Error analysis of summation-by-parts formulations: Dispersion, transmission and accuracy2017Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    In this thesis we consider errors arising from finite difference operators on summation-by-parts (SBP) form, used in the discretisation of partial differential equations. The SBP operators are augmented with simultaneous-approximation-terms (SATs) to weakly impose boundary conditions. The SBP-SAT framework combines high order of accuracy with a systematic construction of provably stable boundary procedures, which renders it suitable for a wide range of problems.

    The first part of the thesis treats wave propagation problems discretised using SBP operators on coarse grids. Unless special care is taken, inaccurate approximations of the underlying dispersion relation materialises in the form of an incorrect propagation speed. We present a procedure for constructing SBP operators with minimal dispersion error. Experiments indicate that they outperform higher order non-optimal SBP operators for flow problems involving high frequencies and long simulation times.

    In the second part of the thesis, the formal order of accuracy of SBP operators near boundaries is analysed. We prove that the order in the interior of a diagonal norm based SBP operator must be at least twice that of the boundary stencil, irrespective of the grid point distribution near the boundary. This generalises the classical theory posed on uniform and conforming grids. We further show that for a common class of SBP operators, the diagonal norm defines a quadrature rule of the same order as the interior stencil. Again, this result is independent of the grid.

    In the final contribution if the thesis, we introduce the notion of a transmission problem to describe a general class of problems where different dynamics are coupled in time. Well-posedness and stability analyses are performed for continuous and discrete problems. A general condition is obtained that is necessary and sufficient for the transmission problem to satisfy an energy estimate. The theory provides insights into the coupling of fluid flow models, multi-block formulations, numerical filters, interpolation and multi-grid implementations.

    Delarbeid
    1. Uniformly Best Wavenumber Approximations by Spatial Central Difference Operators
    Åpne denne publikasjonen i ny fane eller vindu >>Uniformly Best Wavenumber Approximations by Spatial Central Difference Operators
    2015 (engelsk)Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 300, s. 695-709Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    We construct accurate central difference stencils for problems involving high frequency waves or multi-frequency solutions over long time intervals with a relatively coarse spatial mesh, and with an easily obtained bound on the dispersion error. This is done by demonstrating that the problem of constructing central difference stencils that have minimal dispersion error in the infinity norm can be recast into a problem of approximating a continuous function from a finite dimensional subspace with a basis forming a Chebyshev set. In this new formulation, characterising and numerically obtaining optimised schemes can be done using established theory.

    sted, utgiver, år, opplag, sider
    Elsevier, 2015
    Emneord
    Dispersion relation; Wave propagation; Wavenumber approximation; Finite differences; Approximation theory
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-120896 (URN)10.1016/j.jcp.2015.08.005 (DOI)000361573200035 ()
    Tilgjengelig fra: 2015-08-28 Laget: 2015-08-28 Sist oppdatert: 2017-12-04bibliografisk kontrollert
    2. A simple and efficient incompressible Navier-Stokes solver for unsteady complex geometry flows on truncated domains
    Åpne denne publikasjonen i ny fane eller vindu >>A simple and efficient incompressible Navier-Stokes solver for unsteady complex geometry flows on truncated domains
    Vise andre…
    2017 (engelsk)Inngår i: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 150, s. 84-94Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    Incompressible Navier-Stokes solvers based on the projection method often require an expensive numerical solution of a Poisson equation for a pressure-like variable. This often involves linear system solvers based on iterative and multigrid methods which may limit the ability to scale to large numbers of processors. The artificial compressibility method (ACM) [6] introduces a time derivative of the pressure into the incompressible form of the continuity equation creating a coupled closed hyperbolic system that does not require a Poisson equation solution and allows for explicit time-marching and localized stencil numerical methods. Such a scheme should theoretically scale well on large numbers of CPUs, GPU'€™s, or hybrid CPU-GPU architectures. The original ACM was only valid for steady flows and dual-time stepping was often used for time-accurate simulations. Recently, Clausen [7] has proposed the entropically damped artificial compressibility (EDAC) method which is applicable to both steady and unsteady flows without the need for dual-time stepping. The EDAC scheme was successfully tested with both a finite-difference MacCormack'€™s method for the two-dimensional lid driven cavity and periodic double shear layer problem and a finite-element method for flow over a square cylinder, with scaling studies on the latter to large numbers of processors. In this study, we discretize the EDAC formulation with a new optimized high-order centered finite-difference scheme and an explicit fourth-order Runge-€“Kutta method. This is combined with an immersed boundary method to efficiently treat complex geometries and a new robust outflow boundary condition to enable higher Reynolds number simulations on truncated domains. Validation studies for the Taylor-€“Green Vortex problem and the lid driven cavity problem in both 2D and 3D are presented. An eddy viscosity subgrid-scale model is used to enable large eddy simulations for the 3D cases. Finally, an application to flow over a sphere is presented to highlight the boundary condition and performance comparisons to a traditional incompressible Navier-€“Stokes solver is shown for the 3D lid driven cavity. Overall, the combined EDAC formulation and discretization is shown to be both effective and affordable.

