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  • 551.
    Wahlsten, Markus
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    The effect of uncertain geometries on advection-diffusion of scalar quantities2016Rapport (Annet vitenskapelig)
    Abstract [en]

    The two dimensional advection-diffusion equation in a stochastically varying geometry is considered. The varying domain is transformed into afixed one and the numerical solution is computed using a high-order finite difference formulation on summation-by-parts form with weakly imposed boundary conditions.

    Statistics of the solution are computed non-intrusively using quadrature rules given by the probability density function of the random variable. As a quality control, we prove that the continuous problem is strongly well-posed, that the semi-discrete problem is strongly stable and verify the accuracy of the scheme.

    The technique is applied to a heat transfer problem in incompressible flow. Statistical properties such as confidence intervals and variance of the solution in terms of two functionals are computed and discussed. We show that there is a decreasing sensitivity to geometric uncertainty as we gradually lower the frequency and amplitude of the randomness.

    Fulltekst (pdf)
    The effect of uncertain geometries on advection-diffusion of scalar quantities
  • 552.
    Webb, Grayson
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    A Gaussian Mixture Model based Level Set Method for Volume Segmentation in Medical Images2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    This thesis proposes a probabilistic level set method to be used in segmentation of tumors with heterogeneous intensities. It models the intensities of the tumor and surrounding tissue using Gaussian mixture models. Through a contour based initialization procedure samples are gathered to be used in expectation maximization of the mixture model parameters. The proposed method is compared against a threshold-based segmentation method using MRI images retrieved from The Cancer Imaging Archive. The cases are manually segmented and an automated testing procedure is used to find optimal parameters for the proposed method and then it is tested against the threshold-based method. Segmentation times, dice coefficients, and volume errors are compared. The evaluation reveals that the proposed method has a comparable mean segmentation time to the threshold-based method, and performs faster in cases where the volume error does not exceed 40%. The mean dice coefficient and volume error are also improved while achieving lower deviation.

    Fulltekst (pdf)
    fulltext
  • 553.
    Wintermeyer, Niklas
    et al.
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Winters, Andrew Ross
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Gassner, Gregor J
    Mathematisches Institut, Universität zu Köln, Köln, GermanyUniversity of Cologne.
    Kopriva, David A
    Department of Mathematics, The Florida State University, Tallahassee, USA.
    An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry2017Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 340, s. 200-242Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non- constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretisation exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretisation of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.

    Fulltekst (pdf)
    An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry
  • 554.
    Wintermeyer, Niklas
    et al.
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Winters, Andrew Ross
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Gassner, Gregor J
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Warburton, Timothy
    Department of Mathematics, Virginia Tech, Blacksburg, USA.
    An entropy stable discontinuous Galerkin method for the shallow water equations on curvilinear meshes with wet/dry fronts accelerated by GPUs2018Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 375, s. 447-480Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We extend the entropy stable high order nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations presented by Wintermeyer et al. [N. Wintermeyer, A. R. Winters, G. J. Gassner, and D. A. Kopriva. An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry. Journal of Computational Physics, 340:200-242, 2017] with a shock capturing technique and a positivity preservation capability to handle dry areas. The scheme preserves the entropy inequality, is well-balanced and works on unstructured, possibly curved, quadrilateral meshes. For the shock capturing, we introduce an artificial viscosity to the equations and prove that the numerical scheme remains entropy stable. We add a positivity preserving limiter to guarantee non-negative water heights as long as the mean water height is non-negative. We prove that non-negative mean water heights are guaranteed under a certain additional time step restriction for the entropy stable numerical interface flux. We implement the method on GPU architectures using the abstract language OCCA, a unified approach to multi-threading languages. We show that the entropy stable scheme is well suited to GPUs as the necessary extra calculations do not negatively impact the runtime up to reasonably high polynomial degrees (around N = 7). We provide numerical examples that challenge the shock capturing and positivity properties of our scheme to verify our theoretical findings.

    Fulltekst tilgjengelig fra 2020-12-15 08:00
  • 555.
    Winters, Andrew R
    et al.
    Department of Mathematics, The Florida State University, Tallahassee, USA.
    Kopriva, David A
    Department of Mathematics, The Florida State University, Tallahassee, USA.
    Efficient and High-Order Explicit Local Time Stepping on Moving DG Spectral Element Meshes2015Inngår i: Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014: Selected papers from the ICOSAHOM conference, June 23-27, 2014, Salt Lake City, Utah, USA / [ed] Robert M. Kirby, Martin Berzins and Jan S. Hesthaven, Cham: Springer, 2015, s. 513-522Kapittel i bok, del av antologi (Annet vitenskapelig)
    Abstract [en]

    We outline and extend results for an explicit local time stepping (LTS) strategy designed to operate with the discontinuous Galerkin spectral element method (DGSEM). The LTS procedure is derived from Adams-Bashforth multirate time integration methods. The new results of the LTS method focus on parallelization and reformulation of the LTS integrator to maintain conservation. Discussion is focused on a moving mesh implementation, but the procedures remain applicable to static meshes. In numerical tests, we demonstrate the strong scaling of a parallel, LTS implementation and compare the scaling properties to a parallel, global time stepping (GTS) Runge-Kutta implementation. We also present time-step refinement studies to show that the redesigned, conservative LTS approximations are spectrally accurate in space and have design temporal accuracy.

