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  • 101.
    Carpenter, Mark H.
    et al.
    Aerodynamic and Acoustic Methods Branch, NASA Langley Research Center, Hampton, Virginia, USA.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Gottlieb, David
    Division of Applied Mathematics, Brown University, Providence, Rhode Island, USA.
    A stable and conservative interface treatment of arbitrary spatial accuracy1999Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 148, s. 341-365Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Stable and accurate interface conditions based on the SAT penalty method are derived for the linear advection–diffusion equation. The conditions are functionally independent of the spatial order of accuracy and rely only on the form of the discrete operator. We focus on high-order finite-difference operators that satisfy the summation-by-parts (SBP) property. We prove that stability is a natural consequence of the SBP operators used in conjunction with the new, penalty type, boundary conditions. In addition, we show that the interface treatments are conservative. The issue of the order of accuracy of the interface boundary conditions is clarified. New finite-difference operators of spatial accuracy up to sixth order are constructed which satisfy the SBP property. These finite-difference operators are shown to admit design accuracy (pth-order global accuracy) when (p−1)th-order stencil closures are used near the boundaries, if the physical boundary conditions and interface conditions are implemented to at leastpth-order accuracy. Stability and accuracy are demonstrated on the nonlinear Burgers' equation for a 12-subdomain problem with randomly distributed interfaces.

  • 102. Carpenter, Mark H.
    et al.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Gottlieb, David
    Revisiting and extending interface penalties for multi-domain summation-by-parts operators2009Rapport (Annet vitenskapelig)
  • 103.
    Carpenter, Mark H.
    et al.
    NASA Langley Research Center.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Gottlieb, David
    Brown University.
    Revisiting and Extending Interface Penalties for Multidomain Summation-by-Parts Operators2010Inngår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 45, nr 1-3, s. 118-150Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A general interface procedure is presented for multi-domain collocation methods satisfying the summation-by-parts (SBP) spatial discretization convention. Unlike more traditional operators (e.g. FEM) applied to the advection-diffusion equation, the new procedure penalizes the solution and the first p derivatives across the interface. The combined interior/interface operators are proven to be pointwise stable, and conservative, although accuracy deteriorates for p≥2. Penalties between two different sets of variables are compared (motivated by FEM primal and flux formulations), and are shown to be equivalent for certain choices of penalty parameters. Extensive validation studies are presented using two classes of high-order SBP operators: (1) central finite difference, and (2) Legendre spectral collocation.

    Fulltekst (pdf)
    fulltext
  • 104.
    Cederlöf, Jörgen
    Linköpings universitet, Matematiska institutionen.
    Authentication in quantum key growing2005Independent thesis Basic level (professional degree), 20 poäng / 30 hpOppgave
    Abstract [en]

    Quantum key growing, often called quantum cryptography or quantum key distribution, is a method using some properties of quantum mechanics to create a secret shared cryptography key even if an eavesdropper has access to unlimited computational power. A vital but often neglected part of the method is unconditionally secure message authentication. This thesis examines the security aspects of authentication in quantum key growing. Important concepts are formalized as Python program source code, a comparison between quantum key growing and a classical system using trusted couriers is included, and the chain rule of entropy is generalized to any Rényi entropy. Finally and most importantly, a security flaw is identified which makes the probability to eavesdrop on the system undetected approach unity as the system is in use for a long time, and a solution to this problem is provided.

    Fulltekst (pdf)
    FULLTEXT01
  • 105.
    Cheng, Hei Victor
    et al.
    Linköpings universitet, Institutionen för systemteknik, Kommunikationssystem. Linköpings universitet, Tekniska fakulteten.
    Björnson, Emil
    Linköpings universitet, Institutionen för systemteknik, Kommunikationssystem. Linköpings universitet, Tekniska fakulteten.
    Larsson, Erik G
    Linköpings universitet, Institutionen för systemteknik, Kommunikationssystem. Linköpings universitet, Tekniska fakulteten.
    SEMI-CLOSED FORM SOLUTION FOR SUM RATE MAXIMIZATION IN DOWNLINK MULTIUSER MIMO VIA LARGE-SYSTEM ANALYSIS2018Inngår i: 2018 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), IEEE , 2018, s. 3699-3703Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This work introduces a new approach to solve the joint precoding and power allocation for sum rate maximization problem in the downlink multiuser MIMO by a combination of random matrix theory and optimization theory. The new approach results in a simplified problem that, though non-convex, obeys a simple separable structure. The sum rate maximization problem is decomposed into different single-variable optimization problems that can be solved in parallel. A water-filling-like solution is found, which can be applied under some mild conditions on the SNRs of the users. The proposed scheme provides large gains over heuristic solutions when the number of users in the cell is large, which suggests the applicability in massive MIMO systems.

  • 106.
    Connors, Richard
    et al.
    Institute for Transport Studies, Leeds University, Leeds, England, UK.
    Patriksson, Michael
    Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg, Sweden.
    Rydergren, Clas
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten.
    Sumalee, Agachai
    King Mongkut’s Institute of Technology Ladkrabang, Thailand.
    Watling, David
    Institute for Transport Studies, Leeds University, Leeds, England, UK.
    Sensitivity Analysis of Welfare, Equity, and Acceptability Level of Transport Policies2015Inngår i: Optimization, Control, and Applications in the Information Age: In Honor of Panos M. Pardalos’s 60th Birthday / [ed] Athanasios Migdalas, Athanasia Karakitsiou, London: Springer Publishing Company, 2015, s. 39-65Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    Transport planners face a major challenge to devise policies to meet multiple expectations and objectives. While we know that transport networks are complex, multi-modal, and spatially distributed systems, there is now a long history of mathematical tools which assist planners in understanding travel movements. However, the objectives that they are asked to achieve do not always admit such a quantification, and so there is a potential mismatch between seemingly qualitatively driven objectives and quantitatively expressed models of the transport system. In the present chapter we address this mismatch, by focusing on three objectives that we believe represent the typical interests of a planner. These are namely: is the policy economically justifiable (efficient), is it “fair” (equitable), and is it justifiable to a democratic society (acceptable)? We provide mathematical representations of these three objectives and link them to mathematical theory of transport networks, in which we may explore the sensitivity of travel behaviour (and hence the objectives) to various multi-modal transport policies. The detailed steps for representing the policy objectives and sensitivities in the network are set out, and the results of a case study reported in which road tolls, road capacities, and bus fares are the policy variables. Overall, the chapter sets out a systematic method for planners to choose between multi-modal policies based on these three objectives.

  • 107.
    Costa, Antonio F.
    et al.
    Departamento de Matemáticas Fundamentales, Facultad de Ciencias, Universidad Nacional de Educacin a Distancia, 28040 Madrid, Spain.
    Izquierdo, Milagros
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    ON THE CONNECTEDNESS OF THE BRANCH LOCUS OF THE MODULI SPACE OF RIEMANN SURFACES OF GENUS 42010Inngår i: Glasgow Mathematical Journal, ISSN 0017-0895, E-ISSN 1469-509X, Vol. 52, s. 401-408Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Let g be an integer ≥ 3 and let θg = {X ∈ Mg|Aut(X) ≠ 1d}, where Mg denotes the moduli space of a compact Riemann surface. Using uniformization of Riemann surfaces by Fuchsian groups and the equisymmetric stratification of the branch locus of the moduli space we prove that the subloci corresponding to Riemann surfaces with automorphism groups isomorphic to cyclic groups of order 2 and 3 belongs to the same connected component. We also prove the connectedness of θg for g = 5, 6, 7 and 8 with the exception of the isolated points given by Kulkarni.