    sted, utgiver, år, opplag, sider
    Elsevier, 2017
    Emneord
    Artificial compressibility method, EDAC, High-order numerical methods, Large Eddy simulation
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-136507 (URN)10.1016/j.compfluid.2017.03.030 (DOI)000401219000007 ()
    Merknad

    Funding agencies: Rosenblatt Chair within the faculty of Mechanical Engineering; Zeff Fellowship Trust

    Tilgjengelig fra: 2017-04-19 Laget: 2017-04-19 Sist oppdatert: 2017-11-20bibliografisk kontrollert
    3. Summation-by-Parts Operators with Minimal Dispersion Error for Coarse Grid Flow Calculations
    Åpne denne publikasjonen i ny fane eller vindu >>Summation-by-Parts Operators with Minimal Dispersion Error for Coarse Grid Flow Calculations
    2017 (engelsk)Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 340, s. 34s. 160-176Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    We present a procedure for constructing Summation-by-Parts operators with minimal dispersion error both near and far from numerical interfaces. Examples of such operators are constructed and compared with a higher order non-optimised Summation-by-Parts operator. Experiments show that the optimised operators are superior for wave propagation and turbulent flows involving large wavenumbers, long solution times and large ranges of resolution scales.

    sted, utgiver, år, opplag, sider
    Elsevier, 2017. s. 34
    Emneord
    Summation-by-Parts, Dispersion relation, Finite differences, Wave Propagation
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-136474 (URN)10.1016/j.jcp.2017.03.039 (DOI)000401137900009 ()
    Tilgjengelig fra: 2017-04-12 Laget: 2017-04-12 Sist oppdatert: 2017-11-20bibliografisk kontrollert
    4. On the order of Accuracy of Finite Difference Operators on Diagonal Norm Based Summation-By-Parts Form
    Åpne denne publikasjonen i ny fane eller vindu >>On the order of Accuracy of Finite Difference Operators on Diagonal Norm Based Summation-By-Parts Form
    2017 (engelsk)Rapport (Annet vitenskapelig)
    Abstract [en]

    In this paper we generalise results regarding the order of accuracy of finite difference operators on Summation-By-Parts (SBP) form, previously known to hold on uniform grids, to grids with arbitrary point distributions near domain boundaries. We give a definite proof that the order of accuracy in the interior of a diagonal norm based SBP operator must be at least twice that of the boundary stencil, irrespective of the grid point distribution near the boundary. Additionally, we prove that if the order of accuracy in the interior is precisely twice that of the boundary, then the diagonal norm defines a quadrature rule of the same order as the interior stencil. Again, this result is independent of the grid point distribution near the domain boundaries.

