Change search
Refine search result
12 1 - 50 of 80
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Rows per page
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sort
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the Create feeds function.
  • 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.
    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.

  • 3.
    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.

  • 4. 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.

  • 5.
    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.

  • 6. 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.

  • 7. 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.

  • 8. 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.

  • 9. 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.

  • 10.
    de Conchard, Antoine Vermeil
    et al.
    Univ Nantes, Dept Mech Mat & Civil Engn, Ecole Cent Nantes, Nantes, France..
    Mao, Huina
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL.
    Rumpler, Romain
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL. KTH, School of Engineering Sciences (SCI), Centres, VinnExcellence Center for ECO2 Vehicle design.
    A perfectly matched layer formulation adapted for fast frequency sweeps of exterior acoustics finite element models2019In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 398, article id UNSP 108878Article in journal (Refereed)
    Abstract [en]

    Effective treatment of unbounded domains using artificial truncating boundaries are essential in numerical simulation, e.g. using the Finite Element Method (FEM). Among these, Perfectly Matched Layers (PML) have proved to be particularly efficient and flexible. However, an efficient handling of frequency sweeps is not trivial with such absorbing layers since the formulation inherently contains coupled space-and frequency-dependent terms. Using the FEM, this may imply generating system matrices at each step of the frequency sweep. In this paper, an approximation is proposed in order to allow for efficient frequency sweeps. The performance and robustness of the proposed approximation is presented on 2D and 3D acoustic cases. A generic, robust way to truncate the acoustic domain efficiently is also proposed, tested on a range of test cases and for different frequency regions. All rights reserved.

  • 11. 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.

  • 12.
    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.

  • 13. 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.

  • 14.
    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.

  • 15.
    Ekeberg, Magnus
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Hartonen, Tuomo
    Aurell, Erik
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB. Aalto University, Finland.
    Fast pseudolikelihood maximization for direct-coupling analysis of protein structure from many homologous amino-acid sequences2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 276, p. 341-356Article in journal (Refereed)
    Abstract [en]

    Direct-coupling analysis is a group of methods to harvest information about coevolving residues in a protein family by learning a generative model in an exponential family from data. In protein families of realistic size, this learning can only be done approximately, and there is a trade-off between inference precision and computational speed. We here show that an earlier introduced l(2)-regularized pseudolikelihood maximization method called plmDCA can be modified as to be easily parallelizable, as well as inherently faster on a single processor, at negligible difference in accuracy. We test the new incarnation of the method on 143 protein family/structure-pairs from the Protein Families database (PFAM), one of the larger tests of this class of algorithms to date.

  • 16. Engquist, Bjoern
    et al.
    Froese, Brittany D.
    Tsai, Yen-Hsi Richard
    The University of Texas at Austin, United States.
    Fast sweeping methods for hyperbolic systems of conservation laws at steady state II2015In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 286, p. 70-86Article in journal (Refereed)
    Abstract [en]

    The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging class of problems including problems with sonic points, shocks originating in the interior of the domain, rarefaction waves, and two-dimensional systems. We show that fast sweeping methods can produce higher-order accuracy. Computational results validate the claims of accuracy, sharp shock curves, and optimal computational efficiency.

  • 17.
    Engquist, Björn
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Gustafsson, B
    Vreeburg, J
    Numerical solution of a PDE system describing a catalytic converter1978In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 27, no 3, p. 295-314Article in journal (Refereed)
    Abstract [en]

    Numerical approximations are studied for a large hyperbolic system coupled to a parabolic equation and a system of algebraic equations. The equations, which all are nonlinear, describe nonviscous compressible one-dimensional gas flow in a catalytic converter. Chemical reactions within the gas are included in the model. Well-posedness of the partial differential equations is analyzed together with stability of the numerical models. In particular an investigation is made of the effect of numerical dissipation and different boundary conditions. Numerical results are presented.

  • 18.
    Engquist, Björn
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Luo, Erding
    Erding New coarse grid operators for highly oscillatory coefficient elliptic problems1996In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 2, p. 296-306Article in journal (Refereed)
    Abstract [en]

    New coarse grid operators are developed for elliptic problems with highly oscillatory coefficients. The new coarse grid operators are constructed directly based on the homogenized differential operators or hierarchically computed from the finest grid. A detailed description of this construction is provided. Numerical calculations for a two dimensional elliptic model problem show that the homogenized form of the equations is very useful in the design of coarse grid operators for the multigrid method. A more realistic problem of heat conduction in a composite structure is also considered.