    Fulltekst (pdf)
    ON THE CONNECTEDNESS OF THE BRANCH LOCUS OF THE MODULI SPACE OF RIEMANN SURFACES OF GENUS 4
  • 108. Bestill onlineKjøp publikasjonen >>
    Dahlin, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Accelerating Monte Carlo methods for Bayesian inference in dynamical models2016Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Making decisions and predictions from noisy observations are two important and challenging problems in many areas of society. Some examples of applications are recommendation systems for online shopping and streaming services, connecting genes with certain diseases and modelling climate change. In this thesis, we make use of Bayesian statistics to construct probabilistic models given prior information and historical data, which can be used for decision support and predictions. The main obstacle with this approach is that it often results in mathematical problems lacking analytical solutions. To cope with this, we make use of statistical simulation algorithms known as Monte Carlo methods to approximate the intractable solution. These methods enjoy well-understood statistical properties but are often computational prohibitive to employ.

    The main contribution of this thesis is the exploration of different strategies for accelerating inference methods based on sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). That is, strategies for reducing the computational effort while keeping or improving the accuracy. A major part of the thesis is devoted to proposing such strategies for the MCMC method known as the particle Metropolis-Hastings (PMH) algorithm. We investigate two strategies: (i) introducing estimates of the gradient and Hessian of the target to better tailor the algorithm to the problem and (ii) introducing a positive correlation between the point-wise estimates of the target.

    Furthermore, we propose an algorithm based on the combination of SMC and Gaussian process optimisation, which can provide reasonable estimates of the posterior but with a significant decrease in computational effort compared with PMH. Moreover, we explore the use of sparseness priors for approximate inference in over-parametrised mixed effects models and autoregressive processes. This can potentially be a practical strategy for inference in the big data era. Finally, we propose a general method for increasing the accuracy of the parameter estimates in non-linear state space models by applying a designed input signal.

    Delarbeid
    1. Particle Metropolis-Hastings using gradient and Hessian information
    Åpne denne publikasjonen i ny fane eller vindu >>Particle Metropolis-Hastings using gradient and Hessian information
    2015 (engelsk)Inngår i: Statistics and computing, ISSN 0960-3174, E-ISSN 1573-1375, Vol. 25, nr 1, s. 81-92Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    Particle Metropolis-Hastings (PMH) allows for Bayesian parameter inference in nonlinear state space models by combining MCMC and particle filtering. The latter is used to estimate the intractable likelihood. In its original formulation, PMH makes use of a marginal MCMC proposal for the parameters, typically a Gaussian random walk. However, this can lead to a poor exploration of the parameter space and an inefficient use of the generated particles.

    We propose two alternative versions of PMH that incorporate gradient and Hessian information about the posterior into the proposal. This information is more or less obtained as a byproduct of the likelihood estimation. Indeed, we show how to estimate the required information using a fixed-lag particle smoother, with a computational cost growing linearly in the number of particles. We conclude that the proposed methods can: (i) decrease the length of the burn-in phase, (ii) increase the mixing of the Markov chain at the stationary phase, and (iii) make the proposal distribution scale invariant which simplifies tuning.

    sted, utgiver, år, opplag, sider
    Springer, 2015
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-106749 (URN)10.1007/s11222-014-9510-0 (DOI)000349028500013 ()
    Prosjekter
    Probabilistic modelling of dynamical systems
    Forskningsfinansiär
    Swedish Research Council, 621-2013-5524
    Merknad

    On the day of the defence date the status of this article was Manuscript.

    Tilgjengelig fra: 2014-05-21 Laget: 2014-05-21 Sist oppdatert: 2019-12-02bibliografisk kontrollert
    2. Quasi-Newton particle Metropolis-Hastings
    Åpne denne publikasjonen i ny fane eller vindu >>Quasi-Newton particle Metropolis-Hastings
    2015 (engelsk)Inngår i: Proceedings of the 17th IFAC Symposium on System Identification., Elsevier, 2015, Vol. 48 Issue 28, s. 981-986Konferansepaper, Publicerat paper (Fagfellevurdert)
    Abstract [en]

    Particle Metropolis-Hastings enables Bayesian parameter inference in general nonlinear state space models (SSMs). However, in many implementations a random walk proposal is used and this can result in poor mixing if not tuned correctly using tedious pilot runs. Therefore, we consider a new proposal inspired by quasi-Newton algorithms that may achieve similar (or better) mixing with less tuning. An advantage compared to other Hessian based proposals, is that it only requires estimates of the gradient of the log-posterior. A possible application is parameter inference in the challenging class of SSMs with intractable likelihoods.We exemplify this application and the benefits of the new proposal by modelling log-returns offuture contracts on coffee by a stochastic volatility model with alpha-stable observations.

    sted, utgiver, år, opplag, sider
    Elsevier, 2015
    Emneord
    Bayesian parameter inference; state space models; approximate Bayesian computations; particle Markov chain Monte Carlo; α-stable distributions
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-123666 (URN)10.1016/j.ifacol.2015.12.258 (DOI)
    Konferanse
    Proceedings of the 17th IFAC Symposium on System Identification, Beijing, China, October 19-21, 2015.
    Prosjekter
    CADICS
    Forskningsfinansiär
    Swedish Research Council, 637-2014-466Swedish Research Council, 621-2013-5524
    Tilgjengelig fra: 2016-01-07 Laget: 2016-01-07 Sist oppdatert: 2016-04-01
    3. Hierarchical Bayesian approaches for robust inference in ARX models
    Åpne denne publikasjonen i ny fane eller vindu >>Hierarchical Bayesian approaches for robust inference in ARX models
    2012 (engelsk)Inngår i: Proceedings from the 16th IFAC Symposium on System Identification, 2012 / [ed] Michel Kinnaert, International Federation of Automatic Control , 2012, Vol. 16 Part 1, s. 131-136Konferansepaper, Oral presentation only (Fagfellevurdert)
    Abstract [en]

    Gaussian innovations are the typical choice in most ARX models but using other distributions such as the Student's t could be useful. We demonstrate that this choice of distribution for the innovations provides an increased robustness to data anomalies, such as outliers and missing observations. We consider these models in a Bayesian setting and perform inference using numerical procedures based on Markov Chain Monte Carlo methods. These models include automatic order determination by two alternative methods, based on a parametric model order and a sparseness prior, respectively. The methods and the advantage of our choice of innovations are illustrated in three numerical studies using both simulated data and real EEG data.