  • 556.
    Winters, Andrew Ross
    et al.
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Derigs, Dominik
    I. Physikalisches Institut, Universität zu Köln, Köln, Germany.
    Gassner, Gregor J
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Walch, Stefanie
    I. Physikalisches Institut, Universität zu Köln, Köln, Germany.
    A uniquely defined entropy stable matrix dissipation operator for high Mach number ideal MHD and compressible Euler simulations2017Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 332, s. 274-289Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We describe a unique averaging procedure to design an entropy stable dissipation operator for the ideal magnetohydrodynamic (MHD) and compressible Euler equations. Often in the derivation of an entropy conservative numerical flux function much care is taken in the design and averaging of the entropy conservative numerical flux. We demonstrate in this work that if the discrete dissipation operator is not carefully chosen as well it can have deleterious effects on the numerical approximation. This is particularly true for very strong shocks or high Mach number flows present, for example, in astrophysical simulations. We present the underlying technique of how to construct a unique averaging technique for the discrete dissipation operator. We also demonstrate numerically the increased robustness of the approximation.

    Fulltekst (pdf)
    A uniquely defined entropy stable matrix dissipation operator for high Mach number ideal MHD and compressible Euler simulations
  • 557.
    Winters, Andrew Ross
    et al.
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Gassner, Gregor J.
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    A comparison of two entropy stable discontinuous Galerkin spectral element approximations for the shallow water equations with non-constant topography2015Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 301, s. 357-376Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this work, we compare and contrast two provably entropy stable and high-order accurate nodal discontinuous Galerkin spectral element methods applied to the one dimensional shallow water equations for problems with non-constant bottom topography. Of particular importance for numerical approximations of the shallow water equations is the well-balanced property. The well-balanced property is an attribute that a numerical approximation can preserve a steady-state solution of constant water height in the presence of a bottom topography. Numerical tests are performed to explore similarities and differences in the two high-order schemes.

    Fulltekst (pdf)
    A comparison of two entropy stable discontinuous Galerkin spectral element approximations for the shallow water equations with non-constant topography
  • 558.
    Winters, Andrew Ross
    et al.
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Gassner, Gregor J.
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Affordable, entropy conserving and entropy stable flux functions for the ideal MHD equations2016Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 304, s. 72-108Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this work, we design an entropy stable, finite volume approximation for the ideal magnetohydrodynamics (MHD) equations. The method is novel as we design an affordable analytical expression of the numerical interface flux function that discretely preserves the entropy of the system. To guarantee the discrete conservation of entropy requires the addition of a particular source term to the ideal MHD system. Exact entropy conserving schemes cannot dissipate energy at shocks, thus to compute accurate solutions to problems that may develop shocks, we determine a dissipation term to guarantee entropy stability for the numerical scheme. Numerical tests are performed to demonstrate the theoretical findings of entropy conservation and robustness.

    Fulltekst (pdf)
    Affordable, entropy conserving and entropy stable flux functions for the ideal MHD equations
  • 559.
    Winters, Andrew Ross
    et al.
    Mathematical Institute, University of Cologne, Cologne, Germany.
    Gassner, Gregor J.
    Mathematical Institute, University of Cologne, Cologne, Germany.
    An entropy stable finite volume scheme for the equations of shallow water magnetohydrodynamics2016Inngår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 67, nr 2, s. 514-539Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this work, we design an entropy stable, finite volume approximation for the shallow water magnetohydrodynamics (SWMHD) equations. The method is novel as we design an affordable analytical expression of the numerical interface flux function that exactly preserves the entropy, which is also the total energy for the SWMHD equations. To guarantee the discrete conservation of entropy requires a special treatment of a consistent source term for the SWMHD equations. With the goal of solving problems that may develop shocks, we determine a dissipation term to guarantee entropy stability for the numerical scheme. Numerical tests are performed to demonstrate the theoretical findings of entropy conservation and robustness.