  • 19.
    Engquist, Björn
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Majda, A
    Numerical radiation boundary conditions for unsteady transonic flow1981In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 40, no 1, p. 91-103Article in journal (Refereed)
    Abstract [en]

    A family of numerical boundary conditions for far-field-computational boundaries in calculations involving unsteady transonic flow is devised. These boundary conditions are developed in a systematic fashion from general principles. Both numerical and analytic comparisons with other currently used methods are given.

  • 20.
    Engquist, Björn
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Osher, S
    One-sided difference approximations for nonlinear conservation laws1981In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 36, p. 321-351Article in journal (Refereed)
    Abstract [en]

    We analyze one-sided or upwind finite difference approximations to hyperbolic partial differential equations and, in particular, nonlinear conservation laws. Second order schemes are designed for which we prove both nonlinear stability and that the entropy condition is satisfied for limit solutions. We show that no such stable approximation of order higher than two is possible. These one-sided schemes have desirable properties for shock calculations. We show that the proper switch used to change the direction in the upwind differencing across a shock is of great importance. New and simple schemes are developed for which we prove qualitative properties such as sharp monotone shock profiles, existence, uniqueness, and stability of discrete shocks. Numerical examples are given.

  • 21.
    Engquist, Björn
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Runborg, Olof
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Tornberg, Anna Karin
    High-frequency wave propagation by the segment projection method2002In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 178, no 2, p. 373-390Article in journal (Refereed)
    Abstract [en]

    Geometrical optics is a standard technique used for the approximation of high-frequency wave propagation. Computational methods based on partial differential equations instead of the traditional ray tracing have recently been applied to geometrical optics. These new methods have a number of advantages but typically exhibit difficulties with linear superposition of waves. In this paper we introduce a new partial differential technique based on the segment projection method in phase space. The superposition problem is perfectly resolved and so is the problem of computing amplitudes in the neighborhood of caustics. The computational complexity is of the same order as that of ray tracing. The new algorithm is described and a number of computational examples are given. including a simulation of waveguides.

  • 22. Engquist, Björn
    et al.
    Tornberg, Anna-Karin
    Tsai, R.
    Discretization of Dirac delta functions in level set methods2005In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 207, no 1, p. 28-51Article in journal (Refereed)
    Abstract [en]

    Discretization of singular functions is an important component in many problems to which level set methods have been applied. We present two methods for constructing consistent approximations to Dirac delta measures concentrated on piecewise smooth curves or surfaces. Both methods are designed to be convenient for level set simulations and are introduced to replace the commonly used but inconsistent regularization technique that is solely based on a regularization parameter proportional to the mesh size. The first algorithm is based on a tensor product of regularized one-dimensional delta functions. It is independent of the irregularity relative to the grid. In the second method, the regularization is constructed from a one-dimensional regularization that is extended to multi-dimensions with a variable support depending on the orientation of the singularity relative to the computational grid. Convergence analysis and numerical results are given. © 2005 Published by Elsevier Inc.

  • 23. Fatemi, E
    et al.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Osher, S
    Numerical solution of the high frequency asymptotic expansion for the scalar wave equation1995In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 120, no 1, p. 145-155Article in journal (Refereed)
    Abstract [en]

    New numerical methods are derived for calculation of high frequency asymptotic expansion of the scalar wave equation. The nonlinear partial differential equations defining the terms in the expansion are approximated directly rather than via ray tracing, High resolution numerical algorithms are used to handle discontinuities and new devices are introduced to represent the multivalued character of the solution.

  • 24.
    Frachon, Thomas
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Zahedi, Sara
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    A cut finite element method for incompressible two-phase Navier–Stokes flows2019In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 384, p. 77-98Article in journal (Refereed)
    Abstract [en]

    We present a space–time Cut Finite Element Method (CutFEM) for the time-dependent Navier–Stokes equations involving two immiscible incompressible fluids with different viscosities, densities, and with surface tension. The numerical method is able to accurately capture the strong discontinuity in the pressure and the weak discontinuity in the velocity field across evolving interfaces without re-meshing processes or regularization of the problem. We combine the strategy proposed in P. Hansbo et al. (2014) [14] for the Stokes equations with a stationary interface and the space–time strategy presented in P. Hansbo et al. (2016) [20]. We also propose a strategy for computing high order approximations of the surface tension force by computing a stabilized mean curvature vector. The presented space–time CutFEM uses a fixed mesh but includes stabilization terms that control the condition number of the resulting system matrix independently of the position of the interface, ensure stability and a convenient implementation of the space–time method based on quadrature in time. Numerical experiments in two and three space dimensions show that the numerical method is able to accurately capture the discontinuities in the pressure and the velocity field across evolving interfaces without requiring the mesh to be conformed to the interface and with good stability properties.