    sted, utgiver, år, opplag, sider
    International Federation of Automatic Control, 2012
    Serie
    IFAC papers online, ISSN 1474-6670 ; 2012
    Emneord
    Particle Filtering/Monte Carlo Methods; Bayesian Methods
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-81258 (URN)10.3182/20120711-3-BE-2027.00318 (DOI)978-3-902823-06-9 (ISBN)
    Konferanse
    The 16th IFAC Symposium on System Identification, July 11-13, Brussels, Belgium
    Prosjekter
    CADICSCNDS
    Forskningsfinansiär
    Swedish Research Council
    Tilgjengelig fra: 2012-09-10 Laget: 2012-09-10 Sist oppdatert: 2016-05-04bibliografisk kontrollert
    Fulltekst (pdf)
    fulltext
    Download (pdf)
    omslag
    Download (jpg)
    presentationsbild
  • 109.
    Delorme, Yann T.
    et al.
    Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, Israel.
    Puri, Kunal
    Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, Israel.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Linders, Viktor
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Dong, Suchuan
    Department of Mathematics, Purdue University, West Lafayette, IN, USA.
    Frankel, Steven H.
    Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, Israel.
    A simple and efficient incompressible Navier-Stokes solver for unsteady complex geometry flows on truncated domains2017Inngår i: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 150, s. 84-94Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    A simple and efficient incompressible Navier-Stokes solver for unsteady complex geometry flows on truncated domains
  • 110.
    Derigs, Dominik
    et al.
    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.
    Winters, Andrew Ross
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics2018Inngår i: Jahresbericht der Deutschen Mathematiker-Vereinigung (Teubner), ISSN 0012-0456, E-ISSN 1869-7135, Vol. 120, nr 3, s. 153-219Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of magnetized fluids. In order to be self-contained we first motivate the physical properties of a magnetic fluid and how it should behave under the laws of thermodynamics. Next, we introduce a mathematical model built from hyperbolic partial differential equations (PDEs) that translate physical laws into mathematical equations. After an overview of the continuous analysis, we thoroughly describe the derivation of a numerical approximation of the ideal MHD system that remains consistent to the continuous thermodynamic principles. The derivation of the method and the theorems contained within serve as the bulk of the review article. We demonstrate that the derived numerical approximation retains the correct entropic properties of the continuous model and show its applicability to a variety of standard numerical test cases for MHD schemes. We close with our conclusions and a brief discussion on future work in the area of entropy consistent numerical methods and the modeling of plasmas.

    Fulltekst (pdf)
    Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics
  • 111.
    Derigs, Dominik
    et al.
    I. Physikalisches 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.
    Walch, Stefanie
    I. Physikalisches Institut, Universität zu Köln, Köln, Germany.
    A novel averaging technique for discrete entropy-stable dissipation operators for ideal MHD2017Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 330, s. 624-632Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Entropy stable schemes can be constructed with a specific choice of the numerical flux function. First, an entropy conserving flux is constructed. Secondly, an entropy stable dissipation term is added to this flux to guarantee dissipation of the discrete entropy. Present works in the field of entropy stable numerical schemes are concerned with thorough derivations of entropy conservative fluxes for ideal MHD. However, as we show in this work, if the dissipation operator is not constructed in a very specific way, it cannot lead to a generally stable numerical scheme. The two main findings presented in this paper are that the entropy conserving flux of Ismail & Roe can easily break down for certain initial conditions commonly found in astrophysical simulations, and that special care must be taken in the derivation of a discrete dissipation matrix for an entropy stable numerical scheme to be robust. We present a convenient novel averaging procedure to evaluate the entropy Jacobians of the ideal MHD and the compressible Euler equations that yields a discretization with favorable robustness properties.

    Fulltekst (pdf)
    A novel averaging technique for discrete entropy-stable dissipation operators for ideal MHD
  • 112.
    Derigs, Dominik
    et al.
    I. Physikalisches 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.
    Walch, Stefanie
    I. Physikalisches Institut, Universität zu Köln, Köln, Germany.
    A novel high-order, entropy stable, 3D AMR MHD solver with guaranteed positive pressure2016Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 317, s. 223-256Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We describe a high-order numerical magnetohydrodynamics (MHD) solver built upon a novel non-linear entropy stable numerical flux function that supports eight travelling wave solutions. By construction the solver conserves mass, momentum, and energy and is entropy stable. The method is designed to treat the divergence-free constraint on the magnetic field in a similar fashion to a hyperbolic divergence cleaning technique. The solver described herein is especially well-suited for flows involving strong discontinuities. Furthermore, we present a new formulation to guarantee positivity of the pressure. We present the underlying theory and implementation of the new solver into the multi-physics, multi-scale adaptive mesh refinement (AMR) simulation code FLASH (http://flash.uchicago.edu). The accuracy, robustness and computational efficiency is demonstrated with a number of tests, including comparisons to available MHD implementations in FLASH.

    Fulltekst (pdf)
    A novel high-order, entropy stable, 3D AMR MHD solver with guaranteed positive pressure
  • 113.
    Derigs, Dominik
    et al.
    I. Physikalisches 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.
    Walch, Stefanie
    I. Physikalisches Institut, Universität zu Köln, Köln, Germany.
    Bohm, Marvin
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations2018Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 364, s. 420-467Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The paper presents two contributions in the context of the numerical simulation of magnetized fluid dynamics. First, we show how to extend the ideal magnetohydrodynamics (MHD) equations with an inbuilt magnetic field divergence cleaning mechanism in such a way that the resulting model is consistent with the second law of thermodynamics. As a byproduct of these derivations, we show that not all of the commonly used divergence cleaning extensions of the ideal MHD equations are thermodynamically consistent. Secondly, we present a numerical scheme obtained by constructing a specific finite volume discretization that is consistent with the discrete thermodynamic entropy. It includes a mechanism to control the discrete divergence error of the magnetic field by construction and is Galilean invariant. We implement the new high-order MHD solver in the adaptive mesh refinement code FLASH where we compare the divergence cleaning efficiency to the constrained transport solver available in FLASH (unsplit staggered mesh scheme).

    Fulltekst tilgjengelig fra 2020-07-13 08:00
  • 114.
    Domeij Bäckryd, Rebecka
    Linköpings universitet, Matematiska institutionen.
    Simulation of Heat Transfer on a Gas Sensor Component2005Independent thesis Basic level (professional degree)Oppgave
    Abstract [en]

    Gas sensors are today used in many different application areas, and one growing future market is battery operated sensors. As many gas sensor components are heated, one major limit of the operation time is caused by the power dissipated as heat. AppliedSensor is a company that develops and produces gas sensor components, modules and solutions, among which battery operated gas sensors are one targeted market.

    The aim of the diploma work has been to simulate the heat transfer on a hydrogen gas sensor component and its closest surroundings consisting of a carrier mounted on a printed circuit board. The component is heated in order to improve the performance of the gas sensing element.

    Power dissipation occurs by all three modes of heat transfer; conduction from the component through bond wires and carrier to the printed circuit board as well as convection and radiation from all the surfaces. It is of interest to AppliedSensor to understand which factors influence the heat transfer. This knowledge will be used to improve different aspects of the gas sensor, such as the power consumption.

