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  • 1.
    af Klinteberg, Ludvig
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Tornberg, Anna-Karin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    A fast integral equation method for solid particles in viscous flow using quadrature by expansion2016In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 326, p. 420-445Article in journal (Refereed)
    Abstract [en]

    Boundary integral methods are advantageous when simulating viscous flow around rigid particles, due to the reduction in number of unknowns and straightforward handling of the geometry. In this work we present a fast and accurate framework for simulating spheroids in periodic Stokes flow, which is based on the completed double layer boundary integral formulation. The framework implements a new method known as quadrature by expansion (QBX), which uses surrogate local expansions of the layer potential to evaluate it to very high accuracy both on and off the particle surfaces. This quadrature method is accelerated through a newly developed precomputation scheme. The long range interactions are computed using the spectral Ewald (SE) fast summation method, which after integration with QBX allows the resulting system to be solved in M log M time, where M is the number of particles. This framework is suitable for simulations of large particle systems, and can be used for studying e.g. porous media models.

  • 2.
    Ahlkrona, Josefin
    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.
    Kirchner, Nina
    Zwinger, Thomas
    Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method2016In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 308, p. 1-19Article in journal (Refereed)
  • 3. Ahlkrona, Josefin
    et al.
    Lötstedt, Per
    Kirchner, Nina
    Stockholm University, Faculty of Science, Department of Physical Geography.
    Zwinger, Thomas
    Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method2016In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 308, p. 1-19Article in journal (Refereed)
    Abstract [en]

    We propose and implement a new method, called the Ice Sheet Coupled Approximation Levels (ISCAL) method, for simulation of ice sheet flow in large domains during long time-intervals. The method couples the full Stokes (FS) equations with the Shallow Ice Approximation (SIA). The part of the domain where SIA is applied is determined automatically and dynamically based on estimates of the modeling error. For a three dimensional model problem, ISCAL computes the solution substantially faster with a low reduction in accuracy compared to a monolithic FS. Furthermore, ISCAL is shown to be able to detect rapid dynamic changes in the flow. Three different error estimations are applied and compared. Finally, ISCAL is applied to the Greenland Ice Sheet on a quasi-uniform grid, proving ISCAL to be a potential valuable tool for the ice sheet modeling community.

  • 4.
    Ahlkrona, Josefin
    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.
    Shcherbakov, Victor
    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 meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla2017In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 330, p. 633-649Article in journal (Refereed)
  • 5.
    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.
    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.
    Edvinsson, Tomas
    Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Chemistry - Ångström, Inorganic Chemistry.
    High-fidelity numerical solution of the time-dependent Dirac equation2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 262, p. 86-103Article in journal (Refereed)
  • 6.
    Amsallem, David
    et al.
    Department of Aeronautics and Astronautics, Stanford University, USA.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    High-order accurate difference schemes for the Hodgkin-Huxley equations2013In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 252, p. 573-590Article in journal (Refereed)
    Abstract [en]

    A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate difference schemes using the Summation-By-Parts operators with weak boundary and interface conditions applied to the Hodgkin–Huxley equations. This work is the first demonstrating high accuracy for that equation. Several boundary conditions are considered including the non-standard one accounting for the soma presence, which is characterized by its own partial differential equation. Well-posedness for the continuous problem as well as stability of the discrete approximation is proved for all the boundary conditions. Gains in terms of CPU times are observed when high-order operators are used, demonstrating the advantage of the high-order schemes for simulating potential propagation in large neuronal trees.

  • 7.
    Appelö, Daniel
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Kreiss, Gunilla
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    A New Absorbing Layer for Elastic Waves2006In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 215, no 2, p. 642-660Article in journal (Refereed)
    Abstract [en]

    A new perfectly matched layer (PML) for the simulation of elastic waves in anisotropic media on an unbounded domain is constructed. Theoretical and numerical results, showing that the stability properties of the present layer are better than previously suggested layers, are presented. In addition, the layer can be formulated with fewer auxiliary variables than the split-field PML.