    Fulltekst (pdf)
    An entropy stable finite volume scheme for the equations of shallow water magnetohydrodynamics
  • 560.
    Winters, Andrew Ross
    et al.
    Department of Mathematics, The Florida State University, Tallahassee, USA.
    Kopriva, David A.
    Department of Mathematics, The Florida State University, Tallahassee, USA.
    ALE-DGSEM approximation of wave reflection and transmission from a moving medium2014Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 263, s. 233-267Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We derive a spectrally accurate moving mesh method for mixed material interface problems modeled by Maxwell's or the classical wave equation. We use a discontinuous Galerkin spectral element approximation with an arbitrary Lagrangian-Eulerian mapping and derive the exact upwind numerical fluxes to model the physics of wave reflection and transmission at jumps in material properties. Spectral accuracy is obtained by placing moving material interfaces at element boundaries and solving the appropriate Riemann problem. We present numerical examples showing the performance of the method for plane wave reflection and transmission at dielectric and acoustic interfaces.

  • 561.
    Winters, Andrew Ross
    et al.
    Department of Mathematics, The Florida State University, Tallahassee, USA.
    Kopriva, David A.
    Department of Mathematics, The Florida State University, Tallahassee, USA.
    High-order local time stepping on moving DG spectral element meshes2014Inngår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 58, nr 1, s. 176-202Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We derive and evaluate an explicit local time stepping (LTS) integration for the discontinuous Galerkin spectral element method (DGSEM) on moving meshes. The LTS procedure is derived from Adams-Bashforth multirate time integration methods. We also present speedup and memory estimates, which show that the explicit LTS integration scales well with problem size. Time-step refinement studies with static and moving meshes show that the approximations are spectrally accurate in space and have design temporal accuracy. The numerical tests validate theoretical estimates that the LTS procedure can reduce computational cost by as much as an order of magnitude for time accurate problems.

    Fulltekst (pdf)
    High-order local time stepping on moving DG spectral element meshes
  • 562.
    Winters, Andrew Ross
    et al.
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Moura, Rodrigo C.
    Department of Aeronautics, Imperial College London, South Kensington Campus, London, United Kingdom / Depto. de Aerodinâmica, Instituto Tecnológico de Aeronáutica (ITA), Praça Mal. Eduardo Gomes, Brazil.
    Mengaldo, Gianmarco
    Division of Engineering and Applied Science, California Institute of Technology, Pasadena, USA.
    Gassner, Gregor J.
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Walch, Stefanie
    I. Physikalisches Institut, Universität zu Köln, Köln, Germany.
    Peiro, Joaquim
    Department of Aeronautics, Imperial College London, South Kensington Campus, London, United Kingdom.
    Sherwin, Spencer J.
    Department of Aeronautics, Imperial College London, South Kensington Campus, London, United Kingdom.
    A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations2018Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 372, s. 1-21Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This work focuses on the accuracy and stability of high-order nodal discontinuous Galerkin (DG) methods for under-resolved turbulence computations. In particular we consider the inviscid Taylor-Green vortex (TGV) flow to analyse the implicit large eddy simulation (iLES) capabilities of DG methods at very high Reynolds numbers. The governing equations are discretised in two ways in order to suppress aliasing errors introduced into the discrete variational forms due to the under-integration of non-linear terms. The first, more straightforward way relies on consistent/over-integration, where quadrature accuracy is improved by using a larger number of integration points, consistent with the degree of the non-linearities. The second strategy, originally applied in the high-order finite difference community, relies on a split (or skew-symmetric) form of the governing equations. Different split forms are available depending on how the variables in the non-linear terms are grouped. The desired split form is then built by averaging conservative and non-conservative forms of the governing equations, although conservativity of the DG scheme is fully preserved. A preliminary analysis based on Burgers’ turbulence in one spatial dimension is conducted and shows the potential of split forms in keeping the energy of higher-order polynomial modes close to the expected levels. This indicates that the favourable dealiasing properties observed from split-form approaches in more classical schemes seem to hold for DG. The remainder of the study considers a comprehensive set of (under-resolved) computations of the inviscid TGV flow and compares the accuracy and robustness of consistent/over-integration and split form discretisations based on the local Lax-Friedrichs and Roe-type Riemann solvers. Recent works showed that relevant split forms can stabilize higher-order inviscid TGV test cases otherwise unstable even with consistent integration. Here we show that stable high-order cases achievable with both strategies have comparable accuracy, further supporting the good dealiasing properties of split form DG. The higher-order cases achieved only with split form schemes also displayed all the main features expected from consistent/over-integration. Among test cases with the same number of degrees of freedom, best solution quality is obtained with Roe-type fluxes at moderately high orders (around sixth order). Solutions obtained with very high polynomial orders displayed spurious features attributed to a sharper dissipation in wavenumber space. Accuracy differences between the two dealiasing strategies considered were, however, observed for the low-order cases, which also yielded reduced solution quality compared to high-order results.