    Modeling and simulation have been performed in FEMLAB, a tool for solving partial differential equations by the finite element method. The sensor system has been defined by the geometry and the material properties of the objects. The system of partial differential equations, consisting of the heat equation describing conduction and boundary conditions specifying convection and radiation, was solved and the solution was validated against experimental data.

    The convection increases with the increase of hydrogen concentration. A great effort was made to finding a model for the convection. Two different approaches were taken, the first based on known theory from the area and the second on experimental data. When the first method was compared to experiments, it turned out that the theory was insufficient to describe this small system involving hydrogen, which was an unexpected but interesting result. The second method matched the experiments well. For the continuation of the project at the company, a better model of the convection would be a great improvement.

    Fulltekst (pdf)
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  • 115.
    Duru, Kenneth
    Uppsala universitet, Avdelningen för beräkningsvetenskap.
    Perfectly Matched Layers and High Order Difference Methods for Wave Equations2012Doktoravhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    The perfectly matched layer (PML) is a novel technique to simulate the absorption of waves in unbounded domains. The underlying equations are often a system of second order hyperbolic partial differential equations. In the numerical treatment, second order systems are often rewritten and solved as first order systems. There are several benefits with solving the equations in second order formulation, though. However, while the theory and numerical methods for first order hyperbolic systems are well developed, numerical techniques to solve second order hyperbolic systems are less complete.

    We construct a strongly well-posed PML for second order systems in two space dimensions, focusing on the equations of linear elasto-dynamics. In the continuous setting, the stability of both first order and second order formulations are linearly equivalent. We have found that if the so-called geometric stability condition is violated, approximating the first order PML with standard central differences leads to a high frequency instability at most resolutions. In the second order setting growth occurs only if growing modes are well resolved. We determine the number of grid points that can be used in the PML to ensure a discretely stable PML, for several anisotropic elastic materials.

    We study the stability of the PML for problems where physical boundaries are important. First, we consider the PML in a waveguide governed by the scalar wave equation. To ensure the accuracy and the stability of the discrete PML, we derived a set of equivalent boundary conditions. Second, we consider the PML for second order symmetric hyperbolic systems on a half-plane. For a class of stable boundary conditions, we derive transformed boundary conditions and prove the stability of the corresponding half-plane problem. Third, we extend the stability analysis to rectangular elastic waveguides, and demonstrate the stability of the discrete PML.

    Building on high order summation-by-parts operators, we derive high order accurate and strictly stable finite difference approximations for second order time-dependent hyperbolic systems on bounded domains. Natural and mixed boundary conditions are imposed weakly using the simultaneous approximation term method. Dirichlet boundary conditions are imposed strongly by injection. By constructing continuous strict energy estimates and analogous discrete strict energy estimates, we prove strict stability.

  • 116. Efraimsson, Gunilla
    et al.
    Forsberg, Nicolas
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Simulations of acoustic waves in a turbo-fan engine air intake2010Inngår i: Proc. 16th AIAA/CEAS Aeroacoustics Conference, AIAA , 2010Konferansepaper (Fagfellevurdert)
  • 117. Efraimsson, Gunilla
    et al.
    Gong, Jing
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Svärd, Magnus
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    An investigation of the performance of a high-order accurate Navier-Stokes code2006Inngår i: Proc. ECCOMAS CFD Conference 2006, The Netherlands: Tech. Univ. Delft , 2006, s. 11-Konferansepaper (Fagfellevurdert)
  • 118.
    Eiderbrant, Emanuel
    Linköpings universitet, Matematiska institutionen.
    Optimala strategier för whist2004Independent thesis Basic level (professional degree)Oppgave
    Abstract [sv]

    Whist is one of the most played card games of the world. Though there have been many studies made in the field of game theory, whist is still somewhat of an unchartered territory. In this thesis some methods to obtain an optimal strategy for whist are discussed.

    Whist belongs to a group of games called logical games. For this group there exists algorithms which result in an optimal strategy. Two algorithms where examined. The minmax algorithm and the alphbeta algorithm. these algorithms could be adapted to whist

    It is possible that there are methods that use the properties of the cards better the the former algorithms to get an optimal result. A few such methods will also be discussed.

    The practical result of the theoretical investigation was a game where the adapted algorithms were implemented.

    Fulltekst (pdf)
    FULLTEXT01
  • 119.
    Ekblom, Jonas
    et al.
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska fakulteten.
    Blomvall, Jörgen
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska fakulteten.
    Importance sampling in stochastic optimization: An application to intertemporal portfolio choice2020Inngår i: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 285, nr 1, s. 106-119Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we propose an approach to construct an analytical approximation of the zero-variance importance sampling distribution. We show specifically how this can be designed for the classic intertemporal portfolio choice problem with proportional transaction costs and constant relative risk aversion preferences. We compare the method to standard variance reduction techniques in single-period optimization and multi-stage stochastic programming formulations of the problem. The numerical experiments show that the method produces significant improvements in solution quality. In the single-period setting, the number of scenarios can be reduced by a factor of 400 with maintained solution quality compared to the best standard method; Latin hypercube sampling. Using importance sampling in multi-stage formulations, the gaps between lower and upper bound estimates are reduced by a factor of 26-500 with maintained scenario tree size. On a higher level, we consider analytical approximations of the zero-variance importance sampling distribution to be a promising method to improve solution quality in stochastic optimization. (C) 2019 Elsevier B.V. All rights reserved.

  • 120.
    Eldén, Lars
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    Computing Frechet derivatives in partial least squares regression2015Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 473, s. 316-338Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Partial least squares is a common technique for multivariate regression. The pro- cedure is recursive and in each step basis vectors are computed for the explaining variables and the solution vectors. A linear model is fitted by projection onto the span of the basis vectors. The procedure is mathematically equivalent to Golub-Kahan bidiagonalization, which is a Krylov method, and which is equiv- alent to a pair of matrix factorizations. The vectors of regression coefficients and prediction are non-linear functions of the right hand side. An algorithm for computing the Frechet derivatives of these functions is derived, based on perturbation theory for the matrix factorizations. From the Frechet derivative of the prediction vector one can compute the number of degrees of freedom, which can be used as a stopping criterion for the recursion. A few numerical examples are given.

    Fulltekst (pdf)
    fulltext
  • 121.
    Eldén, Lars
    et al.
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    Kilmer, Misha
    Tufts University.
    O'Leary, Dianne
    University of Maryland.
    Updating and Downdating Matrix Decompositions2010Inngår i: Selected Works of G. W. Stewart with Commentaries / [ed] M. Kilmer and D. O'Öeary, Boston: Birkhäuser , 2010, s. 45-58Kapittel i bok, del av antologi (Annet vitenskapelig)
    Abstract [en]

    Published in honor of his 70th birthday, this volume explores and celebrates the work of G.W. (Pete) Stewart, a world-renowned expert in computational linear algebra. This volume includes: forty-four of Stewart's most influential research papers in two subject areas: matrix algorithms, and rounding and perturbation theory; a biography of Stewart; a complete list of his publications, students, and honors; selected photographs; and commentaries on his works in collaboration with leading experts in the field. G.W. Stewart: Selected Works with Commentaries will appeal to graduate students, practitioners, and researchers in computational linear algebra and the history of mathematics.