    sted, utgiver, år, opplag, sider
    Linköping: Linköping University Electronic Press, 2017. s. 15
    Serie
    LiTH-MAT-R, ISSN 0348-2960 ; 2017:11
    Emneord
    Finite difference schemes, summation-by-parts operators, numerical differentiation, quadrature rules, order of accuracy
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-140815 (URN)
    Tilgjengelig fra: 2017-09-12 Laget: 2017-09-12 Sist oppdatert: 2017-11-20bibliografisk kontrollert
    5. Well-posed and Stable Transmission Problems
    Åpne denne publikasjonen i ny fane eller vindu >>Well-posed and Stable Transmission Problems
    2017 (engelsk)Rapport (Annet vitenskapelig)
    Abstract [en]

    We introduce the notion of a transmission problem to describe a general class of problems where different dynamics are coupled in time. Well-posedness and stability is analysed for continuous and discrete problems using both strong and weak formulations, and a general transmission condition is obtained. The theory is applied to several examples including the coupling of fluid flow models, multi-grid implementations, multi-block formulations and numerical filtering.

    sted, utgiver, år, opplag, sider
    Linköping: Linköping University Electronic Press, 2017. s. 28
    Serie
    LiTH-MAT-R, ISSN 0348-2960 ; 15
    Emneord
    Initial-boundary value problems, Transmission problems, Energy estimates, Well-posedness, Multi-block, Numerical Filter. Interpolation, Multi-grid, Summation-by-Parts, Stability
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-142348 (URN)LiTH-MAT-R--2017/15--SE (ISRN)
    Tilgjengelig fra: 2017-10-27 Laget: 2017-10-27 Sist oppdatert: 2017-11-20bibliografisk kontrollert
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    presentationsbild
  • 283.
    Linders, Viktor
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Kupiainen, Marco
    Rossby Centre SMHI, Norrköping, Sweden.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Summation-by-Parts Operators with Minimal Dispersion Error for Coarse Grid Flow Calculations2016Rapport (Annet vitenskapelig)
    Abstract [en]

    We present a procedure for constructing Summation-by-Parts operators with minimal dispersion error both near and far from numerical interfaces. Examples of such operators are constructed and compared with purely periodic stencils as well as non-optimised Summation-by-Parts operators of higher order. Experiments show that the optimised operators are superior for wave propagation and turbulent flows involving large wavenumbers, long solution times and large ranges of resolution scales.

    Fulltekst (pdf)
    fulltext
  • 284.
    Linders, Viktor
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Kupiainen, Marko
    SMHI, SE-601 76 Norrköping, Sweden.
    Frankel, Steven H.
    Technion, Haifa, Israel 320003.
    Delorme, Yann
    Technion, Haifa, Israel 320003.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Summation-by-parts Operators with Minimal Dispersion Error for Accurate and Efficient Flow Calculations2016Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We develop summation-by-parts operators with minimal dispersion errors both near and far from boundaries and interfaces. Such operators are superior to classical stencils for problems involving high frequency waves or multi-frequency solutions over long time intervals with a relatively coarse spatial mesh. This is demonstrated by solving the Taylor-Green vortex flow with optimised and classical operators both in a purely periodic setting as well as in the presence of numerical interfaces.

    Fulltekst (pdf)
    Summation-by-parts Operators with Minimal Dispersion Error for Accurate and Efficient Flow Calculations
  • 285.
    Linders, Viktor
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Lundquist, Tomas
    University of Cape Town, South Africa.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    On the order of Accuracy of Finite Difference Operators on Diagonal Norm Based Summation-By-Parts Form2017Rapport (Annet vitenskapelig)
    Abstract [en]

    In this paper we generalise results regarding the order of accuracy of finite difference operators on Summation-By-Parts (SBP) form, previously known to hold on uniform grids, to grids with arbitrary point distributions near domain boundaries. We give a definite proof that the order of accuracy in the interior of a diagonal norm based SBP operator must be at least twice that of the boundary stencil, irrespective of the grid point distribution near the boundary. Additionally, we prove that if the order of accuracy in the interior is precisely twice that of the boundary, then the diagonal norm defines a quadrature rule of the same order as the interior stencil. Again, this result is independent of the grid point distribution near the domain boundaries.