  • 8.
    Ariel, Gil
    et al.
    Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel.
    Engquist, Björn
    Department of Mathematics, The University of Texas at Austin, Austin, USA.
    Tanushev, Nicolay M.
    Department of Mathematics, The University of Texas at Austin, Austin, USA.
    Tsai, Richard
    Department of Mathematics, The University of Texas at Austin, Austin, USA.
    Gaussian Beam Decomposition of High Frequency Wave Fields Using Expectation-Maximization2011In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, no 6, p. 2303-2321Article in journal (Refereed)
    Abstract [en]

    A new numerical method for approximating highly oscillatory wave fields as a superposition of Gaussian beams is presented. The method estimates the number of beams and their parameters automatically. This is achieved by an expectation–maximization algorithm that fits real, positive Gaussians to the energy of the highly oscillatory wave fields and its Fourier transform. Beam parameters are further refined by an optimization procedure that minimizes the difference between the Gaussian beam superposition and the highly oscillatory wave field in the energy norm.

  • 9.
    Arjmand, Doghonay
    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.
    Runborg, Olof
    Royal Institute of Technology.
    A time dependent approach for removing the cell boundary error in elliptic homogenization problems2016In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 314, p. 206-227Article in journal (Refereed)
  • 10. Arjmand, Doghonay
    et al.
    Runborg, Olof
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    A time dependent approach for removing the cell boundary error in elliptic homogenization problems2016In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 314, p. 206-227Article in journal (Refereed)
    Abstract [en]

    This paper concerns the cell-boundary error present in multiscale algorithms for elliptic homogenization problems. Typical multiscale methods have two essential components: a macro and a micro model. The micro model is used to upscale parameter values which are missing in the macro model. To solve the micro model, boundary conditions are required on the boundary of the microscopic domain. Imposing a naive boundary condition leads to O(epsilon/eta) error in the computation, where epsilon is the size of the microscopic variations in the media and eta is the size of the micro-domain. The removal of this error in modern multiscale algorithms still remains an important open problem. In this paper, we present a time-dependent approach which is general in terms of dimension. We provide a theorem which shows that we have arbitrarily high order convergence rates in terms of epsilon/eta in the periodic setting. Additionally, we present numerical evidence showing that the method improves the O(epsilon/eta) error to O(epsilon) in general non-periodic media.

  • 11.
    Axner, Lilit
    et al.
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for High Performance Computing, PDC.
    Bernsdorf, Joerg M.
    Zeiser, Thomas
    Lammers, Peter
    Linxweiler, Jan
    Hoekstra, Alfonsb G.
    Performance evaluation of a Parallel Sparse Lattice Boltzmann Solver2008In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 227, no 10, p. 4895-4911Article in journal (Refereed)
    Abstract [en]

    We develop a performance prediction model for a parallelized sparse lattice Boltzmann solver and present performance results for simulations of flow in a variety of complex geometries. A special focus is on partitioning and memory/load balancing strategy for geometries with a high solid fraction and/or complex topology such as porous media, fissured rocks and geometries from medical applications. The topology of the lattice nodes representing the fluid fraction of the computational domain is mapped on a graph. Graph decomposition is performed with both multilevel recursive-bisection and multilevel k-way schemes based on modified Kernighan–Lin and Fiduccia–Mattheyses partitioning algorithms. Performance results and optimization strategies are presented for a variety of platforms, showing a parallel efficiency of almost 80% for the largest problem size. A good agreement between the performance model and experimental results is demonstrated.

  • 12. Babkovskaia, Natalia
    et al.
    Haugen, N. E. L.
    Brandenburg, Axel
    Stockholm University, Faculty of Science, Department of Astronomy. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    A high-order public domain code for direct numerical simulations of turbulent combustion2011In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, no 1, p. 1-12Article in journal (Refereed)
    Abstract [en]

    A high-order scheme for direct numerical simulations of turbulent combustion is discussed. Its implementation in the massively parallel and publicly available PENCIL CODE is validated with the focus on hydrogen combustion. This is the first open source DNS code with detailed chemistry available. An attempt has been made to present, for the first time, the full set of evolution and auxiliary equations required for a complete description of single phase non-isothermal fluid dynamics with detailed chemical reactions. Ignition delay times (0D) and laminar flame velocities (1D) are calculated and compared with results from the commercially available Chemkin code. The scheme is verified to be fifth order in space. Upon doubling the resolution, a 32-fold increase in the accuracy of the flame front is demonstrated. Finally, also turbulent and spherical flame front velocities are calculated and the implementation of the non-reflecting so-called Navier-Stokes Characteristic Boundary Condition is validated in all three directions.