  • 122.
    Eldén, Lars
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    Merkel, Magnus
    Linköpings universitet, Institutionen för datavetenskap, Interaktiva och kognitiva system. Linköpings universitet, Tekniska högskolan.
    Ahrenberg, Lars
    Linköpings universitet, Institutionen för datavetenskap, Interaktiva och kognitiva system. Linköpings universitet, Tekniska högskolan.
    Fagerlund, Martin
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    Computing Semantic Clusters by Semantic Mirroring and Spectral Graph Partitioning2013Inngår i: Mathematics in Computer Science, ISSN 1661-8270, Vol. 7, s. 293-313Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Using the technique of semantic mirroring a graph is obtained that represents words and their translationsfrom a parallel corpus or a bilingual lexicon. The connectedness of the graph holds information about the semanticrelations of words that occur in the translations. Spectral graph theory is used to partition the graph, which leadsto a grouping of the words in different clusters. We illustrate the method using a small sample of seed words froma lexicon of Swedish and English adjectives and discuss its application to computational lexical semantics andlexicography.

  • 123.
    Eldén, Lars
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap. Linköpings universitet, Tekniska högskolan.
    Savas, Berkant
    Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap. Linköpings universitet, Tekniska högskolan.
    Perturbation Theory and Optimality Conditions for the Best Multilinear Rank Approximation of a Tensor2011Inngår i: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 32, nr 4, s. 1422-1450Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The problem of computing the best rank-(p,q,r) approximation of a third order tensor is considered. First the problem is reformulated as a maximization problem on a product of three Grassmann manifolds. Then expressions for the gradient and the Hessian are derived in a local coordinate system at a stationary point, and conditions for a local maximum are given. A first order perturbation analysis is performed using the Grassmann manifold framework. The analysis is illustrated in a few examples, and it is shown that the perturbation theory for the singular value decomposition is a special case of the tensor theory.

    Fulltekst (pdf)
    fulltext
  • 124.
    Eldén, Lars
    et al.
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    Simoncini, Valeria
    Department of Mathematics, University of Bologna.
    SOLVING ILL-POSED LINEAR SYSTEMS WITH GMRES AND A SINGULAR PRECONDITIONER2012Inngår i: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 33, s. 1369-1394Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Almost singular linear systems arise in discrete ill-posed problems. Either because ofthe intrinsic structure of the problem or because of preconditioning, the spectrum of the coefficientmatrix is often characterized by a sizable gap between a large group of numerically zero eigenvaluesand the rest of the spectrum. Correspondingly, the right-hand side has leading eigencomponentsassociated with the eigenvalues away from zero. In this paper the effect of this setting in theconvergence of the generalized minimal residual (GMRES) method is considered. It is shown thatin the initial phase of the iterative algorithm, the residual components corresponding to the largeeigenvalues are reduced in norm, and these can be monitored without extra computation. Theanalysis is supported by numerical experiments. In particular, ill-posed Cauchy problems for partialdifferential equations with variable coefficients are considered, where the preconditioner is a fast,low-rank solver for the corresponding problem with constant coefficients.

  • 125.
    Elfving, Tommy
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Row and column based Iterations2018Inngår i: Applied Analysis and Optimization, ISSN 2432-1656, Vol. 2, nr 2, s. 219-236Artikkel i tidsskrift (Annet vitenskapelig)
    Abstract [en]

    We survey old and more recent results on row- and column-action iterative methods for solving ill-conditioned linear systems. Our main application is in X-ray tomography problems with missing and/or noisy data. We consider the stationary case with cyclic control. A unified framework is presented the use of which allows deriving both necessary and sufficient convergence conditions for many of the methods presented.

  • 126.
    Elfving, Tommy
    et al.
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Hansen, Per Christian
    Tech Univ Denmark, Denmark.
    UNMATCHED PROJECTOR/BACKPROJECTOR PAIRS: PERTURBATION AND CONVERGENCE ANALYSIS2018Inngår i: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 40, nr 1, s. A573-A591Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In tomographic reconstruction problems it is not uncommon that there are errors in the implementation of the forward projector and/or the backprojector, and hence we encounter a so-called unmatched projektor/backprojector pair. Consequently, the matrices that represent the two projectors are not each others transpose. Surprisingly, the influence of such errors in algebraic iterative reconstruction methods has received little attention in the literature. The goal of this paper is to perform a rigorous first-order perturbation analysis of the minimization problems underlying the algebraic methods in order to understand the role played by the nonmatch of the matrices. We also study the convergence properties of linear stationary iterations based on unmatched matrix pairs, leading to insight into the behavior of some important row-and column-oriented algebraic iterative methods. We conclude with numerical examples that illustrate the perturbation and convergence results.

  • 127. Eliasson, Peter
    et al.
    Eriksson, Sofia
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    The influence of weak and strong solid wall boundary conditions on the convergence to steady-state of the Navier-Stokes equations2009Inngår i: Proc. 19th AIAA CFD Conference, AIAA , 2009Konferansepaper (Fagfellevurdert)
  • 128.
    Eliasson, Peter
    et al.
    Department of Aeronautics and Autonomous Systems, FOI, Swedish Defense Research Agency, SE-164 90, Stockholm, Sweden .
    Kupiainen, Marco
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Higher Order Accurate Solutions for Flow in a Cavity: Experiences and Lessons Learned2015Inngår i: Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014 / [ed] Mejdi Azaïez, Henda El Fekih, Jan S. Hesthaven, Springer, 2015, s. 189-196Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    Experiences from using a higher order accurate finite difference multiblock solver to compute the time dependent flow over a cavity is summarized. The work has been carried out as part of a work in a European project called IDIHOM in a collaboration between the Swedish Defense Research Agency (FOI) and University of Linköping (LiU). The higher order code is based on Summation By Parts operators combined with the Simultaneous Approximation Term approach for boundary and interface conditions. The spatial accuracy of the code is verified by calculations over a cyclinder by monitoring the decay of the errors of known wall quantities as the grid is refined. The focus is on the validation for a test case of transonic flow over a rectangular cavity with hybrid RANS/LES calculations. The results are compared to reference numerical results from a second order finite volume code as well as with experimental results with a good overall agreement between the results.