  • 25.
    Fryklund, Fredrik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Lehto, Erik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Tornberg, Anna-Karin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Partition of unity extension of functions on complex domains2018In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 375, p. 57-79Article in journal (Refereed)
    Abstract [en]

    We introduce an efficient algorithm, called partition of unity extension or PUX, to construct an extension of desired regularity of a function given on a complex multiply connected domain in 2D. Function extension plays a fundamental role in extending the applicability of boundary integral methods to inhomogeneous partial differential equations with embedded domain techniques. Overlapping partitions are placed along the boundaries, and a local extension of the function is computed on each patch using smooth radial basis functions; a trivially parallel process. A partition of unity method blends the local extrapolations into a global one, where weight functions impose compact support. The regularity of the extended function can be controlled by the construction of the partition of unity function. We evaluate the performance of the PUX method in the context of solving the Poisson equation on multiply connected domains using a boundary integral method and a spectral solver. With a suitable choice of parameters the error converges as a tenth order method down to 10−14.

  • 26.
    Ge, Zhouyang
    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.
    Loiseau, Jean Christophe
    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. Arts et Métiers ParisTech, France.
    Tammisola, Outi
    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.
    Brandt, Luca
    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.
    An efficient mass-preserving interface-correction level set/ghost fluid method for droplet suspensions under depletion forces2018In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 353, p. 435-459Article in journal (Refereed)
    Abstract [en]

    Aiming for the simulation of colloidal droplets in microfluidic devices, we present here a numerical method for two-fluid systems subject to surface tension and depletion forces among the suspended droplets. The algorithm is based on an efficient solver for the incompressible two-phase Navier–Stokes equations, and uses a mass-conserving level set method to capture the fluid interface. The four novel ingredients proposed here are, firstly, an interface-correction level set (ICLS) method; global mass conservation is achieved by performing an additional advection near the interface, with a correction velocity obtained by locally solving an algebraic equation, which is easy to implement in both 2D and 3D. Secondly, we report a second-order accurate geometric estimation of the curvature at the interface and, thirdly, the combination of the ghost fluid method with the fast pressure-correction approach enabling an accurate and fast computation even for large density contrasts. Finally, we derive a hydrodynamic model for the interaction forces induced by depletion of surfactant micelles and combine it with a multiple level set approach to study short-range interactions among droplets in the presence of attracting forces.

  • 27.
    Gong, Jing
    et al.
    Uppsala Univ., IT dept..
    Nordström, Jan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering.
    A stable and efficient hybrid scheme for viscous problems in complex geometries2007In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 226, no 2, p. 1291-1309Article in journal (Refereed)
    Abstract [en]

    In this paper, we present a stable hybrid scheme for viscous problems. The hybrid method combines the unstructured finite volume method with high-order finite difference methods on complex geometries. The coupling procedure between the two numerical methods is based on energy estimates and stable interface conditions are constructed. Numerical calculations show that the hybrid method is efficient and accurate.

  • 28.
    Gotovac, Hrvoje
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
    Gotovac, Blaz
    Maximum entropy algorithm with inexact upper entropy bound based on Fup basis functions with compact support2009In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 228, no 24, p. 9079-9091Article in journal (Refereed)
    Abstract [en]

    The maximum entropy (MaxEnt) principle is a versatile tool for statistical inference of the probability density function (pdf) from its moments as a least-biased estimation among all other possible pdfs. It maximizes Shannon entropy, satisfying the moment constraints. Thus, the MaxEnt algorithm transforms the original constrained optimization problem to the unconstrained dual optimization problem using Lagrangian multipliers. The Classic Moment Problem (CMP) uses algebraic power moments, causing typical conventional numerical methods to fail for higher-order moments (m > 5-10) due to different sensitivities of Lagrangian multipliers and unbalanced nonlinearities. Classic MaxEnt algorithms overcome these difficulties by using orthogonal polynomials, which enable roughly the same sensitivity for all Lagrangian multipliers. In this paper, we employ an idea based on different principles, using Fup(n) basis functions with compact support, which can exactly describe algebraic polynomials, but only if the Fup order-n is greater than or equal to the polynomial's order. Our algorithm solves the CMP with respect to the moments of only low order Fup(2) basis functions, finding a Fup(2) optimal pdf with better balanced Lagrangian multipliers. The algorithm is numerically very efficient due to localized properties of Fup(2) basis functions implying a weaker dependence between Lagrangian multipliers and faster convergence. Only consequences are an iterative scheme of the algorithm where power moments are a sum of Fup(2) and residual moments and an inexact entropy upper bound. However, due to small residual moments, the algorithm converges very quickly as demonstrated on two continuous pdf examples - the beta distribution and a bi-modal pdf, and two discontinuous pdf examples - the step and double Dirac pdf. Finally, these pdf examples present that Fup MaxEnt algorithm yields smaller entropy value than classic MaxEnt algorithm, but differences are very small for all practical engineering purposes.