  • 13.
    Bashardanesh, Zahedeh
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Cell and Molecular Biology, Computational Biology and Bioinformatics.
    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.
    Efficient Green's function reaction dynamics (GFRD) simulations for diffusion-limited, reversible reactions2018In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 357, p. 78-99Article in journal (Refereed)
  • 14. Beck, A.
    et al.
    Innocenti, M. E.
    Lapenta, G.
    Markidis, Stefano
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Multi-level multi-domain algorithm implementation for two-dimensional multiscale particle in cell simulations2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 271, p. 430-443Article in journal (Refereed)
    Abstract [en]

    There are a number of modeling challenges posed by space weather simulations. Most of them arise from the multiscale and multiphysics aspects of the problem. The multiple scales dramatically increase the requirements, in terms of computational resources, because of the need of performing large scale simulations with the proper small-scales resolution. Lately, several suggestions have been made to overcome this difficulty by using various refinement methods which consist in splitting the domain into regions of different resolutions separated by well defined interfaces. The multiphysics issues are generally treated in a similar way: interfaces separate the regions where different equations are solved. This paper presents an innovative approach based on the coexistence of several levels of description, which differ by their resolutions or, potentially, by their physics. Instead of interacting through interfaces, these levels are entirely simulated and are interlocked over the complete extension of the overlap area. This scheme has been applied to a parallelized, two-dimensional, Implicit Moment Method Particle in Cell code in order to investigate its multiscale description capabilities. Simulations of magnetic reconnection and plasma expansion in vacuum are presented and possible implementation options for this scheme on very large systems are also discussed.

  • 15. Benamou, J. D.
    et al.
    Collino, F.
    Runborg, Olof
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Numerical microlocal analysis of harmonic wavefields2004In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 199, no 2, p. 717-741Article in journal (Refereed)
    Abstract [en]

    We present and test a numerical method which, given an analytical or numerical solution of the Helmholtz equation in a neighborhood of a fixed observation point and assuming that the geometrical optics approximation is relevant, determines at this point the number of crossing rays and computes their directions and associated complex amplitudes.

  • 16.
    Berg, Jens
    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.
    Nordström, Jan
    Duality based boundary conditions and dual consistent finite difference discretizations of the Navier–Stokes and Euler equations2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 259, p. 135-153Article in journal (Refereed)
  • 17.
    Berg, Jens
    et al.
    Uppsala University, Sweden.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    Duality based boundary conditions and dual consistent finite difference discretizations of the Navier–Stokes and Euler equations2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 259, p. 135-153Article in journal (Refereed)
    Abstract [en]

    In this paper we derive new farfield boundary conditions for the time-dependent Navier–Stokes and Euler equations in two space dimensions. The new boundary conditions are derived by simultaneously considering well-posedess of both the primal and dual problems. We moreover require that the boundary conditions for the primal and dual Navier–Stokes equations converge to well-posed boundary conditions for the primal and dual Euler equations.

    We perform computations with a high-order finite difference scheme on summation-by-parts form with the new boundary conditions imposed weakly by the simultaneous approximation term. We prove that the scheme is both energy stable and dual consistent and show numerically that both linear and non-linear integral functionals become superconvergent.

  • 18.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology, SE-751 05, Uppsala, Sweden.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    On the impact of boundary conditions on dual consistent finite difference discretizations2013In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 236, p. 41-55Article in journal (Refereed)
    Abstract [en]

    In this paper we derive well-posed boundary conditions for a linear incompletely parabolic system of equations, which can be viewed as a model problem for the compressible Navier{Stokes equations. We show a general procedure for the construction of the boundary conditions such that both the primal and dual equations are wellposed.

    The form of the boundary conditions is chosen such that reduction to rst order form with its complications can be avoided.

    The primal equation is discretized using finite difference operators on summation-by-parts form with weak boundary conditions. It is shown that the discretization can be made energy stable, and that energy stability is sufficient for dual consistency.

    Since reduction to rst order form can be avoided, the discretization is significantly simpler compared to a discretization using Dirichlet boundary conditions.

