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  • 1. Abarbanel, Saul
    et al.
    Ditkowski, Adi
    Gustafsson, Bertil
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    On error bounds of finite difference approximations to partial differential equations: Temporal behavior and rate of convergence2000In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 15, p. 79-116Article in journal (Refereed)
  • 2. Almquist, Martin
    et al.
    Karasalo, Ilkka
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL.
    Mattsson, Ken
    Atmospheric Sound Propagation Over Large-Scale Irregular Terrain2014In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 61, no 2, p. 369-397Article in journal (Refereed)
    Abstract [en]

    A benchmark problem on atmospheric sound propagation over irregular terrain has been solved using a stable fourth-order accurate finite difference approximation of a high-fidelity acoustic model. A comparison with the parabolic equation method and ray tracing methods is made. The results show that ray tracing methods can potentially be unreliable in the presence of irregular terrain.

  • 3.
    Almquist, Martin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Karasalo, Ilkka
    Mattsson, Ken
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Atmospheric sound propagation over large-scale irregular terrain2014In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 61, p. 369-397Article in journal (Refereed)
  • 4. Birken, Philipp
    et al.
    Bull, Jonathan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Jameson, Antony
    Preconditioned smoothers for the Full Approximation Scheme for the RANS equations2019In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 78, p. 995-1022Article in journal (Refereed)
  • 5.
    Bohm, Marvin
    et al.
    University of Cologne, Cologne, Germany.
    Schermeng, Sven
    University of Cologne, Cologne, Germany.
    Winters, Andrew Ross
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Gassner, Gregor J
    University of Cologne, Cologne, Germany.
    Jacobs, Gustaaf B
    San Diego State University, San Diego, USA.
    Multi-element SIAC Filter for Shock Capturing Applied to High-Order Discontinuous Galerkin Spectral Element Methods2019In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, ISSN 0885-7474, Vol. 81, no 2, p. 820-844Article in journal (Refereed)
    Abstract [en]

    We build a multi-element variant of the smoothness increasing accuracy conserving (SIAC) shock capturing technique proposed for single element spectral methods by Wissink et al. (J Sci Comput 77:579–596, 2018). In particular, the baseline scheme of our method is the nodal discontinuous Galerkin spectral element method (DGSEM) for approximating the solution of systems of conservation laws. It is well known that high-order methods generate spurious oscillations near discontinuities which can develop in the solution for nonlinear problems, even when the initial data is smooth. We propose a novel multi-element SIAC filtering technique applied to the DGSEM as a shock capturing method. We design the SIAC filtering such that the numerical scheme remains high-order accurate and that the shock capturing is applied adaptively throughout the domain. The shock capturing method is derived for general systems of conservation laws. We apply the novel SIAC filter to the two-dimensional Euler and ideal magnetohydrodynamics equations to several standard test problems with a variety of boundary conditions.

  • 6.
    Brandén, Henrik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Holmgren, Sverker
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Convergence acceleration for hyperbolic systems using semicirculant approximations1999In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 14, p. 357-393Article in journal (Refereed)
  • 7.
    Brandén, Henrik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Holmgren, Sverker
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Sundqvist, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Discrete fundamental solution preconditioning for hyperbolic systems of PDE2007In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 30, p. 35-60Article in journal (Refereed)
  • 8. Brüger, Arnim
    et al.
    Nilsson, Jonas
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Kress, Wendy
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    A Compact Higher Order Finite Difference Method for the Incompressible Navier-Stokes Equations2002In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 17, p. 551-560Article in journal (Refereed)
  • 9.
    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 Operators2010In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 45, no 1-3, p. 118-150Article in journal (Refereed)
    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.

  • 10. Carpenter, Mark H.
    et al.
    Nordström, Jan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering.
    Gottlieb, David
    Revisiting and Extending Interface Penalties for Multi-domain Summation-by-Parts Operators2010In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 45, no 1-3, p. 118-150Article in journal (Refereed)
    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 pa parts per thousand yen2. 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.