  • 29. Harten, A
    et al.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Osher, S
    Chakravarthy, S.R.
    Uniformly High Order Accurate Essentially Non-oscillatory Schemes, III1997In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 131, no 1, p. 3-47Article in journal (Refereed)
    Abstract [en]

    We continue the construction and the analysis of essentially non-oscillatory shock capturing methods for the approximation of hyperbolic conservation laws. We present an hierarchy of uniformly high-order accurate schemes which generalizes Godunov's scheme and its second-order accurate MUSCL extension to an arbitrary order of accuracy. The design involves an essentially non-oscillatory piecewise polynomial reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell. The reconstruction algorithm is derived from a new interpolation technique that, when applied to piecewise smooth data, gives high-order accuracy whenever the function is smooth but avoids a Gibbs phenomenon at discontinuities. Unlike standard finite difference methods this procedure uses an adaptive stencil of grid points and, consequently, the resulting schemes are highly nonlinear.

  • 30. Innocenti, M. E.
    et al.
    Beck, A.
    Markidis, Stefano
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for High Performance Computing, PDC.
    Lapenta, G.
    Momentum conservation in Multi-Level Multi-Domain (MLMD) simulations2016In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 312, p. 14-18Article in journal (Refereed)
    Abstract [en]

    Momentum conservation and self-forces reduction are challenges for all Particle-In-Cell (PIC) codes using spatial discretization schemes which do not fulfill the requirement of translational invariance of the grid Green's function. We comment here on the topic applied to the recently developed Multi-Level Multi-Domain (MLMD) method. The MLMD is a semi-implicit method for PIC plasma simulations. The multi-scale nature of plasma processes is addressed by using grids with different spatial resolutions in different parts of the domain.

  • 31. Innocenti, M. E.
    et al.
    Lapenta, G.
    Markidis, Stefano
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for High Performance Computing, PDC.
    Beck, A.
    Vapirev, A.
    A Multi Level Multi Domain Method for Particle In Cell plasma simulations2013In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 238, p. 115-140Article in journal (Refereed)
    Abstract [en]

    A novel adaptive technique for electromagnetic Particle In Cell (PIC) plasma simulations is presented here. Two main issues are identified as regards the development of the algorithm. First, the choice of the size of the particle shape function in progressively refined grids, with the decision to avoid both time-dependent shape functions and cumbersome particle-to-grid interpolation techniques, and, second, the necessity to comply with the strict stability constraints of the explicit PIC algorithm. The adaptive implementation presented responds to these demands with the introduction of a Multi Level Multi Domain (MLMD) system, where a cloud of self-similar domains is fully simulated with both fields and particles, and the use of an Implicit Moment PIC method as baseline algorithm for the adaptive evolution. Information is exchanged between the levels with the projection of the field information from the refined to the coarser levels and the interpolation of the boundary conditions for the refined levels from the coarser level fields. Particles are bound to their level of origin and are prevented from transitioning to coarser levels, but are repopulated at the refined grid boundaries with a splitting technique. The presented algorithm is tested against a series of simulation challenges.

  • 32.
    Johnsson, Lennart
    et al.
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for High Performance Computing, PDC.
    Jacquemin, Michael
    Krawitz, Robert L.
    Communication Efficient Multi–Processor FFT1992In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 102, no 2, p. 381-397Article in journal (Refereed)
    Abstract [en]

    Computing the fast Fourier transform on a distributed memory architecture by a direct pipelined radix-2, a bi-section, or a multisection algorithm, all yield the same communications requirement, if communication for all FFT stages can be performed concurrently, the input data is in normal order, and the data allocation is consecutive. With a cyclic data allocation, or bit-reversed input data and a consecutive allocation, multi-sectioning offers a reduced communications requirement by approximately a factor of two. For a consecutive data allocation, normal input order, a decimation-in-time FFT requires that P/N + d−2 twiddle factors be stored for P elements distributed evenly over N processors, and the axis that is subject to transformation be distributed over 2d processors. No communication of twiddle factors is required. The same storage requirements hold for a decimation-in-frequency FFT, bit-reversed input order, and consecutive data allocation. The opposite combination of FFT type and data ordering requires a factor of log2N more storage for N processors. The peak performance for a Connection Machine system CM-200 implementation is 12.9 Gflops/s in 32-bit precision, and 10.7 Gflops/s in 64-bit precision for unordered transforms local to each processor. The corresponding execution rates for ordered transforms are 11.1 Gflops/s and 8.5 Gflops/s, respectively. For distributed one- and two-dimensional transforms the peak performance for unordered transforms exceeds 5 Gflops/s in 32-bit precision and 3 Gflops/s in 64-bit precision. Three-dimensional transforms execute at a slightly lower rate. Distributed ordered transforms execute at a rate of about 1/2 to 2/3 of the unordered transforms.