    Fulltekst tilgjengelig fra 2020-11-01 08:00
  • 563. Bestill onlineKjøp publikasjonen >>
    Wokiyi, Dennis
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Non-linear inverse geothermal problems2017Licentiatavhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    The inverse geothermal problem consist of estimating the temperature distribution below the earth’s surface using temperature and heat-flux measurements on the earth’s surface. The problem is important since temperature governs a variety of the geological processes including formation of magmas, minerals, fosil fuels and also deformation of rocks. Mathematical this problem is formulated as a Cauchy problem for an non-linear elliptic equation and since the thermal properties of the rocks depend strongly on the temperature, the problem is non-linear. This problem is ill-posed in the sense that it does not satisfy atleast one of Hadamard’s definition of well-posedness.

    We formulated the problem as an ill-posed non-linear operator equation which is defined in terms of solving a well-posed boundary problem. We demonstrate existence of a unique solution to this well-posed problem and give stability estimates in appropriate function spaces. We show that the operator equation is well-defined in appropriate function spaces.

    Since the problem is ill-posed, regularization is needed to stabilize computations. We demostrate that Tikhonov regularization can be implemented efficiently for solving the operator equation. The algorithm is based on having a code for solving a well- posed problem related to the operator equation. In this study we demostrate that the algorithm works efficiently for 2D calculations but can also be modified to work for 3D calculations.

    Delarbeid
    1. An efficient regularization method for a large scale ill-posed geothermal problem
    Åpne denne publikasjonen i ny fane eller vindu >>An efficient regularization method for a large scale ill-posed geothermal problem
    2017 (engelsk)Inngår i: Computers & Geosciences, ISSN 0098-3004, E-ISSN 1873-7803, Vol. 105, s. 1-9Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    The inverse geothermal problem consists of estimating the temperature distribution below the earth's surface using measurements on the surface. The problem is important since temperature governs a variety of geologic processes, including the generation of magmas and the deformation style of rocks. Since the thermal properties of rocks depend strongly on temperature the problem is non-linear.

    The problem is formulated as an ill-posed operator equation, where the righthand side is the heat-flux at the surface level. Since the problem is ill-posed regularization is needed. In this study we demonstrate that Tikhonov regularization can be implemented efficiently for solving the operator equation. The algorithm is based on having a code for solving a well-posed problem related to the above mentioned operator. The algorithm is designed in such a way that it can deal with both 2D and 3D calculations.

    Numerical results, for 2D domains, show that the algorithm works well and the inverse problem can be solved accurately with a realistic noise level in the surface data.

    sted, utgiver, år, opplag, sider
    Elsevier, 2017
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-139052 (URN)10.1016/j.cageo.2017.04.010 (DOI)000404697000001 ()
    Tilgjengelig fra: 2017-06-29 Laget: 2017-06-29 Sist oppdatert: 2017-11-16bibliografisk kontrollert
    Fulltekst (pdf)
    Non-linear inverse geothermal problems
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  • 564.
    You, Lei
    et al.
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten.
    Yuan, Di
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten.
    Load Optimization With User Association in Cooperative and Load-Coupled LTE Networks2017Inngår i: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 16, nr 5, s. 3218-3231Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We extend the problem of optimizing user association for load balancing in cellular networks along 2-dimensions. First, we consider joint transmission, which is one of the coordinated multipoint techniques with which a user may be simultaneously served by multiple base stations. Second, we account for, mathematically, the coupling relation between the base stations load levels that are dependent on each other due to inter-cell interference. We formulate two optimization problems, sum load minimization (MinSumL) and maximum load minimization (MinMaxL). We prove that both MinSumL and MinMaxL are NP-hard. We propose a mixed integer linear programming based scheme by means of linearization. This approach also leads to a bounding scheme for performance benchmarking. Then, we derive a set of partial optimality conditions. Fulfillment of the conditions will guarantee performance improvement for both MinSumL and MinMaxL. A solution algorithm is then derived based on the conditions. Simulation results are provided to demonstrate the effectiveness of the approaches.

    Fulltekst (pdf)
    fulltext
  • 565.
    Zhang, Yingfeng
    et al.
    Key Laboratory of Contemporary Design and Integrated Manufacturing Technology, School of Mechanical Engineering, Northwestern Polytechnical University, Shaanxi, China.
    Liu, Sichao
    Key Laboratory of Contemporary Design and Integrated Manufacturing Technology, School of Mechanical Engineering, Northwestern Polytechnical University, Shaanxi, China.
    Liu, Yang
    Department of Production, University of Vaasa, Vaasa, Finland.
    Li, Rui
    Key Laboratory of Contemporary Design and Integrated Manufacturing Technology, School of Mechanical Engineering, Northwestern Polytechnical University, Shaanxi, China.
    Smart box-enabled product–service system for cloud logistics2016Inngår i: International Journal of Production Research, ISSN 0020-7543, E-ISSN 1366-588X, Vol. 54, nr 22, s. 6693-6706Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Modern logistics takes significant progress and rapid developments with the prosperity of E-commerce, particularly in China. Typical challenges that logistics industry is facing now are composed by a lack of sharing, standard, cost-effective and environmental package and efficient optimisation method for logistics tasks distribution. As a result, it is difficult to implement green, sustainable logistics services. Three important technologies, Physical Internet (PI), product–service system (PSS) and cloud computing (CC), are adopted and developed to address the above issues. PI is extended to design a world-standard green recyclable smart box that is used to encapsulate goods. Smart box-enabled PSS is constructed to provide an innovative sustainable green logistics service, and high-quality packaging, as well as reduce logistics cost and environmental pollution. A real-time information-driven logistics tasks optimisation method is constructed by designing a cloud logistics platform based on CC. On this platform, a hierarchical tree-structure network for customer orders (COs) is built up to achieve the order-box matching of function. Then, a distance clustering analysis algorithm is presented to group and form the optimal clustering results for all COs, and a real-time information-driven optimisation method for logistics orders is proposed to minimise the unused volume of containers. Finally, a case study is simulated to demonstrate the efficiency and feasibility of proposed cloud logistics optimisation method. © 2016 Informa UK Limited, trading as Taylor & Francis Group.