  • 11. Carpenter, Mark H.
    et al.
    Nordström, Jan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Gottlieb, David
    Revisiting and Extending Interface Penalties for Multidomain Summation-by-Parts Operators2010In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 45, p. 118-150Article in journal (Refereed)
  • 12. Celledoni, Elena
    et al.
    Kingsley Kometa, Bawfeh
    Verdier, Olivier
    Institutt for matematiske fag, NTNU, Trondheim, Norway.
    High order semi-Lagrangian methods for the incompressible Navier–Stokes equations2016In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 66, no 1, p. 91-115Article in journal (Refereed)
    Abstract [en]

    We propose a class of semi-Lagrangian methods of high approximation order in space and time, based on spectral element space discretizations and exponential integrators of Runge–Kutta type. The methods were presented in Celledoni and Kometa (J Sci Comput 41(1):139–164, 2009) for simpler convection–diffusion equations. We discuss the extension of these methods to the Navier–Stokes equations, and their implementation using projections. Semi-Lagrangian methods up to order three are implemented and tested on various examples. The good performance of the methods for convection-dominated problems is demonstrated with numerical experiments.

  • 13. Chen, Minghua
    et al.
    Deng, Weihua
    Serra-Capizzano, Stefano
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Uniform convergence of V-cycle multigrid algorithms for two-dimensional fractional Feynman–Kac equation2018In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 74, p. 1034-1059Article in journal (Refereed)
  • 14.
    Duru, Kenneth
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Kreiss, Gunilla
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    On the accuracy and stability of the perfectly matched layer in transient waveguides2012In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 53, p. 642-671Article in journal (Refereed)
  • 15.
    Edelvik, Fredrik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Ledfelt, Gunnar
    Explicit Hybrid Time Domain Solver for the Maxwell Equations in 3D2000In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 15, p. 61-78Article in journal (Refereed)
  • 16.
    Eliasson, Bengt
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Astronomy and Space Physics.
    Outflow boundary conditions for the Fourier transformed one-dimensional Vlasov–Poisson system2001In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 16, p. 1-28Article in journal (Refereed)
  • 17.
    Erickson, Brittany A.
    et al.
    Department of Computer and Information Science 1202, University of Oregon, Eugene, USA / Department of Earth Science 1272 University of Oregon, Eugene, USA.
    O’Reilly, Ossian
    Southern California Earthquake Center, University of Southern California, Los Angeles, USA.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Accuracy of Stable, High-order Finite Difference Methods for Hyperbolic Systems with Non-smooth Wave Speeds2019In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 81, p. 2356-2387Article in journal (Refereed)
    Abstract [en]

    We derive analytic solutions to the scalar and vector advection equation with variable coefficients in one spatial dimension using Laplace transform methods. These solutions are used to investigate how accuracy and stability are influenced by the presence of discontinuous wave speeds when applying high-order-accurate, skew-symmetric finite difference methods designed for smooth wave speeds. The methods satisfy a summation-by-parts rule with weak enforcement of boundary conditions and formal order of accuracy equal to 2, 3, 4 and 5. We study accuracy, stability and convergence rates for linear wave speeds that are (a) constant, (b) non-constant but smooth, (c) continuous with a discontinuous derivative, and (d) constant with a jump discontinuity. Cases (a) and (b) correspond to smooth wave speeds and yield stable schemes and theoretical convergence rates. Non-smooth wave speeds [cases (c) and (d)], however, reveal reductions in theoretical convergence rates and in the latter case, the presence of an instability.

    The full text will be freely available from 2020-11-11 08:00
  • 18.
    Eriksson, Sofia
    Technische Universität Darmstadt, Germany.
    A Dual Consistent Finite Difference Method with Narrow Stencil Second Derivative Operators2018In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 75, no 2, p. 906-940Article in journal (Refereed)
    Abstract [en]

    We study the numerical solutions of time-dependent systems of partial differential equations, focusing on the implementation of boundary conditions. The numerical method considered is a finite difference scheme constructed by high order summation by parts operators, combined with a boundary procedure using penalties (SBP-SAT). Recently it was shown that SBP-SAT finite difference methods can yield superconvergent functional output if the boundary conditions are imposed such that the discretization is dual consistent. We generalize these results so that they include a broader range of boundary conditions and penalty parameters. The results are also generalized to hold for narrow-stencil second derivative operators. The derivations are supported by numerical experiments.

  • 19.
    Feng, Tao
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Gulliksson, Mårten
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Liu, W
    Institute of Mathematics and Statistics, University of Kent, Canterbury, CT2 7NF, United Kingdom.
    Adaptive finite element methods for the identification of elastic constants2006In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 26, no 2, p. 217-235Article in journal (Refereed)
    Abstract [en]

    In this paper, the elastic constants of a material are recovered from measured displacements where the model is the equilibrium equations for the orthotropic case. The finite element method is used for the discretization of the state equation and the Gauss–Newton method is used to solve the nonlinear least squares problem attained from the parameter estimation problem. A posteriori error estimators are derived and used to improve the accuracy by an appropriate mesh refinement. A numerical experiment is presented to show the applicability of the approach.