  • 33. Kanevsky, Alex
    et al.
    Shelley, Michael J.
    Tornberg, Anna-Karin
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Modeling simple locomotors in Stokes flow2010In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 229, no 4, p. 958-977Article in journal (Refereed)
    Abstract [en]

    Motivated by the locomotion of flagellated micro-organisms and by recent experiments of chemically driven nanomachines, we study the dynamics of bodies of simple geometric shape that are propelled by specified tangential surface stresses. We develop a mathematical description of the body dynamics based on a mixed-type boundary integral formulation. We also derive analytic axisymmetric solutions for the case of a single locomoting sphere and ellipsoid based on spherical and ellipsoidal harmonics, and compare our numerical results to these. The hydrodynamic interactions between two spherical and ellipsoidal swimmers in an infinite fluid are then simulated using second-order accurate spatial and temporal discretizations. We find that the near-field interactions result in complex and interesting changes in the locomotors' orientations and trajectories. Stable as well as unstable pairwise swimming motions are observed, similar to the recent findings of Pooley et al. [C.M. Pooley, G.P. Alexander, J.M. Yeomans, Hydrodynamic interaction between two swimmers at low Reynolds number, Phys. Rev. Lett. 99 (2007) 228103].

  • 34. Khatri, Shilpa
    et al.
    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.
    An embedded boundary method for soluble surfactants with interface tracking for two-phase flows2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 256, p. 768-790Article in journal (Refereed)
    Abstract [en]

    Surfactants, surface reacting agents, lower the surface tension of the interface between fluids in multiphase flow. This capability of surfactants makes them ideal for many applications, including wetting, foaming, and dispersing. Due to their molecular composition, surfactants are adsorbed from the bulk fluid to the interface between the fluids, leading to different concentrations on the interface and in the fluid. In a previous paper [21], we introduced a new second order method using uniform grids to simulate insoluble surfactants in multiphase flow. This method used Strang splitting allowing for a fully second order treatment in time. Here, we use the same numerical methods to explicitly represent the singular interface, treat the interfacial surfactant concentration, and couple with the Navier-Stokes equations. Now, we introduce a second order method for the surfactants in the bulk that continues to allow the use of regular grids for the full problem. Difficulties arise since the boundary condition for the bulk concentration, which handles the flux of surfactant between the interface and bulk fluid, is applied at the interface which cuts arbitrarily through the regular grid. We extend the embedded boundary method, introduced in [22], to handle this challenge. Through our results, we present the effect of the solubility of the surfactants. We show results of drop dynamics due to resulting Marangoni stresses and of drop deformations in shear flow in the presence of soluble surfactants. There is a large nondimensional parameter space over which we try to understand the drop dynamics.

  • 35.
    Lacis, Ugis
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Taira, Kunihiko
    Bagheri, Shervin
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    A stable fluid-structure-interaction solver for low-density rigid bodies using the immersed boundary projection method2016In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 305, p. 300-318Article in journal (Refereed)
    Abstract [en]

    Dispersion of low-density rigid particles with complex geometries is ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newton's equations of motion are often sufficient to solve for the motion of cylindrical particles with low density ratios, for more complex particles - such as a body with a protrusion - they become unstable. We present an implicit formulation of the coupling between rigid body dynamics and fluid dynamics within the framework of the immersed boundary projection method. Similarly to previous work on this method, the resulting matrix equation in the present approach is solved using a block-LU decomposition. Each step of the block-LU decomposition is modified to incorporate the rigid body dynamics. We show that our method achieves second-order accuracy in space and first-order in time (third-order for practical settings), only with a small additional computational cost to the original method. Our implicit coupling yields stable solution for density ratios as low as 10(-4). We also consider the influence of fictitious fluid located inside the rigid bodies on the accuracy and stability of our method.