  • 566.
    Zhao, Yixin
    et al.
    Nanjing University of Science and Technology, School of Automation.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Rönnberg, Elina
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    An integer programming column generation principlefor heuristic search methods2019Inngår i: International Transactions in Operational Research, ISSN 0969-6016, E-ISSN 1475-3995, Vol. 27, nr 1, s. 665-695Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    There is an increasing interest in integrating column generation and heuristic approaches to efficiently solve large-scale discrete optimisation problems. We contribute in this direction. Based on the insights from Lagrangian duality theory, we present an auxiliary problem that can be used for finding near-optimal solutions to a discrete column-oriented model. The structure of this auxiliary problem makes it suitable for being addressed with a heuristic search method involving column generation. To this end, we suggest a large neighbourhood search strategy where the repair step is to solve a column generation type subproblem. The suggested search strategy and mathematical models involved need to be tailored to the problem structure. To illustrate important design options and computational behaviour, four applications are studied: bin packing, generalised assignment, a resource allocation problem and the fixed-charge transportation problem.

  • 567.
    Zhao, Yixin
    et al.
    Nanjing University of Science and Technology, School of Automation.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Rönnberg, Elina
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Pardalos, Panos
    University of Florida, Department of Industrial and System Engineering.
    The fixed charge transportation problem: a strong formulation based on Lagrangian decomposition and column generation2018Inngår i: Journal of Global Optimization, ISSN 0925-5001, E-ISSN 1573-2916, Vol. 72, nr 3, s. 517-538Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A new and strong convexified formulation of the fixed charge transportation problem is provided. This formulation is obtained by integrating the concepts of Lagrangian decomposition and column generation. The decomposition is made by splitting the shipping variables into supply and demand side copies, while the columns correspond to extreme flow patterns for single sources or sinks. It is shown that the combination of Lagrangian decomposition and column generation provides a formulation whose strength dominates those of three other convexified formulations of the problem. Numerical results illustrate that our integrated approach has the ability to provide strong lower bounds. The Lagrangian decomposition yields a dual problem with an unbounded set of optimal solutions. We propose a regularized column generation scheme which prioritizes an optimal dual solution with a small 1-norm. We further demonstrate numerically that information gained from the strong formulation can also be used for constructing a small-sized core problem which yields high-quality upper bounds.

  • 568.
    Zhao, Yixin
    et al.
    Nanjing Univ Sci and Technol, Peoples R China.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Yuan, Di
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten.
    Rönnberg, Elina
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Lei, Lei
    Linköpings universitet, Institutionen för teknik och naturvetenskap. Linköpings universitet, Tekniska fakulteten.
    Correction: Power efficient uplink scheduling in SC-FDMA: benchmarking by column generation (vol 17, pg 695, 2016)2019Inngår i: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 20, nr 3, s. 959-959Artikkel i tidsskrift (Annet vitenskapelig)
    Abstract [en]

    At the time of the final publication of the paper, in December 2016, Yixin Zhaos affiliation had changed.

  • 569. Bestill onlineKjøp publikasjonen >>
    Zhao, Yuxin
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Position Estimation in Uncertain Radio Environments and Trajectory Learning2017Licentiatavhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    To infer the hidden states from the noisy observations and make predictions based on a set of input states and output observations are two challenging problems in many research areas. Examples of applications many include position estimation from various measurable radio signals in indoor environments, self-navigation for autonomous cars, modeling and predicting of the traffic flows, and flow pattern analysis for crowds of people. In this thesis, we mainly use the Bayesian inference framework for position estimation in an indoor environment, where the radio propagation is uncertain. In Bayesian inference framework, it is usually hard to get analytical solutions. In such cases, we resort to Monte Carlo methods to solve the problem numerically. In addition, we apply Bayesian nonparametric modeling for trajectory learning in sport analytics.