  • 20.
    Ferm, Lars
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Lötstedt, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Space-Time Adaptive Solution of First Order PDES2006In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 26, p. 83-110Article in journal (Refereed)
  • 21.
    Ferm, Lars
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Lötstedt, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Hellander, Andreas
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    A hierarchy of approximations of the master equation scaled by a size parameter2008In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 34, p. 127-151Article in journal (Refereed)
  • 22.
    Friedrich, Lucas
    et al.
    Mathematical Institute, University of Cologne, Cologne, Germany.
    Fernández, David C Del Rey
    Institute for Aerospace Studies, University of Toronto, Toronto, Canada.
    Winters, Andrew Ross
    Mathematical Institute, University of Cologne, Cologne, Germany.
    Gassner, Gregor J
    Mathematical Institute, University of Cologne, Cologne, Germany.
    Zingg, David W
    Institute for Aerospace Studies, University of Toronto, Toronto, Canada.
    Hicken, Jason
    Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, USA.
    Conservative and stable degree preserving SBP operators for non-conforming meshes2018In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 75, no 2, p. 657-686Article in journal (Refereed)
    Abstract [en]

    Non-conforming numerical approximations offer increased flexibility for applications that require high resolution in a localized area of the computational domain or near complex geometries. Two key properties for non-conforming methods to be applicable to real world applications are conservation and energy stability. The summation-by-parts (SBP) property, which certain finite-difference and discontinuous Galerkin methods have, finds success for the numerical approximation of hyperbolic conservation laws, because the proofs of energy stability and conservation can discretely mimic the continuous analysis of partial differential equations. In addition, SBP methods can be developed with high-order accuracy, which is useful for simulations that contain multiple spatial and temporal scales. However, existing non-conforming SBP schemes result in a reduction of the overall degree of the scheme, which leads to a reduction in the order of the solution error. This loss of degree is due to the particular interface coupling through a simultaneous-approximation-term (SAT). We present in this work a novel class of SBP-SAT operators that maintain conservation, energy stability, and have no loss of the degree of the scheme for non-conforming approximations. The new degree preserving discretizations require an ansatz that the norm matrix of the SBP operator is of a degree ≥ 2p, in contrast to, for example, existing finite difference SBP operators, where the norm matrix is 2p − 1 accurate. We demonstrate the fundamental properties of the new scheme with rigorous mathematical analysis as well as numerical verification.

  • 23.
    Friedrich, Lucas
    et al.
    Mathematical Institute, University of Cologne, Cologne, Germany.
    Schnücke, Gero
    Mathematical Institute, University of Cologne, Cologne, Germany.
    Winters, Andrew Ross
    Mathematical Institute, University of Cologne, Cologne, Germany.
    Fernández, David C Del Rey
    National Institute of Aerospace and Computational Aero, Sciences Branch, NASA Langley Research Center, Hampton, USA.
    Gassner, Gregor J
    Mathematical Institute, University of Cologne, Cologne, Germany.
    Carpenter, Mark H
    Computational Aero, Sciences Branch, NASA Langley Research Center, Hampton, USA.
    Entropy Stable Space-Time Discontinuous Galerkin Schemes with Summation-by-Parts Property for Hyperbolic Conservation Laws2019In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 80, no 1, p. 175-222Article in journal (Refereed)
    Abstract [en]

    This work examines the development of an entropy conservative (for smooth solutions) or entropy stable (for discontinuous solutions) space-time discontinuous Galerkin (DG) method for systems of nonlinear hyperbolic conservation laws. The resulting numerical scheme is fully discrete and provides a bound on the mathematical entropy at any time according to its initial condition and boundary conditions. The crux of the method is that discrete derivative approximations in space and time are summation-by-parts (SBP) operators. This allows the discrete method to mimic results from the continuous entropy analysis and ensures that the complete numerical scheme obeys the second law of thermodynamics. Importantly, the novel method described herein does not assume any exactness of quadrature in the variational forms that naturally arise in the context of DG methods. Typically, the development of entropy stable schemes is done on the semidiscrete level ignoring the temporal dependence. In this work, we demonstrate that creating an entropy stable DG method in time is similar to the spatial discrete entropy analysis, but there are important (and subtle) differences. Therefore, we highlight the temporal entropy analysis throughout this work. For the compressible Euler equations, the preservation of kinetic energy is of interest besides entropy stability. The construction of kinetic energy preserving (KEP) schemes is, again, typically done on the semidiscrete level similar to the construction of entropy stable schemes. We present a generalization of the KEP condition from Jameson to the space-time framework and provide the temporal components for both entropy stability and kinetic energy preservation. The properties of the space-time DG method derived herein are validated through numerical tests for the compressible Euler equations. Additionally, we provide, in appendices, how to construct the temporal entropy stable components for the shallow water or ideal magnetohydrodynamic (MHD) equations.