    We compare the new boundary conditions with standard Dirichlet boundary conditions in terms of rate of convergence, errors and discrete spectra. It is shown that the scheme with the new boundary conditions is not only far simpler, but also has smaller errors, error bounded properties, and highly optimizable eigenvalues, while maintaining all desirable properties of a dual consistent discretization.

  • 19.
    Berg, Jens
    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.
    Nordström, Jan
    On the impact of boundary conditions on dual consistent finite difference discretizations2013In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 236, p. 41-55Article in journal (Refereed)
  • 20.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology.
    Nordström, Jan
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Scientific Computing.
    Stable Robin solid wall boundary conditions for the Navier-Stokes equations2011In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, no 19, p. 7519-7532Article in journal (Refereed)
    Abstract [en]

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

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

  • 21.
    Berg, Jens
    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.
    Nordström, Jan
    Stable Robin solid wall boundary conditions for the Navier-Stokes equations2011In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, p. 7519-7532Article in journal (Refereed)
  • 22.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology, Sweden.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form2012In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 231, no 20, p. 6846-6860Article in journal (Refereed)
    Abstract [en]

    Finitedifference operators satisfying the summation-by-parts (SBP) rules can be used to obtain high order accurate, energy stable schemes for time-dependent partial differential equations, when the boundary conditions are imposed weakly by the simultaneous approximation term (SAT).

    In general, an SBP-SAT discretization is accurate of order p + 1 with an internal accuracy of 2p and a boundary accuracy of p. Despite this, it is shown in this paper that any linear functional computed from the time-dependent solution, will be accurate of order 2p when the boundary terms are imposed in a stable and dual consistent way.

    The method does not involve the solution of the dual equations, and superconvergent functionals are obtained at no extra computational cost. Four representative model problems are analyzed in terms of convergence and errors, and it is shown in a systematic way how to derive schemes which gives superconvergentfunctionaloutputs.

  • 23.
    Berg, Jens
    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.
    Nordström, Jan
    Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form2012In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 231, p. 6846-6860Article in journal (Refereed)
  • 24.
    Berg, Jens
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Nyström, Kaj
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Data-driven discovery of PDEs in complex datasets2019In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 384, p. 239-252Article in journal (Refereed)
    Abstract [en]

    Many processes in science and engineering can be described by partial differential equations (PDEs). Traditionally, PDEs are derived by considering first principles of physics to derive the relations between the involved physical quantities of interest. A different approach is to measure the quantities of interest and use deep learning to reverse engineer the PDEs which are describing the physical process. In this paper we use machine learning, and deep learning in particular, to discover PDEs hidden in complex data sets from measurement data. We include examples of data from a known model problem, and real data from weather station measurements. We show how necessary transformations of the input data amounts to coordinate transformations in the discovered PDE, and we elaborate on feature and model selection. It is shown that the dynamics of a non-linear, second order PDE can be accurately described by an ordinary differential equation which is automatically discovered by our deep learning algorithm. Even more interestingly, we show that similar results apply in the context of more complex simulations of the Swedish temperature distribution

  • 25.
    Berggren, Martin
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Bernland, Anders
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Noreland, Daniel
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Acoustic boundary layers as boundary conditions2018In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 371, p. 633-650Article in journal (Refereed)
    Abstract [en]

    The linearized, compressible Navier-Stokes equations can be used to model acoustic wave propagation in the presence of viscous and thermal boundary layers. However, acoustic boundary layers are notorious for invoking prohibitively high resolution requirements on numerical solutions of the equations. We derive and present a strategy for how viscous and thermal boundary-layer effects can be represented as a boundary condition on the standard Helmholtz equation for the acoustic pressure. This boundary condition constitutes an O (delta) perturbation, where delta is the boundary-layer thickness, of the vanishing Neumann condition for the acoustic pressure associated with a lossless sound-hard wall. The approximate model is valid when the wavelength and the minimum radius of curvature of the wall is much larger than the boundary layer thickness. In the special case of sound propagation in a cylindrical duct, the model collapses to the classical Kirchhoff solution. We assess the model in the case of sound propagation through a compression driver, a kind of transducer that is commonly used to feed horn loudspeakers. Due to the presence of shallow chambers and thin slits in the device, it is crucial to include modeling of visco-thermal losses in the acoustic analysis. The transmitted power spectrum through the device calculated numerically using our model agrees well with computations using a hybrid model, where the full linearized, compressible Navier-Stokes equations are solved in the narrow regions of the device and the inviscid Helmholtz equations elsewhere. However, our model needs about two orders of magnitude less memory and computational time than the more complete model. 