  • 36.
    Lenaers, Peter
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Mechanics of Industrial Processes. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Brethouwer, Geert
    KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Johansson, Arne
    KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    A new high-order method for the simulation of incompressible wall-bounded turbulent flows2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 272, p. 108-126Article in journal (Refereed)
    Abstract [en]

    A new high-order method for the accurate simulation of incompressible wall-bounded flows is presented. In the stream- and spanwise directions the discretisation is performed by standard Fourier series, while in the wall-normal direction the method combines high-order collocated compact finite differences with the influence matrix method to calculate the pressure boundary conditions that render the velocity field exactly divergence-free. The main advantage over Chebyshev collocation is that in wall-normal direction, the grid can be chosen freely and thus excessive clustering near the wall is avoided. This can be done while maintaining the high-order approximation as offered by compact finite differences. The discrete Poisson equation is solved in a novel way that avoids any full matrices and thus improves numerical efficiency. Both explicit and implicit discretisations of the viscous terms are described, with the implicit method being more complex, but also having a wider range of applications. The method is validated by simulating two-dimensional Tollmien-Schlichting waves, forced transition in turbulent channel flow, and fully turbulent channel flow at friction Reynolds number Re-tau = 395, and comparing our data with analytical and existing numerical results. In all cases, the results show excellent agreement showing that the method simulates all physical processes correctly.

  • 37.
    Lin, Zhili
    et al.
    KTH, School of Information and Communication Technology (ICT), Microelectronics and Applied Physics, MAP.
    Thylén, Lars
    KTH, School of Information and Communication Technology (ICT), Microelectronics and Applied Physics, MAP. KTH, School of Information and Communication Technology (ICT), Centres, Zhejiang-KTH Joint Research Center of Photonics, JORCEP.
    An analytical derivation of the optimum source patterns for the pseudospectral time-domain method2009In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 228, no 19, p. 7375-7387Article in journal (Refereed)
    Abstract [en]

    In the computational electromagnetics and acoustics, spatially smoothed sources are often utilized to alleviate the aliasing errors in the pseudospectral time-domain (PSTD) algorithms. In our work, an analytical derivation of the optimum source patterns is presented according to the accurately derived expressions of the dominant source-introduced aliasing errors according to the circular discrete convolution and Tailor series expansion method. We quantitatively demonstrate, for the first time in literature, that the aliasing errors can be optimally suppressed and rapidly reduced to the negligible levels by these optimum patterns and with the increment of source cells. We also provide the different implementation schemes of the optimal patterns both for the soft and hard source cases. The numerical calculation and 1D PSTD transient simulations are conducted to verify the excellent performance of these optimum sources.

  • 38.
    Lindbo, Dag
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Tornberg, Anna-Karin
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Spectral accuracy in fast Ewald-based methods for particle simulations2011In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, no 24, p. 8744-8761Article in journal (Refereed)
    Abstract [en]

    A spectrally accurate fast method for electrostatic calculations under periodic boundary conditions is presented. We follow the established framework of FFT-based Ewald summation, but obtain a method with an important decoupling of errors: it is shown, for the proposed method, that the error due to frequency domain truncation can be separated from the approximation error added by the fast method. This has the significance that the truncation of the underlying Ewald sum prescribes the size of the grid used in the FFT-based fast method, which clearly is the minimal grid. Both errors are of exponential-squared order, and the latter can be controlled independently of the grid size. We compare numerically to the established SPME method by Essmann et al. and see that the memory required can be reduced by orders of magnitude. We also benchmark efficiency (i.e. error as a function of computing time) against the SPME method, which indicates that our method is competitive. Analytical error estimates are proven and used to select parameters with a great degree of reliability and ease.

  • 39.
    Lindbo, Dag
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Tornberg, Anna-Karin
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Spectrally accurate fast summation for periodic Stokes potentials2010In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 229, no 23, p. 8994-9010Article in journal (Refereed)
    Abstract [en]

    A spectrally accurate method for the fast evaluation of N-particle sums of the periodic Stokeslet is presented. Two different decomposition methods, leading to one sum in real space and one in reciprocal space, are considered. An FFT based method is applied to the reciprocal part of the sum, invoking the equivalence of multiplications in reciprocal space to convolutions in real space, thus using convolutions with a Gaussian function to place the point sources on a grid. Due to the spectral accuracy of the method, the grid size needed is low and also in practice, for a fixed domain size, independent of N. The leading cost, which is linear in N, arises from the to-grid and from-grid operations. Combining this FFT based method for the reciprocal sum with the direct evaluation of the real space sum, a spectrally accurate algorithm with a total complexity of 0(N log N) is obtained. This has been shown numerically as the system is scaled up at constant density. (C) 2010 Elsevier Inc. All rights reserved.