    Fulltekst (pdf)
    On the order of Accuracy of Finite Difference Operators on Diagonal Norm Based Summation-By-Parts Form
  • 286.
    Linders, Viktor
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Uniformly Best Wavenumber Approximations by Spatial Central Difference Operators2015Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 300, s. 695-709Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We construct accurate central difference stencils for problems involving high frequency waves or multi-frequency solutions over long time intervals with a relatively coarse spatial mesh, and with an easily obtained bound on the dispersion error. This is done by demonstrating that the problem of constructing central difference stencils that have minimal dispersion error in the infinity norm can be recast into a problem of approximating a continuous function from a finite dimensional subspace with a basis forming a Chebyshev set. In this new formulation, characterising and numerically obtaining optimised schemes can be done using established theory.

    Fulltekst (pdf)
    Uniformly Best Wavenumber Approximations by Spatial Central Difference Operators
  • 287.
    Linders, Viktor
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Uniformly Best Wavenumber Approximations by Spatial Central Difference Operators: An Initial Investigation2015Inngår i: Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014 / [ed] Mejdi Azaïez, Henda El Fekih, Jan S. Hesthaven, Springer, 2015, s. 325-333Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    A characterisation theorem for best uniform wavenumber approximations by central difference schemes is presented. A central difference stencil is derived based on the theorem and is compared with dispersion relation preserving schemes and with classical central differences for a relevant test problem.

    Fulltekst (pdf)
    Uniformly Best Wavenumber Approximations by Spatial Central Difference Operators: An Initial Investigation
  • 288.
    Linders, Viktor
    et al.
    Facultyof, Mechanica, Engineering,Technion, Israel Institute of Technology, Haifa, Israel.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Frankel, Steven H.
    Facultyof, Mechanica, Engineering,Technion, Israel Institute of Technology, Haifa, Israel.
    Convergence and stability properties of summation-by-parts in time2019Rapport (Annet vitenskapelig)
    Abstract [en]

    We extend the list of stability properties satisfied by Summation-By-Parts (SBP) in time to include strong S-stability, dissipative stability and stiff accuracy. Further, it is shown that SBP in time is B-convergent for strictly contractive non-linear problems and weakly convergent for non-linear problems that are both contractive and dissipative

    Fulltekst (pdf)
    Convergence and stability properties of summation-by-parts in time
  • 289.
    Linders, Viktor
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Kupiainen, Marco
    Rossby Centre SMHI, Norrköping, Sweden.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Summation-by-Parts Operators with Minimal Dispersion Error for Coarse Grid Flow Calculations2017Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 340, s. 34s. 160-176Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We present a procedure for constructing Summation-by-Parts operators with minimal dispersion error both near and far from numerical interfaces. Examples of such operators are constructed and compared with a higher order non-optimised Summation-by-Parts operator. Experiments show that the optimised operators are superior for wave propagation and turbulent flows involving large wavenumbers, long solution times and large ranges of resolution scales.

    Fulltekst (pdf)
    fulltext
  • 290.
    Lindholm, Anna
    et al.
    Lund University, Sweden.
    Giselsson, Pontus
    Lund University, Sweden.
    Quttineh, Nils-Hassan
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Lidestam, Helene
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Johnsson, Charlotta
    Lund University, Sweden.
    Forsman, Krister
    Perstorp AB, Sweden.
    Production Scheduling in the Process Industry2013Inngår i: Proceedings for 22nd International Conference on Production Research, 2013, 2013Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The purpose of this paper is to formulate an optimization model for the production scheduling problem at continuous production sites. The production scheduling activity should produce a monthly schedule that accounts for orders and forecasts of all products. The plan should be updated every day, with feedback on the actual production the previous day. The actual daily production may be lower than the planned production due to disturbances, e.g. disruptions in the supply of a utility. The work is performed in collaboration with Perstorp, a world-leading company within several sectors of the specialty chemicals market. Together with Perstorp, a list of specifications for the production scheduling has been formulated. These are formulated mathematically in a mixed-integer linear program that is solved in receding horizon fashion. The formulation of the model aims to be general, such that it may be used for any process industrial site.