  • 26.
    Blanc, Emilie
    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.
    Chiavassa, Guillaume
    Lombard, Bruno
    Wave simulation in 2D heterogeneous transversely isotropic porous media with fractional attenuation: A Cartesian grid approach2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 275, p. 118-142Article in journal (Refereed)
  • 27.
    Bobylev, Alexander
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Potapenko, Irina
    Russia.
    Monte Carlo methods and their analysis for Coulomb collisions in multicomponent plasmas2013In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 246, p. 123-144Article in journal (Refereed)
    Abstract [en]

    A general approach to Monte Carlo methods for Coulomb collisions is proposed. Its key idea is an approximation of Landau-Fokker-Planck equations by Boltzmann equations of quasi-Maxwellian kind. It means that the total collision frequency for the corresponding Boltzmann equation does not depend on the velocities. This allows to make the simulation process very simple since the collision pairs can be chosen arbitrarily, without restriction. It is shown that this approach includes the well-known methods of Takizuka and Abe (1977) [12] and Nanbu (1997) as particular cases, and generalizes the approach of Bobylev and Nanbu (2000). The numerical scheme of this paper is simpler than the schemes by Takizuka and Abe [12] and by Nanbu. We derive it for the general case of multicomponent plasmas and show some numerical tests for the two-component (electrons and ions) case. An optimal choice of parameters for speeding up the computations is also discussed. It is also proved that the order of approximation is not worse than O(root epsilon), where epsilon is a parameter of approximation being equivalent to the time step Delta t in earlier methods. A similar estimate is obtained for the methods of Takizuka and Abe and Nanbu. (C) 2013 Elsevier Inc. All rights reserved.

  • 28.
    Bohm, Marvin
    et al.
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Winters, Andrew Ross
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Gassner, Gregor J
    Mathematisches Institut, Universität zu Köln, Köln, Germany.
    Derigs, Dominik
    I. Physikalisches Institut, Universität zu Köln, Köln, Germany.
    Hindenlang, Florian
    Max-Planck Institut für Plasmaphysik, Garching, Germany.
    Saur, Joachim
    Institut für Geophysik und Meteorologie, Universität zu Köln, Köln, Germany.
    An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part I: Theory and numerical verification2018In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716Article in journal (Refereed)
    Abstract [en]

    The first paper of this series presents a discretely entropy stable discontinuous Galerkin (DG) method for the resistive magnetohydrodynamics (MHD) equations on three-dimensional curvilinear unstructured hexahedral meshes. Compared to other fluid dynamics systems such as the shallow water equations or the compressible Navier-Stokes equations, the resistive MHD equations need special considerations because of the divergence-free constraint on the magnetic field. For instance, it is well known that for the symmetrization of the ideal MHD system as well as the continuous entropy analysis a non-conservative term proportional to the divergence of the magnetic field, typically referred to as the Powell term, must be included. As a consequence, the mimicry of the continuous entropy analysis in the discrete sense demands a suitable DG approximation of the non-conservative terms in addition to the ideal MHD terms.

    This paper focuses on the resistive MHD equations: Our first contribution is a proof that the resistive terms are symmetric and positive-definite when formulated in entropy space as gradients of the entropy variables, which enables us to show that the entropy inequality holds for the resistive MHD equations. This continuous analysis is the key for our DG discretization and guides the path for the construction of an approximation that discretely mimics the entropy inequality, typically termed entropy stability. Our second contribution is a detailed derivation and analysis of the discretization on three-dimensional curvilinear meshes. The discrete analysis relies on the summation-by-parts property, which is satisfied by the DG spectral element method (DGSEM) with Legendre-Gauss-Lobatto (LGL) nodes. Although the divergence-free constraint is included in the non-conservative terms, the resulting method has no particular treatment of the magnetic field divergence errors, which might pollute the solution quality. Our final contribution is the extension of the standard resistive MHD equations and our DG approximation with a divergence cleaning mechanism that is based on a generalized Lagrange multiplier (GLM).

    As a conclusion to the first part of this series, we provide detailed numerical validations of our DGSEM method that underline our theoretical derivations. In addition, we show a numerical example where the entropy stable DGSEM demonstrates increased robustness compared to the standard DGSEM.