    Fulltekst (pdf)
    Higher Order Accurate Solutions for Flow in a Cavity: Experiences and Lessons Learned
  • 129.
    Eliasson, Peter
    et al.
    FOI, Swedish Defence Research Agency, SE-16490 Stockholm, Sweden.
    Lundquist, Tomas
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    A global time integration approach for realistic unsteady flow computations2016Konferansepaper (Fagfellevurdert)
    Abstract [en]

    A novel time integration approach is explored for unsteady flow computations. It is a multi-block formulation in time where one solves for all time levels within a block simultaneously. The time discretization within a block is based on the summation-by-parts (SBP) technique in time combined with the simultaneous-approximation-term (SAT) technique for imposing the initial condition. The approach is implicit, unconditionally stable and can be made high order accurate in time. The implicit system is solved by a dual time stepping technique. The technique has been implemented in a flow solver for unstructured grids and applied to an unsteady flow problem with vortex shedding over a cylinder. Four time integration approaches being 2nd to 5th order accurate in time are evaluated and compared to the conventional 2nd order backward difference (BDF2) method and a 4th order diagonally implicit Runge-Kutta scheme (ESDIRK64). The obtained orders of accuracy are higher than expected and correspond to the accuracy in the interior of the blocks, up to 8th order accuracy is obtained. The influence on the accuracy from the size of the time blocks is small. Smaller blocks are computationally more efficient though, and the efficiency increases with increased accuracy of the SBP operator and reduced size of time steps. The most accurate scheme, with a small time step and block size, is approximately as efficient as the ESDIRK64 scheme. There is a significant potential for improvements ranging from convergence acceleration techniques in dual time, alternative initialization of time blocks, and by introducing smaller time blocks based on alternative SBP operators.

    Fulltekst (pdf)
    A global time integration approach for realistic unsteady flow computations
  • 130.
    Eliasson, Peter
    et al.
    Swedish Defence Research Agency (FOI), Stockholm, Sweden.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    The Influence of Viscous Operator and Wall Boundary Conditions on the Accuracy of the Navier-Stokes Equations2013Inngår i: AIAA Aerospace Sciences - Fluid Sciences Event, 2013, s. 1-15Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    The discretization of the viscous operator in an edge-based flow solver for unstructured grids has been investigated. A compact discretization of the Laplace and thin-layer operators in the viscous terms is used with two different wall boundary conditions. Furthermore, a wide discretization of the same operators is investigated. The resulting numerical operators are all formally second order accurate in space; the wide operator has higher truncation errors. The operators are implemented weakly using a penalty formulation and are shown to be stable for a scalar model problem with given constraints on the penalty coefficients. The different operators are applied to a set of grid convergence test cases for laminar flow in two dimensions up to a large-scale three dimensional turbulent flow problem. The operators converge to the same solutions as the grids are refined with one exception where the wide operator converges to a solution with higher drag. The 2nd compact discretization, being locally more accurate at a wall boundary than the original 1st compact operator, reduces the grid dependency somewhat for most test cases. The wide operator performs very well and leads for most test cases to results with minimum spread between coarsest and finest grids. For one test case though, the wide operator has a negative influence on the steady state convergence.

    Fulltekst (pdf)
    fulltext
  • 131. Eliasson, Peter
    et al.
    Weinerfelt, Per
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Application of a line-implicit scheme on stretched unstructured grids2009Inngår i: Proc. 47th AIAA Aerospace Sciences Meeting, AIAA , 2009Konferansepaper (Annet vitenskapelig)
  • 132.
    Erickson, Brittany. A.
    et al.
    Department of Geological Science, San Diego State University, 5500 Campanile Drive, San Diego, California, 92182-1020..
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    Stable, High Order Accurate Adaptive Schemes for Long Time, Highly Intermittent Geophysics Problems2013Rapport (Annet vitenskapelig)
    Abstract [en]

    Many geophysical phenomena are characterized by properties that evolve over a wide range of scales which introduce difficulties when attempting to model these features in one computational method. We have developed a high-order finite difference method for the elastic wave equation that is able to efficiently handle varying temporal scales in a single, stand-alone framework. We apply this method to earthquake cycle models characterized by extremely long interseismic periods interspersed with abrupt, short periods of dynamic rupture. Through the use of summation-by-parts operators and weak enforcement of boundary conditions we derive a provably stable discretization. Time stepping is achieved through the implicit θ-method which allows us to take large time steps during the intermittent period between earthquakes and adapts appropriately to fully resolve rupture.

    Fulltekst (pdf)
    Stable, High Order Accurate Adaptive Schemes for Long Time, Highly Intermittent Geophysics Problem
  • 133.
    Erickson, Brittany A.
    et al.
    Department of Geological Sciences, San Diego State University, San Diego, CA 92182-1020, USA.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    Stable, high order accurate adaptive schemes for long time, highly intermittent geophysics problems2014Inngår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 271, s. 328-338Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Many geophysical phenomena are characterized by properties that evolve over a wide range of scales which introduce difficulties when attempting to model these features in one computational method. We have developed a high-order finite difference method for the elastic wave equation that is able to efficiently handle varying temporal and spatial scales in a single, stand-alone framework. We apply this method to earthquake cycle models characterized by extremely long interseismic periods interspersed with abrupt, short periods of dynamic rupture. Through the use of summation-by-parts operators and weak enforcement of boundary conditions we derive a provably stable discretization. Time stepping is achieved through the implicit θθ-method which allows us to take large time steps during the intermittent period between earthquakes and adapts appropriately to fully resolve rupture.

    Fulltekst (pdf)
    Stable, high order accurate adaptive schemes for long time, highly intermittent geophysics problems
  • 134.
    Eriksson, Sofia
    Uppsala universitet, Avdelningen för beräkningsvetenskap.
    Stable Numerical Methods with Boundary and Interface Treatment for Applications in Aerodynamics2012Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    In numerical simulations, problems stemming from aerodynamics pose many challenges for the method used. Some of these are addressed in this thesis, such as the fluid interacting with objects, the presence of shocks, and various types of boundary conditions.

    Scenarios of the kind mentioned above are described mathematically by initial boundary value problems (IBVPs). We discretize the IBVPs using high order accurate finite difference schemes on summation by parts form (SBP), combined with weakly imposed boundary conditions, a technique called simultaneous approximation term (SAT). By using the energy method, stability can be shown.

    The weak implementation is compared to the more commonly used strong implementation, and it is shown that the weak technique enhances the rate of convergence to steady state for problems with solid wall boundary conditions. The analysis is carried out for a linear problem and supported numerically by simulations of the fully non-linear Navier–Stokes equations.

    Another aspect of the boundary treatment is observed for fluid structure interaction problems. When exposed to eigenfrequencies, the coupled system starts oscillating, a phenomenon called flutter. We show that the strong implementation sometimes cause instabilities that can be mistaken for flutter.

    Most numerical schemes dealing with flows including shocks are first order accurate to avoid spurious oscillations in the solution. By modifying the SBP-SAT technique, a conservative and energy stable scheme is derived where the order of accuracy can be lowered locally. The new scheme is coupled to a shock-capturing scheme and it retains the high accuracy in smooth regions.

    For problems with complicated geometry, one strategy is to couple the finite difference method to the finite volume method. We analyze the accuracy of the latter on unstructured grids. For grids of bad quality the truncation error can be of zeroth order, indicating that the method is inconsistent, but we show that some of the accuracy is recovered.

    We also consider artificial boundary closures on unbounded domains. Non-reflecting boundary conditions for an incompletely parabolic problem are derived, and it is shown that they yield well-posedness. The SBP-SAT methodology is employed, and we prove that the discretized problem is stable.