    The main contribution of this thesis is to propose sequential Monte Carlo methods, namely particle filtering and smoothing, for a novel indoor positioning framework based on proximity reports. The experiment results have been further compared with theoretical bounds derived for this proximity based positioning system. To improve the performance, Bayesian non-parametric modeling, namely Gaussian process, has been applied to better indicate the radio propagation conditions. Then, the position estimates obtained sequentially using filtering and smoothing are further compared with a static solution, which is known as fingerprinting.

    Moreover, we propose a trajectory learning framework for flow estimation in sport analytics based on Gaussian processes. To mitigate the computation deficiency of Gaussian process, a grid-based on-line algorithm has been adopted for real-time applications. The resulting trajectory modeling for individual athlete can be used for many purposes, such as performance prediction and analysis, health condition monitoring, etc. Furthermore, we aim at modeling the flow of groups of athletes, which could be potentially used for flow pattern recognition, strategy planning, etc.

    Delarbeid
    1. Received-Signal-Strength Threshold Optimization Using Gaussian Processes
    Åpne denne publikasjonen i ny fane eller vindu >>Received-Signal-Strength Threshold Optimization Using Gaussian Processes
    2017 (engelsk)Inngår i: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 65, nr 8, s. 2164-2177Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    There is a big trend nowadays to use event-triggered proximity report for indoor positioning. This paper presents a generic received-signal-strength (RSS) threshold optimization framework for generating informative proximity reports. The proposed framework contains five main building blocks, namely the deployment information, RSS model, positioning metric selection, optimization process and management. Among others, we focus on Gaussian process regression (GPR)-based RSS models and positioning metric computation. The optimal RSS threshold is found through minimizing the best achievable localization root-mean-square-error formulated with the aid of fundamental lower bound analysis. Computational complexity is compared for different RSS models and different fundamental lower bounds. The resulting optimal RSS threshold enables enhanced performance of new fashioned low-cost and low-complex proximity report-based positioning algorithms. The proposed framework is validated with real measurements collected in an office area where bluetooth-low-energy (BLE) beacons are deployed.

    sted, utgiver, år, opplag, sider
    Institute of Electrical and Electronics Engineers (IEEE), 2017
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-135065 (URN)10.1109/TSP.2017.2655480 (DOI)000395827100018 ()
    Prosjekter
    TRAX
    Merknad

    Funding agencies: European Union FP7 Marie Curie training programme on Tracking in Complex Sensor Systems [607400]

    Tilgjengelig fra: 2017-03-08 Laget: 2017-03-08 Sist oppdatert: 2019-02-12bibliografisk kontrollert
    2. Gaussian Process for Propagation modeling and Proximity Reports Based Indoor Positioning
    Åpne denne publikasjonen i ny fane eller vindu >>Gaussian Process for Propagation modeling and Proximity Reports Based Indoor Positioning
    Vise andre…
    2016 (engelsk)Inngår i: 2016 IEEE 83rd Vehicular Technology Conference (VTC Spring), IEEE , 2016, s. 1-5Konferansepaper, Publicerat paper (Fagfellevurdert)
    Abstract [en]

    The commercial interest in proximity services is increasing. Application examples include location-based information and advertisements, logistics, social networking, file sharing, etc. In this paper, we consider network-based positioning based on times series of proximity reports from a mobile device, either only a proximity indicator, or a vector of RSS from observed nodes. Such positioning corresponds to a latent and nonlinear observation model. To address these problems, we combine two powerful tools, namely particle filtering and Gaussian process regression (GPR) for radio signal propagation modeling. The latter also provides some insights into the spatial correlation of the radio propagation in the considered area. Radio propagation modeling and positioning performance are evaluated in a typical office area with Bluetooth-Low-Energy (BLE) beacons deployed for proximity detection and reports. Results show that the positioning accuracy can be improved by using GPR.

    sted, utgiver, år, opplag, sider
    IEEE, 2016
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-128255 (URN)10.1109/VTCSpring.2016.7504255 (DOI)000386528400206 ()9781509016983 (ISBN)
    Konferanse
    2016 IEEE 83rd Vehicular Technology Conference: VTC2016-Spring, 15–18 May 2016, Nanjing, China
    Tilgjengelig fra: 2016-05-24 Laget: 2016-05-24 Sist oppdatert: 2019-02-12bibliografisk kontrollert
    3. Gaussian Processes for Flow Modeling and Prediction of Positioned Trajectories Evaluated with Sports Data
    Åpne denne publikasjonen i ny fane eller vindu >>Gaussian Processes for Flow Modeling and Prediction of Positioned Trajectories Evaluated with Sports Data
    Vise andre…
    2016 (engelsk)Inngår i: 19th International Conference on  Information Fusion (FUSION), 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, s. 1461-1468Konferansepaper, Publicerat paper (Fagfellevurdert)
    Abstract [en]