  • 29. Bruger, A
    et al.
    Gustafsson, Bertil
    Lotstedt, Per
    Nilsson, J
    High order accurate solution of the incompressible Navier-Stokes equations2005In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 203, no 1, p. 49-71Article in journal (Refereed)
    Abstract [en]

    High order methods are of great interest in the study of turbulent flows in complex geometries by means of direct simulation. With this goal in mind, the incompressible Navier-Stokes equations are discretized in space by a compact fourth order finite difference method on a staggered grid. The equations are integrated in time by a second order semi-implicit method. Stable boundary conditions are implemented and the grid is allowed to be curvilinear in two space dimensions. The method is extended to three dimensions by a Fourier expansion. In every time step, a system of linear equations is solved for the velocity and the pressure by an outer and an inner iteration with preconditioning. The convergence properties of the iterative method are analyzed. The order of accuracy of the method is demonstrated in numerical experiments. The method is used to compute the flow in a channel, the driven cavity and a constricted channel.

  • 30. Brüger, Arnim
    et al.
    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.
    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.
    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.
    High order accurate solution of the incompressible Navier-Stokes equations2005In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 203, p. 49-71Article in journal (Refereed)
  • 31.
    Bull, Jonathan R.
    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.
    Jameson, Antony
    Explicit filtering and exact reconstruction of the sub-filter stresses in large eddy simulation2016In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 306, p. 117-136Article in journal (Refereed)
  • 32.
    Burdakov, Oleg
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Kapyrin, Ivan
    Russian Academy of Science.
    Vassilevski, Yuri
    Russian Academy of Science.
    Monotonicity recovering and accuracy preserving optimization methods for postprocessing finite element solutions2012In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 231, no 8, p. 3126-3142Article in journal (Refereed)
    Abstract [en]

    We suggest here a least-change correction to available finite element (FE) solution. This postprocessing procedure is aimed at recovering the monotonicity and some other important properties that may not be exhibited by the FE solution. Although our approach is presented for FEs, it admits natural extension to other numerical schemes, such as finite differences and finite volumes. For the postprocessing, a priori information about the monotonicity is assumed to be available, either for the whole domain or for a subdomain where the lost monotonicity is to be recovered. The obvious requirement is that such information is to be obtained without involving the exact solution, e.g. from expected symmetries of this solution. less thanbrgreater than less thanbrgreater thanThe postprocessing is based on solving a monotonic regression problem with some extra constraints. One of them is a linear equality-type constraint that models the conservativity requirement. The other ones are box-type constraints, and they originate from the discrete maximum principle. The resulting postprocessing problem is a large scale quadratic optimization problem. It is proved that the postprocessed FE solution preserves the accuracy of the discrete FE approximation. less thanbrgreater than less thanbrgreater thanWe introduce an algorithm for solving the postprocessing problem. It can be viewed as a dual ascent method based on the Lagrangian relaxation of the equality constraint. We justify theoretically its correctness. Its efficiency is demonstrated by the presented results of numerical experiments.

  • 33. Carpenter, Mark H.
    et al.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Gottlieb, David
    A stable and conservative interface treatment of arbitrary spatial accuracy1999In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 148, p. 341-365Article in journal (Refereed)
  • 34. 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
    A stable and conservative interface treatment of arbitrary spatial accuracy1999In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 148, p. 341-365Article in journal (Refereed)
  • 35.
    Carpenter, Mark H
    et al.
    Computational Aerosciences Branch, NASA Langley Research Center, Hampton, VA 23681, USA.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Gottlieb, David
    cDivision of Applied Mathematics, Brown University, Providence, RI 02912, USA.
    Corrigendum to “A stable and conservative interface treatment of arbitrary spatial accuracy” [J.Comput.Phys.148(1999)341–365]2017In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 351, p. 534-Article in journal (Other academic)
  • 36.
    Cheng, Gong
    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.
    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.
    Accurate and stable time stepping in ice sheet modeling2017In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 329, p. 29-47Article in journal (Refereed)
  • 37.
    Cheng, Gong
    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.
    Shcherbakov, Victor
    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.
    Anisotropic radial basis function methods for continental size ice sheet simulations2018In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 372, p. 161-177Article in journal (Refereed)
  • 38.
    Cohen, David
    et al.
    Department of Mathematical Sciences, NTNU.
    Owren, Brynjulf
    Department of Mathematical Sciences, NTNU.
    Raynaud, Xavier
    Department of Mathematical Sciences, NTNU.
    Multi-symplectic integration of the Camassa-Holm equation2008In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 227, no 11, p. 5492-5512Article in journal (Refereed)
    Abstract [en]