  • 40. Lorstad, D.
    et al.
    Fuchs, Laszlo
    High-order surface tension VOF-model for 3D bubble flows with high density ratio2004In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 200, no 1, p. 153-176Article in journal (Refereed)
    Abstract [en]

    An improved Volume of Fluid (VOF) method is presented which is applicable to high density ratio 3D flows for a large range of bubble Reynolds number (Re). The method is based on the Navier-Stokes equations for incompressible multi-phase flows which are discretized on a Cartesian staggered grid. The multi-grid technique together with the pressure-velocity coupling scheme for multi-phase flows have resulted in an efficient solver which nearly exponentially converge with the number of iterations. The convergence speed also shows negligible dependence on density ratio, viscosity ratio and Re. A second-order accurate, non-diffusive, mass conservative phase transport model is presented which does not suffer from unphysical over- or under-shoots of the phase variable. The high accurate normal, curvature and surface tension force model in combination with the high-order defect-correction scheme for multi-phase flows shows second-order global accuracy when applied to the transient bubble rise where the viscosity ratio is equal to one. In contrast, the commonly used viscosity model for VOF introduces a first order error for the same problem. The VOF method has been tested for different types of bubble flows at low Re and for path-oscillating and wobbling air bubbles (in water) with a diameter range of 1.82 < D < 6 mm. The numerical results agree quantitatively with the available experimental data. The investigations show that the proposed high accurate surface tension model can be used successfully for wobbling flows with bubble deformation while maintaining the mass of the phases. The error in mass conservation is directly proportional to the residual in solving the discrete problem.

  • 41. Manzini, G.
    et al.
    Delzanno, G. L.
    Vencels, J.
    Markidis, Stefano
    KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST).
    A Legendre-Fourier spectral method with exact conservation laws for the Vlasov-Poisson system2016In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 317, p. 82-107Article in journal (Refereed)
    Abstract [en]

    We present the design and implementation of an L-2-stable spectral method for the discretization of the Vlasov-Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank-Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations is iteratively solved at any time cycle by a Jacobian-Free Newton-Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre-Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L-2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.

  • 42.
    Markidis, Stefano
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Henri, Pierre
    Lapenta, Giovanni
    Ronnmark, Kjell
    Hamrin, Maria
    Meliani, Zakaria
    Laure, Erwin
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    The Fluid-Kinetic Particle-in-Cell method for plasma simulations2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 271, p. 415-429Article in journal (Refereed)
    Abstract [en]

    A method that solves concurrently the multi-fluid and Maxwell's equations has been developed for plasma simulations. By calculating the stress tensor in the multi-fluid momentum equation by means of computational particles moving in a self-consistent electromagnetic field, the kinetic effects are retained while solving the multi-fluid equations. The Maxwell's and multi-fluid equations are discretized implicitly in time enabling kinetic simulations over time scales typical of the fluid simulations. The Fluid-Kinetic Particle-in-Cell method has been implemented in a three-dimensional electromagnetic code, and tested against the two-stream instability, the Weibel instability, the ion cyclotron resonance and magnetic reconnection problems. The method is a promising approach for coupling fluid and kinetic methods in a unified framework.

  • 43.
    Motamed, Mohammad
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Runborg, Olof
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    A fast phase space method for computing creeping rays2006In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 219, no 1, p. 276-295Article in journal (Refereed)
    Abstract [en]

    Creeping rays can give an important contribution to the solution of medium to high frequency scattering problems. They are generated at the shadow lines of the illuminated scatterer by grazing incident rays and propagate along geodesics on the scatterer surface, continuously shedding diffracted rays in their tangential direction. In this paper, we show how the ray propagation problem can be formulated as a partial differential equation (PDE) in a three-dimensional phase space. To solve the PDE we use a fast marching method. The PDE solution contains information about all possible creeping rays. This information includes the phase and amplitude of the field, which are extracted by a fast post-processing. Computationally, the cost of solving the PDE is less than tracing all rays individually by solving a system of ordinary differential equations. We consider an application to mono-static radar cross section problems where creeping rays from all illumination angles must be computed. The numerical results of the fast phase space method and a comparison with the results of ray tracing are presented.