  • 291.
    Lindholm, Anna
    et al.
    Lund University, Sweden.
    Johnsson, Charlotta
    Lund University, Sweden.
    Quttineh, Nils-Hassan
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Lidestam, Helene
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Henningsson, Mathias
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Wikner, Joakim
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Tang, Ou
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Nytzén, Nils-Petter
    Perstorp AB, Sweden.
    Forsman, Krister
    Perstorp AB, Sweden.
    Hierarchical Scheduling and Utility Disturbance Management in the Process Industry2013Inngår i: Proceedings for IFAC Conference on Manufacturing Modelling, Management and Control (MIM2013), 2013, Elsevier, 2013, s. 140-145Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The integration of scheduling and control in the process industry is a topic that has been frequently discussed during the recent years, but many challenges remain in order to achieve integrated solutions that can be implemented for large-scale industrial sites. In this paper we consider production control under disturbances in the supply of utilities at integrated sites together with the integration towards production scheduling. Utilities, such as steam and cooling water, are often shared between the production areas of a site, which enables formulation of an optimization problem for determining the optimal supply of utilities to each area at the occurrence of a disturbance. Optimization in two timescales is suggested to handle the scheduling and disturbance management problems in a hierarchical fashion. The suggested structure has been discussed with companies within the chemical process industry. A simple example is provided to show how the structure may be used

  • 292.
    Lindmark, Gustav
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Altafini, Claudio
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Controllability of complex networks with unilateral inputs2017Inngår i: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 7, artikkel-id 1824Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we study the problem of controlling complex networks with unilateral controls, i.e., controls which can assume only positive or negative values, not both. Given a complex network represented by the adjacency matrix A, an algorithm is developed that constructs an input matrix B such that the resulting system (A, B) is controllable with a near minimal number of unilateral control inputs. This is made possible by a reformulation of classical conditions for controllability that casts the minimal unilateral input selection problem into well known optimization problems. We identify network properties that make unilateral controllability relatively easy to achieve as compared to unrestricted controllability. The analysis of the network topology for instance allows us to establish theoretical bounds on the minimal number of controls required. For various categories of random networks as well as for a number of real-world networks these lower bounds are often achieved by our heuristics.

    Fulltekst (pdf)
    fulltext
  • 293.
    Lindström Berg, Jens
    et al.
    Uppsala University, Department of Information Technology, SE-751 05, Uppsala, Sweden.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap. Linköpings universitet, Tekniska högskolan.
    Stable Robin boundary conditions for the Navier-Stokes equations2011Rapport (Annet vitenskapelig)
    Abstract [en]

    In this paper we prove stability of Robin solid wall boundary conditions for the compressible Navier-Stokes equations. Applications include the no-slip boundary conditions with prescribed temperature or temperature gradient and the rst order slip-ow boundary conditions. The formulation is uni-form and the transitions between dierent boundary conditions are done by a change of parameters. We give dierent sharp energy estimates depending on the choice of parameters.

    The discretization is done using nite dierences on Summation-By-Parts form with weak boundary conditions using the Simultaneous Approximation Term. We verify convergence by the method of manufactured solutions and show computations of ows ranging from no-slip to substantial slip.