    The Camassa-Holm equation is rich in geometric structures, it is completely integrable, bi-Hamiltonian, and it represents geodesics for a certain metric in the group of diffeomorphism. Here two new multi-symplectic formulations for the Camassa-Holm equation are presented, and the associated local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. The multi-symplectic discretisation of each formulation is exemplified by means of the Euler box scheme. Numerical experiments show that the schemes have good conservative properties, and one of them is designed to handle the conservative continuation of peakon-antipeakon collisions. (c) 2008 Elsevier Inc. All rights reserved.

  • 39. Daldorff, Lars K. S.
    et al.
    Toth, Gabor
    Gombosi, Tamas I.
    Lapenta, Giovanni
    Amaya, Jorge
    Markidis, Stefano
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Brackbill, Jeremiah U.
    Two-way coupling of a global Hall magnetohydrodynamics model with a local implicit particle-in-cell model2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 268, p. 236-254Article in journal (Refereed)
    Abstract [en]

    Computational models based on a fluid description of the plasma, such as magnetohydrodynamic (MHD) and extended magnetohydrodynamic (XMHD) codes are highly efficient, but they miss the kinetic effects due to the assumptions of small gyro radius, charge neutrality, and Maxwellian thermal velocity distribution. Kinetic codes can properly take into account the kinetic effects, but they are orders of magnitude more expensive than the fluid codes due to the increased degrees of freedom. If the fluid description is acceptable in a large fraction of the computational domain, it makes sense to confine the kinetic model to the regions where kinetic effects are important. This coupled approach can be much more efficient than a pure kinetic model. The speed up is approximately the volume ratio of the full domain relative to the kinetic regions assuming that the kinetic code uses a uniform grid. This idea has been advocated by [1] but their coupling was limited to one dimension and they employed drastically different grid resolutions in the fluid and kinetic models. We describe a fully two-dimensional two-way coupling of a Hall MHD model BATS-R-US with an implicit Particle-in-Cell (PIC) model iPIC3D. The coupling can be performed with identical grid resolutions and time steps. We call this coupled computational plasma model MHD-EPIC (MHD with Embedded PIC regions). Our verification tests show that MHD-EPIC works accurately and robustly. We show a two-dimensional magnetosphere simulation as an illustration of the potential future applications of MHD-EPIC.

  • 40.
    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 MHD2017In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 330, p. 624-632Article in journal (Refereed)
    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.

  • 41.
    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 pressure2016In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 317, p. 223-256Article in journal (Refereed)
    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.

  • 42.
    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 equations2018In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 364, p. 420-467Article in journal (Refereed)
    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).

    The full text will be freely available from 2020-07-13 08:00
  • 43. Donatelli, Marco
    et al.
    Mazza, Mariarosa
    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.
    Spectral analysis and structure preserving preconditioners for fractional diffusion equations2016In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 307, p. 262-279Article in journal (Refereed)
  • 44. Donev, Aleksandar
    et al.
    Bulatov, Vasily V.
    Oppelstrup, Tomas
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Gilmer, George H.
    Sadigh, Babak
    Kalos, Malvin H.
    A First-Passage Kinetic Monte Carlo algorithm for complex diffusion-reaction systems2010In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 229, no 9, p. 3214-3236Article in journal (Refereed)
    Abstract [en]