  • 135.
    Eriksson, Sofia
    et al.
    Department of Information Technology, Scientific Computing, Uppsala University, SE-751 05 Uppsala, Sweden.
    Abbas, Qaisar
    Department of Information Technology, Scientific Computing, Uppsala University, SE-751 05 Uppsala, Sweden.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap. Linköpings universitet, Tekniska högskolan.
    A stable and conservative method for locally adapting the design order of finite difference schemes2011Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, nr 11, s. 4216-4231Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A procedure to locally change the order of accuracy of finite difference schemes is developed. The development is based on existing Summation-By-Parts operators and a weak interface treatment. The resulting scheme is proven to be accurate and stable.

     

    Numerical experiments verify the theoretical accuracy for smooth solutions. In addition, shock calculations are performed, using a scheme where the developed switching procedure is combined with the MUSCL technique.

    Fulltekst (pdf)
    fulltext
  • 136.
    Eriksson, Sofia
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Abbas, Qaisar
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    A Stable and Conservative Method of Locally Adapting the Design Order of Finite Difference Schemes2010Inngår i: Proc. 7th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2010, s. 20:1-9Konferansepaper (Annet vitenskapelig)
    Fulltekst (pdf)
    fulltext
  • 137.
    Eriksson, Sofia
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Law, Craig
    Gong, Jing
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Shock Calculations using a Very High Order Accurate Euler and Navier-Stokes Solver2008Inngår i: Proc. 6th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2008, s. 63-73Konferansepaper (Annet vitenskapelig)
  • 138.
    Eriksson, Sofia
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Analysis of mesh and boundary effects on the accuracy of node-centered finite volume schemes2009Inngår i: Proc. 19th AIAA CFD Conference, AIAA , 2009Konferansepaper (Fagfellevurdert)
  • 139.
    Eriksson, Sofia
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Analysis of the order of accuracy for node-centered finite volume schemes2009Rapport (Annet vitenskapelig)
  • 140.
    Eriksson, Sofia
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Analysis of the order of accuracy for node-centered finite volume schemes2009Inngår i: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 59, nr 10, s. 2659-2676Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The order of accuracy of the node-centered finite volume methods is analyzed, and the analysis is based on an exact derivation of the numerical errors in one dimension. The accuracy for various types of grids are considered. Numerical simulations and analysis are performed for both a hyperbolic and a elliptic case, and the results agree. The impact of weakly imposed boundary conditions is analyzed and verified numerically. We show that the error contribution from the primal and dual grid can be treated separately.

    Fulltekst (pdf)
    fulltext
  • 141.
    Eriksson, Sofia
    et al.
    Department of Mathematics, Technische Universität Darmstadt, 64293 Darmstadt, Germany.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Exact Non-reflecting Boundary Conditions Revisited: Well-Posedness and Stability2017Inngår i: Foundations of Computational Mathematics, ISSN 1615-3375, E-ISSN 1615-3383, Vol. 17, nr 4, s. 957-986Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Exact non-reflecting boundary conditions for a linear incompletely parabolic system in one dimension have been studied. The system is a model for the linearized compressible Navier-Stokes equations, but is less complicated which allows for a detailed analysis without approximations. It is shown that well-posedness is a fundamental property of the exact non-reflecting boundary conditions. By using summation by parts operators for the numerical approximation and a weak boundary implementation, it is also shown that energy stability follows automatically.

    Fulltekst (pdf)
    Exact Non-reflecting Boundary Conditions Revisited: Well-Posedness and Stability
  • 142.
    Eriksson, Sofia
    et al.
    Department of Information Technology, Uppsala University, Uppsala, Sweden.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    Well-posedness and Stability of Exact Non-reflecting Boundary Conditions2013Inngår i: AIAA Aerospace Sciences - Fluid Sciences Event, 2013, s. 1-18Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    Exact non-reflecting boundary conditions for an incompletely parabolic system have been studied. It is shown that well-posedness is a fundamental property of the non-reflecting boundary conditions. By using summation by parts operators for the numerical approximation and a weak boundary implementation, energy stability follows automatically. The stability in combination with the high order accuracy results in a reliable, efficient and accurate method. The theory is supported by numerical simulations.

    Fulltekst (pdf)
    fulltext
  • 143.
    Eriksson, Sofia
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Svärd, Magnus
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Simulations of Ground Effects on Wake Vortices at Runways2007Rapport (Annet vitenskapelig)
  • 144.
    Eriksson, Sofia
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Svärd, Magnus
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Simulations of Ground Effects on Wake Vortices at Runways2008Inngår i: Proc. 6th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2008, s. 101-108Konferansepaper (Fagfellevurdert)
  • 145.
    Eriksson, T.
    et al.
    Linköpings universitet, Institutionen för systemteknik. Linköpings universitet, Tekniska högskolan.
    Körner, J.
    Bell Laboratories, Murray Hill, USA / Mathematical Institute of the Hungari an Academy of Sciences, Budapest, Hungary.
    Successive Encoding of Correlated Sources1982Rapport (Annet vitenskapelig)
    Abstract [en]

    The encoding of a discrete memoryless multiple source  for reconstruction of a sequence  with  is considered. We require that the encoding should be such that  is encoded first without any consideration of  , while in a seeond part of the encoding this latter sequence is encoded based on knowledge of the outcome of the first encoding. The resulting scheme is called successive encoding. We find general outer and inner bounds for the corresponding set of achievable rates along with a complete single letter characterization for the special case  . Comparisons with the Slepian-Wolf problem [3] and the Ahlswede-Körner-Wyner side information problem [2 ], [9) are carried out.

    Fulltekst (pdf)
    Successive Encoding of Correlated Sources
  • 146.
    Erlander, Sven
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Cost-Minimizing Choice Behavior in Transportation Planning: A Theoretical Framework fo Logit Models2010Bok (Annet vitenskapelig)
    Abstract [en]

    This book stems from a desire to understand the underlying assumptions and structureof the choice probability models most often used in transportation planning. The bookinvestigates how far a new way of defining cost minimizing behavior can take us. Allcommonly used choice probability distributions of the logit type – log linear probabilityfunctions – follow from cost minimizing behavior defined in the new way; some newnested models also appear. The new approach provides a deeper understanding of whatis at work in the models. The new way of defining cost minimizing behavior is as follows:cost minimizing behavior pertains if the likelihood (probability) of any independentsample of observations is a decreasing function of the average cost of the sample.Extreme value distributed random variables are not used in the derivation of models. Ameasure of freedom of choice related to the Shannon measure of how much "choice" isinvolved is used to obtain a welfare measure which is equal to composite cost.... more on http://springer.com/978-3-642-11910-1