    Kernel-based machine learning methods are gaining increasing interest in flow modeling and prediction in recent years. Gaussian process (GP) is one example of such kernelbased methods, which can provide very good performance for nonlinear problems. In this work, we apply GP regression to flow modeling and prediction of athletes in ski races, but the proposed framework can be generally applied to other use cases with device trajectories of positioned data. Some specific aspects can be addressed when the data is periodic, like in sports where the event is split up over multiple laps along a specific track. Flow models of both the individual skier and a cluster of skiers are derived and analyzed. Performance has been evaluated using data from the Falun Nordic World Ski Championships 2015, in particular the Men’s cross country 4 × 10 km relay. The results show that the flow models vary spatially for different skiers and clusters. We further demonstrate that GP regression provides powerful and accurate models for flow prediction.

    sted, utgiver, år, opplag, sider
    Institute of Electrical and Electronics Engineers (IEEE), 2016
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-129758 (URN)9780996452748 (ISBN)9781509020126 (ISBN)
    Konferanse
    19th International Conference on Information Fusion, 5-8 July 2016, Heidelberg, Germany
    Tilgjengelig fra: 2016-06-27 Laget: 2016-06-27 Sist oppdatert: 2019-02-12bibliografisk kontrollert
    Fulltekst (pdf)
    Position Estimation in Uncertain Radio Environments and Trajectory Learning
    Download (pdf)
    omslag
    Download (jpg)
    presentationsbild
  • 570. Bestill onlineKjøp publikasjonen >>
    Zikrin, Spartak
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Large-Scale Optimization Methods with Application to Design of Filter Networks2014Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Nowadays, large-scale optimization problems are among those most challenging. Any progress in developing methods for large-scale optimization results in solving important applied problems more effectively. Limited memory methods and trust-region methods represent two ecient approaches used for solving unconstrained optimization problems. A straightforward combination of them deteriorates the efficiency of the former approach, especially in the case of large-scale problems. For this reason, the limited memory methods are usually combined with a line search. We develop new limited memory trust-region algorithms for large-scale unconstrained optimization. They are competitive with the traditional limited memory line-search algorithms.

    In this thesis, we consider applied optimization problems originating from the design of lter networks. Filter networks represent an ecient tool in medical image processing. It is based on replacing a set of dense multidimensional lters by a network of smaller sparse lters called sub-filters. This allows for improving image processing time, while maintaining image quality and the robustness of image processing.

    Design of lter networks is a nontrivial procedure that involves three steps: 1) choosing the network structure, 2) choosing the sparsity pattern of each sub-filter and 3) optimizing the nonzero coecient values. So far, steps 1 and 2 were mainly based on the individual expertise of network designers and their intuition. Given a sparsity pattern, the choice of the coecients at stage 3 is related to solving a weighted nonlinear least-squares problem. Even in the case of sequentially connected lters, the resulting problem is of a multilinear least-squares (MLLS) type, which is a non-convex large-scale optimization problem. This is a very dicult global optimization problem that may have a large number of local minima, and each of them is singular and non-isolated. It is characterized by a large number of decision variables, especially for 3D and 4D lters.

    We develop an effective global optimization approach to solving the MLLS problem that reduces signicantly the computational time. Furthermore, we  develop efficient methods for optimizing sparsity of individual sub-filters  in lter networks of a more general structure. This approach offers practitioners a means of nding a proper trade-o between the image processing quality and time. It allows also for improving the network structure, which makes automated some stages of designing lter networks.

    Delarbeid
    1. On Efficiently Combining Limited Memory and Trust-Region Techniques
    Åpne denne publikasjonen i ny fane eller vindu >>On Efficiently Combining Limited Memory and Trust-Region Techniques
    2013 (engelsk)Rapport (Annet vitenskapelig)
    Abstract [en]

    Limited memory quasi-Newton methods and trust-region methods represent two efficient approaches used for solving unconstrained optimization problems. A straightforward combination of them deteriorates the efficiency of the former approach, especially in the case of large-scale problems. For this reason, the limited memory methods are usually combined with a line search. We show how to efficiently combine limited memory and trust-region techniques. One of our approaches is based on the eigenvalue decomposition of the limited memory quasi-Newton approximation of the Hessian matrix. The decomposition allows for finding a nearly-exact solution to the trust-region subproblem defined by the Euclidean norm with an insignificant computational overhead compared with the cost of computing the quasi-Newton direction in line-search limited memory methods. The other approach is based on two new eigenvalue-based norms. The advantage of the new norms is that the trust-region subproblem is separable and each of the smaller subproblems is easy to solve. We show that our eigenvalue-based limited-memory trust-region methods are globally convergent. Moreover, we propose improved versions of the existing limited-memory trust-region algorithms. The presented results of numerical experiments demonstrate the efficiency of our approach which is competitive with line-search versions of the L-BFGS method.