    The full text will be freely available from 2020-03-15 08:00
  • 24.
    Friedrich, Lucas
    et al.
    Mathematical Institute, University of Cologne, Cologne, Germany.
    Winters, Andrew Ross
    Mathematical Institute, University of Cologne, Cologne, Germany.
    Fernández, David C Del Rey
    National Institute of Aerospace and Computational Aero, Sciences Branch, NASA Langley Research Center, Hampton, USA.
    Gassner, Gregor J
    Mathematical Institute, University of Cologne, Cologne, Germany.
    Parsani, Matteo
    King Abdullah University of Science and Technology (KAUST), Computer Electrical and Mathematical Science and Engineering Division (CEMSE), Extreme Computing Research Center (ECRC), Thuwal, Saudi Arabia.
    Carpenter, Mark H
    Computational Aero, Sciences Branch, NASA Langley Research Center, Hampton, USANASA Langley Research Center.
    An Entropy Stable h/p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property2018In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 77, no 2, p. 689-725Article in journal (Refereed)
    Abstract [en]

    This work presents an entropy stable discontinuous Galerkin (DG) spectral element approximation for systems of non-linear conservation laws with general geometric (h) and polynomial order (p) non-conforming rectangular meshes. The crux of the proofs presented is that the nodal DG method is constructed with the collocated Legendre–Gauss–Lobatto nodes. This choice ensures that the derivative/mass matrix pair is a summation-by-parts (SBP) operator such that entropy stability proofs from the continuous analysis are discretely mimicked. Special attention is given to the coupling between non-conforming elements as we demonstrate that the standard mortar approach for DG methods does not guarantee entropy stability for non-linear problems, which can lead to instabilities. As such, we describe a precise procedure and modify the mortar method to guarantee entropy stability for general non-linear hyperbolic systems on h / p non-conforming meshes. We verify the high-order accuracy and the entropy conservation/stability of fully non-conforming approximation with numerical examples.

  • 25.
    Gassner, Gregor J
    et al.
    Mathematical Institute, University of Cologne, Cologne, Germany.
    Winters, Andrew Ross
    Mathematical Institute, University of Cologne, Cologne, Germany.
    Hindenlang, Florian J
    Max Planck Institute for Plasma Physics, Garching, Germany.
    Kopriva, David A
    Department of Mathematics, The Florida State UniversityTallahassee, USA.
    The BR1 scheme is stable for the compressible Navier–Stokes equations2018In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 77, no 1, p. 154-200Article in journal (Refereed)
    Abstract [en]

    We show how to modify the original Bassi and Rebay scheme (BR1) [F. Bassi and S. Rebay, A High Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations, Journal of Computational Physics, 131:267–279, 1997] to get a provably stable discontinuous Galerkin collocation spectral element method (DGSEM) with Gauss-Lobatto (GL) nodes for the compressible Navier-Stokes equations (NSE) on three dimensional curvilinear meshes.

    Specifically, we show that the BR1 scheme can be provably stable if the metric identities are discretely satisfied, a two-point average for the metric terms is used for the contravariant fluxes in the volume, an entropy conserving split form is used for the advective volume integrals, the auxiliary gradients for the viscous terms are computed from gradients of entropy variables, and the BR1 scheme is used for the interface fluxes.

    Our analysis shows that even with three dimensional curvilinear grids, the BR1 fluxes do not add artificial dissipation at the interior element faces. Thus, the BR1 interface fluxes preserve the stability of the discretization of the advection terms and we get either energy stability or entropy-stability for the linear or nonlinear compressible NSE, respectively.