  • 147.
    Ernestus, Maximilian
    et al.
    TU Braunschweig, Germany.
    Friedrichs, Stephan
    Max Planck Institute Informat, Germany; Saarbrucken Grad School Comp Science, Germany.
    Hemmer, Michael
    TU Braunschweig, Germany.
    Kokemueller, Jan
    TU Braunschweig, Germany.
    Kroeller, Alexander
    TU Braunschweig, Germany.
    Moeini, Mahdi
    Technical University of Kaiserslautern, Germany.
    Schmidt, Christiane
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten.
    Algorithms for art gallery illumination2017Inngår i: Journal of Global Optimization, ISSN 0925-5001, E-ISSN 1573-2916, Vol. 68, nr 1, s. 23-45Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The art gallery problem (AGP) is one of the classical problems in computational geometry. It asks for the minimum number of guards required to achieve visibility coverage of a given polygon. The AGP is well-known to be NP-hard even in restricted cases. In this paper, we consider the AGP with fading (AGPF): A polygonal region is to be illuminated with light sources such that every point is illuminated with at least a global threshold, light intensity decreases over distance, and we seek to minimize the total energy consumption. Choosing fading exponents of zero, one, and two are equivalent to the AGP, laser scanner applications, and natural light, respectively. We present complexity results as well as a negative solvability result. Still, we propose two practical algorithms for AGPF with fixed light positions (e.g. vertex guards) independent of the fading exponent, which we demonstrate to work well in practice. One is based on a discrete approximation, the other on non-linear programming by means of simplex-partitioning strategies. The former approach yields a fully polynomial-time approximation scheme for the AGPF with fixed light positions. The latter approach obtains better results in our experimental evaluation.

    Fulltekst (pdf)
    fulltext
  • 148.
    Evarest, Emanuel
    et al.
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Berntsson, Fredrik
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska fakulteten.
    Singull, Martin
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Charles, Wilson M.
    Department od Mathematics, University of Dar el Salaam, Tanzania.
    Regime Switching models on Temperature Dynamics2017Inngår i: International Journal of Applied Mathematics and Statistics, ISSN 0973-1377, E-ISSN 0973-7545, Vol. 56, nr 2Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Two regime switching models for predicting temperature dynamics are presented in this study for the purpose to be used for weather derivatives pricing. One is an existing model in the literature (Elias model) and the other is presented in this paper. The new model we propose in this study has a mean reverting heteroskedastic process in the base regime and a Brownian motion in the shifted regime. The parameter estimation of the two models is done by the use expectation-maximization (EM) method using historical temperature data. The performance of the two models on prediction of temperature dynamics is compared using historical daily average temperature data from five weather stations across Sweden. The comparison is based on the heating degree days (HDDs), cooling degree days (CDDs) and cumulative average temperature (CAT) indices. The expected HDDs, CDDs and CAT of the models are compared to the true indices from the real data. Results from the expected HDDs, CDDs and CAT together with their corresponding daily average plots demonstrate that, our model captures temperature dynamics relatively better than Elias model.

  • 149. Bestill onlineKjøp publikasjonen >>
    Evarest Sinkwembe, Emanuel
    Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska fakulteten.
    Modelling Weather Dynamics for Weather Derivatives Pricing2017Licentiatavhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This thesis focuses on developing an appropriate stochastic model for temperature dynamics as a means of pricing weather derivative contracts based on temperature. There are various methods for pricing weather derivatives ranging from simple one like historical burn analysis, which does not involve modeling the underlying weather variable to complex ones that require Monte Carlo simulations to achieve explicit weather derivatives contract prices, particularly the daily average temperature (DAT) dynamics models. Among various DAT models, appropriate regime switching models are considered relative better than single regime models due to its ability to capture most of the temperature dynamics features caused by urbanization, deforestation, clear skies and changes of measurement station. A new proposed model for DAT dynamics, is a two regime switching models with heteroskedastic mean-reverting process in the base regime and Brownian motion with nonzero drift in the shifted regime. Before using the model for pricing temperature derivative contracts, we compare the performance of the model with a benchmark model proposed by Elias et al. (2014), interms of the HDDs, CDDs and CAT indices. Using ve data sets from dierent measurement locations in Sweden, the results shows that, a two regime switching models with heteroskedastic mean-reverting process gives relatively better results than the model given by Elias et al. We develop mathematical expressions for pricing futures and option contracts on HDDs, CDDs and CAT indices. The local volatility nature of the model in the base regime captures very well the dynamics of the underlying process, thus leading to a better pricing processes for temperature derivatives contracts written on various index variables. We use the Monte Carlo simulation method for pricing weather derivatives call option contracts.

    Delarbeid
    1. Regime Switching models on Temperature Dynamics
    Åpne denne publikasjonen i ny fane eller vindu >>Regime Switching models on Temperature Dynamics
    2017 (engelsk)Inngår i: International Journal of Applied Mathematics and Statistics, ISSN 0973-1377, E-ISSN 0973-7545, Vol. 56, nr 2Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    Two regime switching models for predicting temperature dynamics are presented in this study for the purpose to be used for weather derivatives pricing. One is an existing model in the literature (Elias model) and the other is presented in this paper. The new model we propose in this study has a mean reverting heteroskedastic process in the base regime and a Brownian motion in the shifted regime. The parameter estimation of the two models is done by the use expectation-maximization (EM) method using historical temperature data. The performance of the two models on prediction of temperature dynamics is compared using historical daily average temperature data from five weather stations across Sweden. The comparison is based on the heating degree days (HDDs), cooling degree days (CDDs) and cumulative average temperature (CAT) indices. The expected HDDs, CDDs and CAT of the models are compared to the true indices from the real data. Results from the expected HDDs, CDDs and CAT together with their corresponding daily average plots demonstrate that, our model captures temperature dynamics relatively better than Elias model.

    Emneord
    Weather derivatives, Regime switching, temperature dynamics, expectationmaximization, temperature indices
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-135541 (URN)
    Tilgjengelig fra: 2017-03-22 Laget: 2017-03-22 Sist oppdatert: 2017-11-29
    Fulltekst (pdf)
    Modelling Weather Dynamics for Weather Derivatives Pricing
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    presentationsbild
  • 150. Fagerlund, Martin
    et al.
    Merkel, Magnus
    Linköpings universitet, Institutionen för datavetenskap, NLPLAB - Laboratoriet för databehandling av naturligt språk. Linköpings universitet, Tekniska högskolan.
    Eldén, Lars
    Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap. Linköpings universitet, Tekniska högskolan.
    Ahrenberg, Lars
    Linköpings universitet, Institutionen för datavetenskap, NLPLAB - Laboratoriet för databehandling av naturligt språk. Linköpings universitet, Tekniska högskolan.
    Computing Word Senses by Semantic Mirroring and Spectral Graph Partitioning2010Inngår i: Proceedings of TextGraphs-5 - 2010 Workshop on Graph-based Methods for Natural Language Processing / [ed] Carmen Banea, Alessandro Moschitti, Swapna Somasundaran and Fabio Massimo Zanzotto, Stroudsburg, PA, USA: The Association for Computational Linguistics , 2010, s. 103-107Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Using the technique of ”semantic mirroring”a graph is obtained that representswords and their translations from a parallelcorpus or a bilingual lexicon. The connectednessof the graph holds informationabout the different meanings of words thatoccur in the translations. Spectral graphtheory is used to partition the graph, whichleads to a grouping of the words accordingto different senses. We also report resultsfrom an evaluation using a small sample ofseed words from a lexicon of Swedish andEnglish adjectives.

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