    sted, utgiver, år, opplag, sider
    Linköping: Linköping University Electronic Press, 2013. s. 33
    Serie
    LiTH-MAT-R, ISSN 0348-2960 ; 2013:13
    Emneord
    Unconstrained Optimization; Large-scale Problems; Limited Memory Methods;
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-102005 (URN)LiTH-MAT-R--2013/13--SE (ISRN)
    Tilgjengelig fra: 2013-11-26 Laget: 2013-11-26 Sist oppdatert: 2016-01-12bibliografisk kontrollert
    2. Global search strategies for solving multilinear least-squares problems
    Åpne denne publikasjonen i ny fane eller vindu >>Global search strategies for solving multilinear least-squares problems
    2012 (engelsk)Inngår i: Sultan Qaboos University Journal for Science, ISSN 1027-524X, Vol. 17, nr 1, s. 12-21Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear leastsquares problem. The difference is that a multilinear operator is used in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows for moving from one local minimizer to a better one. The efficiency of this strategy is illustrated by results of numerical experiments performed for some problems related to the design of filter networks.

    sted, utgiver, år, opplag, sider
    Sultan Qaboos University, 2012
    Emneord
    Global optimization; Global search strategies; Multilinear least-squares; Filter
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-78918 (URN)
    Tilgjengelig fra: 2012-08-28 Laget: 2012-06-25 Sist oppdatert: 2015-09-03bibliografisk kontrollert
    3. Sparsity Optimization in Design of Multidimensional Filter Networks
    Åpne denne publikasjonen i ny fane eller vindu >>Sparsity Optimization in Design of Multidimensional Filter Networks
    2013 (engelsk)Rapport (Annet vitenskapelig)
    Abstract [en]

    Filter networks is a powerful tool used for reducing the image processing time, while maintaining its reasonably high quality.They are composed of sparse sub-filters whose low sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. If to disregard the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers. Each of the local minimizers is singular and non-isolated.The cardinality constraint makes the problem even more difficult to solve.An approach for approximately solving the cardinality-constrained MLLS problem is presented.It is then applied to solving a bi-criteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

    sted, utgiver, år, opplag, sider
    Linköping: Linköping University Electronic Press, 2013. s. 21
    Serie
    LiTH-MAT-R, ISSN 0348-2960 ; 2013:16
    Emneord
    Sparse optimization; Cardinality Constraint; Multicriteria Optimization; Multilinear Least-Squares Problem; Filter networks; Medical imaging
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-103915 (URN)LiTH-MAT-R-2013/16-SE (ISRN)
    Tilgjengelig fra: 2014-02-03 Laget: 2014-02-03 Sist oppdatert: 2016-11-24bibliografisk kontrollert
    Fulltekst (pdf)
    Large-Scale Optimization Methods with Application to Design of Filter Networks
    Download (pdf)
    omslag
  • 571.
    Ålund, Oskar
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    A provably stable, non-iterative domain decomposition technique for the advection-diffusion equation2016Rapport (Annet vitenskapelig)
    Abstract [en]

    We describe an efficient, non-iterative domain decomposition approach for the onedimensional advection–diffusion equation based on the Summation-by-Parts technique in both time and space. A fully discrete multidomain analogue of the continuous equation is formulated and a linear system consisting only of the solution components involved in the coupling between the subdomain interfaces is isolated. Once the coupling system is solved, the full solution is found by computing linear combinations of known vectors, weighted by the coupling components. Both stability and invertibility of the discrete scheme is proved using standard Summation-by-Parts procedures.

    In a numerical study we show that perfunctory implementations of monodomain Summation-by-Parts based time integration can be improved upon significantly. Using our proposed method we are able to reduce execution time and memory footprint by up to 80% and 95% respectively. Similar improvements in execution time is shown also when compared against explicit Runge–Kutta time integration.

    Fulltekst (pdf)
    Provably Stable, Non-iterative Domain Decomposition Technique for the Advection-Diffusion Equation
  • 572.
    Ålund, Oskar
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    A stable, high order accurate and efficient hybrid method for flow calculations in complex geometries2018Inngår i: 2018 AIAA Aerospace Sciences Meeting, AIAA SciTech Forum, (AIAA 2018-1096), American Institute of Aeronautics and Astronautics, 2018, nr 210059, s. 1-9Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The suitability of a discretization method is highly dependent on the shape of the domain. Finite difference schemes are typically efficient, but struggle with complex geometry, while finite element methods are expensive but well suited for complex geometries. In this paper we propose a provably stable hybrid method for a 2D advection–diffusion problem, using a class of inner product compatible projection operators to couple the non-conforming grids that arise due to varying the discretization method throughout the domain.

    Fulltekst (pdf)
    A stable, high order accurate and efficient hybrid method for flow calculations in complex geometries
9101112 551 - 572 of 572
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