  • 26.
    Gustafsson, Bertil
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Saul Abarbanel; Half a century of scientific work2019In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 81, p. 1124-1135Article, review/survey (Refereed)
  • 27.
    Gustafsson, Bertil
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Unsymmetric hyperbolic systems and the Euler equations at low Mach numbers1987In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 2, p. 123-136Article in journal (Refereed)
  • 28.
    Gustafsson, Bertil
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Hemmingsson-Frändén, Lina
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    A fast domain decomposition high order Poisson solver1999In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 14, p. 223-243Article in journal (Refereed)
  • 29.
    Gustafsson, Bertil
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Hemmingsson-Frändén, Lina
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Deferred correction in space and time2002In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 17, p. 541-550Article in journal (Refereed)
  • 30.
    Gustafsson, Bertil
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Khalighi, Yaser
    The shifted box scheme for scalar transport problems2006In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 28, p. 319-335Article in journal (Refereed)
  • 31.
    Gustafsson, Bertil
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Nilsson, Jonas
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Boundary Conditions and Estimates for the Steady Stokes Equations on Staggered Grids2000In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 15, p. 29-59Article in journal (Refereed)
  • 32.
    Gustafsson, Bertil
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Olsson, Pelle
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    High-order centered difference methods with sharp shock resolution1996In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 11, p. 229-260Article in journal (Refereed)
  • 33.
    Gustafsson, Bertil
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Wahlund, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Time compact high order difference methods for wave propagation, 2D2005In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 25, p. 195-211Article in journal (Refereed)
  • 34. Heryudono, Alfa
    et al.
    Larsson, Elisabeth
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Ramage, Alison
    von Sydow, Lina
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Preconditioning for radial basis function partition of unity methods2016In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 67, p. 1089-1109Article in journal (Refereed)
  • 35.
    Holmström, Mats
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Waldén, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Adaptive wavelet methods for hyperbolic PDEs1998In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 13, p. 19-49Article in journal (Refereed)
  • 36.
    Hörnell, Karl
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Lötstedt, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Adaptive iteration to steady state of flow problems2004In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 20, p. 331-354Article in journal (Refereed)
  • 37.
    Kopriva, David A.
    et al.
    Department of Mathematics, The Florida State University.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Gassner, Gregor J.
    Mathematisches Institut, Universität zu Köln.
    Error Boundedness of Discontinuous Galerkin Spectral Element Approximations of Hyperbolic Problems2017In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 72, no 1, p. 314-330Article in journal (Refereed)
    Abstract [en]

    We examine the long time error behavior of discontinuous Galerkin spectral element approximations to hyperbolic equations. We show that the choice of numerical flux at interior element boundaries affects the growth rate and asymptotic value of the error. Using the upwind flux, the error reaches the asymptotic value faster, and to a lower value than a central flux gives, especially for low resolution computations. The differences in the error caused by the numerical flux choice decrease as the solution becomes better resolved.

  • 38.
    Kormann, Katharina
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science.
    Kronbichler, Martin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Müller, Bernhard
    Derivation of strictly stable high order difference approximations for variable-coefficient PDE2012In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 50, p. 167-197Article in journal (Refereed)
  • 39.
    Kozdon, Jeremy E.
    et al.
    Department of Geophysics, Stanford University.
    Dunham, Eric M.
    Department of Geophysics, Stanford University.
    Nordström, Jan
    Linköping University, Department of Mathematics, Scientific Computing. Linköping University, The Institute of Technology.
    Interaction of Waves with Frictional Interfaces Using Summation-by-Parts Difference Operators: Weak Enforcement of Nonlinear Boundary Conditions2012In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 50, no 2, p. 341-367Article in journal (Refereed)
    Abstract [en]

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

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

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

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

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

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

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

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

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

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

    extremely stiff, preventing efficient solution using explicit time integrators.

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

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

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

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

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

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

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

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

    and the accuracy of the energy balance.

  • 40.
    Kozdon, Jeremy E.
    et al.
    Department of Geophysics, Stanford University, USA.
    Dunham, Eric M.
    Department of Geophysics, Stanford University, USA.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    Simulation of Dynamic Earthquake Ruptures in Complex Geometries Using High-Order Finite Difference Methods2013In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 55, no 1, p. 92-124Article in journal (Refereed)
    Abstract [en]

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

  • 41.
    Kress, Wendy
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Gustafsson, Bertil
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Deferred Correction Methods for Initial Boundary Value Problems2002In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 17, p. 241-251Article in journal (Refereed)
  • 42.
    Kupiainen, Marco
    et al.
    Universitè Pierre et Marie Curie, Paris , France.
    Sjögreen, B.
    A Cartesian Embedded Boundary Method for the Compressible Navier-Stokes Equations2009In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, ISSN 0885-7474, Vol. 41, no 1, p. 94-117Article in journal (Refereed)
    Abstract [en]

    We here generalize the embedded boundary method that was developed for boundary discretizations of the wave equation in second order formulation in Kreiss et al. (SIAM J. Numer. Anal. 40(5):1940-1967, 2002) and for the Euler equations of compressible fluid flow in Sjogreen and Peterson (Commun. Comput. Phys. 2:1199-1219, 2007), to the compressible Navier-Stokes equations. We describe the method and we implement it on a parallel computer. The implementation is tested for accuracy and correctness. The ability of the embedded boundary technique to resolve boundary layers is investigated by computing skin-friction profiles along the surfaces of the embedded objects. The accuracy is assessed by comparing the computed skin-friction profiles with those obtained by a body fitted discretization.