    Fulltekst (pdf)
    FULLTEXT01
  • 294.
    Lindström, Jens
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Bejhed, Johan
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Measurements and numerical modelling of orifice flow in microchannels2009Inngår i: Proc. 41st AIAA Thermophysics Conference, AIAA , 2009Konferansepaper (Fagfellevurdert)
  • 295.
    Lindström, Jens
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    A stable and high order accurate conjugate heat transfer problem2009Rapport (Annet vitenskapelig)
    Abstract [en]

    This paper analyzes well-posedness and stability of a conjugate heat transfer problem in one space dimension. We study a model problem for heat transfer between a fluid and a solid. The energy method is used to derive boundary and interface conditions that make the continuous problem well-posed and the semi-discrete problem stable. The numerical scheme is implemented using 2nd, 3rd and 4th order finite difference operators on Summation-By-Parts (SBP) form. The boundary and interface conditions are implemented weakly. We investigate the spectrum of the spatial discretization to determine which type of coupling that gives attractive convergence properties. The rate of convergence is verified using the method of manufactured solutions.

  • 296.
    Lindström, Jens
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    A stable and high order interface procedure for conjugate heat transfer problems2010Inngår i: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, s. 599-607Konferansepaper (Fagfellevurdert)
  • 297.
    Lindström, Jens
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    A stable and high-order accurate conjugate heat transfer problem2010Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 229, nr 14, s. 5440-5456Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper analyzes well-posedness and stability of a conjugate heat transfer problem in one space dimension. We study a model problem for heat transfer between a fluid and a solid. The energy method is used to derive boundary and interface conditions that make the continuous problem well-posed and the semi-discrete problem stable. The numerical scheme is implemented using 2nd-, 3rd- and 4th-order finite difference operators on Summation-By-Parts (SBP) form. The boundary and interface conditions are implemented weakly. We investigate the spectrum of the spatial discretization to determine which type of coupling that gives attractive convergence properties. The rate of convergence is verified using the method of manufactured solutions.

    Fulltekst (pdf)
    fulltext
  • 298. Lindström, Jens
    et al.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap. Linköpings universitet, Tekniska högskolan.
    Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains2010Rapport (Annet vitenskapelig)
    Abstract [en]

    In this paper we study the heat and advection equation in single and multiple domains. We discretize using a second order accurate finite difference method on Summation-By-Parts form with weak boundary and interface conditions. We derive analytic expressions for the spectrum of the continuous problem and for their corresponding discretization matrices. We show how the spectrum of the single domain operator is contained in the multi domain operator spectrum when artificial interfaces are introduced. We study the impact on the spectrum and discretization errors depending on the interface treatment and verify that the results are carried over to higher order accurate schemes.

    Fulltekst (pdf)
    FULLTEXT01
  • 299.
    Lindström, Jens
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Stable and High Order Accurate Heat Transfer2010Inngår i: Proc. 7th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2010, s. 12:1-11Konferansepaper (Annet vitenskapelig)
    Fulltekst (pdf)
    fulltext
  • 300.
    Liu, Yang
    et al.
    Department of Information Technology, Vaasa University of Applied Sciences, Finland / School of Electrical and Electronic Engineering, Hubei University of Technology, China.
    Vinh Vo, Thanh
    Department of Information Technology, Vaasa Univers ity of Applied Sciences, Finland.
    Bin packing solution for automated packaging application2012Inngår i: 2011 International Conference on Electrical Information and Mechatronics, ICEIM2011,  December 23-25, Jiaozuo, China / [ed] Xudong Wang, Baoyu Xu and Shaobo Zhong, Trans Tech Publications, 2012, Vol. 143-144, s. 279-283Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    This paper introduces the implementation of a new heuristic recursive algorithm for bin packing solution used in automated packaging application. The theoretical method proposed in this paper is successfully implemented on a real ABB robot arm with some important improvements such as added rotation flexibility and removing an added product from the structure. The computational results on a class of benchmark problems have shown that this algorithm not only finds shorter height than the known meta-heuristic ones, but also runs in shorter time. The average running time is very suitable for such kind of automated packaging application.

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