    We develop an asynchronous event-driven First-Passage Kinetic Monte Carlo (FPKMC) algorithm for continuous time and space systems involving multiple diffusing and reacting species of spherical particles in two and three dimensions. The FPKMC algorithm presented here is based on the method introduced in Oppelstrup et al. [10] and is implemented in a robust and flexible framework. Unlike standard KMC algorithms such as the n-fold algorithm, FPKMC is most efficient at low densities where it replaces the many small hops needed for reactants to find each other with large first-passage hops sampled from exact time-dependent Green's functions, without sacrificing accuracy. We describe in detail the key components of the algorithm, including the event-loop and the sampling of first-passage probability distributions, and demonstrate the accuracy of the new method. We apply the FPKMC algorithm to the challenging problem of simulation of long-term irradiation of metals, relevant to the performance and aging of nuclear materials in current and future nuclear power plants. The problem of radiation damage spans many decades of time-scales, from picosecond spikes caused by primary cascades, to years of slow damage annealing and microstructure evolution. Our implementation of the FPKMC algorithm has been able to simulate the irradiation of a metal sample for durations that are orders of magnitude longer than any previous simulations using the standard Object KMC or more recent asynchronous algorithms. (C) 2010 Elsevier Inc. All rights reserved.

  • 45.
    Do-Quang, Minh
    et al.
    KTH.
    Amberg, Gustav
    KTH.
    Simulation of free dendritic crystal growth in a gravity environment2008In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 227, no 3, p. 1772-1789Article in journal (Refereed)
    Abstract [en]

    In this paper we simulate the evolution and free particle motion of an individual nucleus that grows into a dendritic crystal. The melt flow and the convective heat transfer around the crystal are simulated as they settle due to gravity. There is an intricate coupling between the settling and the evolution of the crystal. The relative flow induced by the settling enhances the growth at the downward facing parts, which in its turn affects the subsequent settling motion. Simulations have been done in two dimensions using a semi-sharp phase-field model. The flow was constrained to a rigid body motion by using Lagrange multipliers inside the solidified part. The model was formulated using two different meshes. One is a fixed background mesh, which covers the whole domain. The other is an adaptive mesh, where the node points are also translated and rotated with the movement of the solid particle. In the latter, the dendritic growth is simulated by the semi-sharp phase-field method.

  • 46.
    Do-Quang, Minh
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics.
    Amberg, Gustav
    KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics.
    Simulation of free dendritic crystal growth in a gravity environment2008In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 227, no 3, p. 1772-1789Article in journal (Refereed)
    Abstract [en]

    In this paper we simulate the evolution and free particle motion of an individual nucleus that grows into a dendritic crystal. The melt flow and the convective heat transfer around the crystal are simulated as they settle due to gravity. There is an intricate coupling between the settling and the evolution of the crystal. The relative flow induced by the settling enhances the growth at the downward facing parts, which in its turn affects the subsequent settling motion. Simulations have been done in two dimensions using a semi-sharp phase-field model. The flow was constrained to a rigid body motion by using Lagrange multipliers inside the solidified part. The model was formulated using two different meshes. One is a fixed background mesh, which covers the whole domain. The other is an adaptive mesh, where the node points are also translated and rotated with the movement of the solid particle. In the latter, the dendritic growth is simulated by the semi-sharp phase-field method.

  • 47. Durlofsky, L. J.
    et al.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Osher, S
    Triangle based adaptive stencils for the solution of hyperbolic conservation laws1992In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, ISSN 0021-9991, Vol. 98, no 1, p. 64-73Article in journal (Refereed)
    Abstract [en]

    A triangle based total variation diminishing (TVD) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this scheme, approximate the flux up to second order accuracy. Numerical results for linear advection and Burgers' equation are presented.

  • 48. Duru, Kenneth
    et al.
    Kozdon, Jeremy E.
    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.
    Boundary conditions and stability of a perfectly matched layer for the elastic wave equation in first order form2015In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 303, p. 372-395Article in journal (Refereed)
  • 49. Duru, Kenneth
    et al.
    Virta, Kristoffer
    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 high order accurate difference methods for the elastic wave equation in discontinuous media2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 279, p. 37-62Article in journal (Refereed)
  • 50.
    Efraimsson, Gunilla
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    A 2D Analysis of the Influence of Artificial Viscosity Terms on Solutions of the Euler Equations1997In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 138, no 1, p. 103-120Article in journal (Refereed)
    Abstract [en]

    We analyze the influence of artificial viscosity on solutions of the Euler equations in the neighborhood of oblique shocks in 2D by studying a discrete, linear model equation. Based on the linear analysis an artificial viscosity model is derived. It is tested on two different test cases with the Euler equations: flow over a wedge and Mach-3 flow in a wind tunnel with a step.

123456 1 - 50 of 257
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