  • 43.
    Ludvigsson, Gustav
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Steffen, Kyle R.
    Sticko, Simon
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Wang, Siyang
    Xia, Qing
    Epshteyn, Yekaterina
    Kreiss, Gunilla
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    High-order numerical methods for 2D parabolic problems in single and composite domains2018In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 76, p. 812-847Article in journal (Refereed)
  • 44.
    Malm, Johan
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Fischer, Paul F.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Stabilization of the Spectral Element Method in Convection Dominated Flows by Recovery of Skew-Symmetry2013In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 57, no 2, p. 254-277Article in journal (Refereed)
    Abstract [en]

    We investigate stability properties of the spectral element method for advection dominated incompressible flows. In particular, properties of the widely used convective form of the nonlinear term are studied. We remark that problems which are usually associated with the nonlinearity of the governing Navier-Stokes equations also arise in linear scalar transport problems, which implicates advection rather than nonlinearity as a source of difficulty. Thus, errors arising from insufficient quadrature of the convective term, commonly referred to as 'aliasing errors', destroy the skew-symmetric properties of the convection operator. Recovery of skew-symmetry can be efficiently achieved by the use of over-integration. Moreover, we demonstrate that the stability problems are not simply connected to underresolution. We combine theory with analysis of the linear advection-diffusion equation in 2D and simulations of the incompressible Navier-Stokes equations in 2D of thin shear layers at a very high Reynolds number and in 3D of turbulent and transitional channel flow at moderate Reynolds number. For the Navier-Stokes equations, where the divergence-free constraint needs to be enforced iteratively to a certain accuracy, small divergence errors can be detrimental to the stability of the method and it is therefore advised to use additional stabilization (e.g. so-called filter-based stabilization, spectral vanishing viscosity or entropy viscosity) in order to assure a stable spectral element method.

  • 45. Massing, Andre
    et al.
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Logg, Anders
    Rognes, Marie E.
    A Stabilized Nitsche Fictitious Domain Method for the Stokes Problem2014In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 61, no 3, p. 604-628Article in journal (Refereed)
    Abstract [en]

    We present a novel finite element method for the Stokes problem on fictitious domains. We prove inf-sup stability, optimal order convergence and uniform boundedness of the condition number of the discrete system. The finite element formulation is based on a stabilized Nitsche method with ghost penalties for the velocity and pressure to obtain stability in the presence of small cut elements. We demonstrate for the first time the applicability of the Nitsche fictitious domain method to three-dimensional Stokes problems. We further discuss a general, flexible and freely available implementation of the method and present numerical examples supporting the theoretical results.

  • 46. Mattsson, K.
    et al.
    Svärd, Magnus
    Nordstrom, J.
    Stable and accurate artificial dissipation2004In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 21, no 1, p. 57-79Article in journal (Refereed)
    Abstract [en]

    Stability for nonlinear convection problems using centered difference schemes require the addition of artificial dissipation. In this paper we present dissipation operators that preserve both stability and accuracy for high order finite difference approximations of initial boundary value problems.

  • 47.
    Mattsson, Ken
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Boundary Procedures for Summation-by-Parts Operators2003In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 18, p. 133-153Article in journal (Refereed)
  • 48.
    Mattsson, Ken
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Summation by parts operators for finite difference approximations of second-derivatives with variable coefficients2012In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 51, p. 650-682Article in journal (Refereed)
  • 49.
    Mattsson, Ken
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Ham, Frank
    Iaccarino, Gianluca
    Stable Boundary Treatment for the Wave Equation on Second-Order Form2009In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 41, p. 366-383Article in journal (Refereed)
  • 50.
    Mattsson, Ken
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Svärd, Magnus
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Nordström, Jan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Stable and Accurate Artificial Dissipation2004In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 21, p. 57-79Article in journal (Refereed)
12 1 - 50 of 93
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