  • 44.
    Nguyen, Van Dang
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Jansson, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Hoffman, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computational Science and Technology (CST).
    Li, Jing-Rebecca
    INRIA Saclay-Equipe DEFI, CMAP, Ecole Polytechnique Route de Saclay, 91128, Palaiseau Cedex, France.
    A partition of unity finite element method for computational diffusion MRI2018In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 375, p. 271-290Article in journal (Refereed)
    Abstract [en]

    The Bloch–Torrey equation describes the evolution of the spin (usually water proton) magnetization under the influence of applied magnetic field gradients and is commonly used in numerical simulations for diffusion MRI and NMR. Microscopic heterogeneity inside the imaging voxel is modeled by interfaces inside the simulation domain, where a discontinuity in the magnetization across the interfaces is produced via a permeability coefficient on the interfaces. To avoid having to simulate on a computational domain that is the size of an entire imaging voxel, which is often much larger than the scale of the microscopic heterogeneity as well as the mean spin diffusion displacement, smaller representative volumes of the imaging medium can be used as the simulation domain. In this case, the exterior boundaries of a representative volume either must be far away from the initial positions of the spins or suitable boundary conditions must be found to allow the movement of spins across these exterior boundaries.

    Many approaches have been taken to solve the Bloch–Torrey equation but an efficient high-performance computing framework is still missing. In this paper, we present formulations of the interface as well as the exterior boundary conditions that are computationally efficient and suitable for arbitrary order finite elements and parallelization. In particular, the formulations are based on the partition of unity concept which allows for a discontinuous solution across interfaces conforming with the mesh with weak enforcement of real (in the case of interior interfaces) and artificial (in the case of exterior boundaries) permeability conditions as well as an operator splitting for the exterior boundary conditions. The method is straightforward to implement and it is available in FEniCS for moderate-scale simulations and in FEniCS-HPC for large-scale simulations. The order of accuracy of the resulting method is validated in numerical tests and a good scalability is shown for the parallel implementation. We show that the simulated dMRI signals offer good approximations to reference signals in cases where the latter are available and we performed simulations for a realistic model of a neuron to show that the method can be used for complex geometries.

  • 45.
    Nguyen, Van Dang
    et al.
    Ecole Polytechnique, France.
    Li, Jing-Rebecca
    Grebenkov, Denis
    Le Bihan, Denis
    A finite element method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 263, p. 283-302Article in journal (Refereed)
    Abstract [en]

    The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch-Torrey partial differential equation (PDE). In addition, steady-state Laplace PDEs can be formulated to produce the homogenized diffusion tensor that describes the diffusion characteristics of the medium in the long time limit. In spatial domains that model biological tissues at the cellular level, these two types of PDEs have to be completed with permeability conditions on the cellular interfaces. To solve these PDEs, we implemented a finite elements method that allows jumps in the solution at the cell interfaces by using double nodes. Using a transformation of the Bloch-Torrey PDE we reduced oscillations in the searched-for solution and simplified the implementation of the boundary conditions. The spatial discretization was then coupled to the adaptive explicit Runge-Kutta-Chebyshev time-stepping method. Our proposed method is second order accurate in space and second order accurate in time. We implemented this method on the FEniCS C++ platform and show time and spatial convergence results. Finally, this method is applied to study some relevant questions in diffusion MRI.

  • 46. Nordström, Jan
    et al.
    Gong, Jing
    Uppsala Univ..
    A stable hybrid method for hyperbolic problems2006In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 212, no 2, p. 436-453Article in journal (Refereed)
    Abstract [en]

    A stable hybrid method for hyperbolic problems that combines the unstructured finite volume method with high-order finite difference methods has been developed. The coupling procedure is based on energy estimates and stability can be guaranteed. Numerical calculations verify that the hybrid method is efficient and accurate.

  • 47. Nordström, Jan
    et al.
    Gong, Jing
    Uppsala Univ., IT dept..
    van der Weide, Edwin
    Svärd, Magnus
    A stable and conservative high order multi-block method for the compressible Navier-Stokes equations2009In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 228, no 24, p. 9020-9035Article in journal (Refereed)
    Abstract [en]

    A stable and conservative high order multi-block method for the time-dependent compressible Navier-Stokes equations has been developed. Stability and conservation are proved using summation-by-parts operators, weak interface conditions and the energy method. This development makes it possible to exploit the efficiency of the high order finite difference method for non-trivial geometries. The computational results corroborate the theoretical analysis.

  • 48.
    Nordström, Jan
    et al.
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering.
    Mattsson, Ken
    Swanson, Charles
    Boundary conditions for a divergence free velocity-pressure formulation of the Navier-Stokes equations2007In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 225, no 1, p. 874-890Article in journal (Refereed)
    Abstract [en]

    New sets of boundary conditions for the velocity-pressure formulation of the incompressible Navier-Stokes equations are derived. The boundary conditions have the same form on both inflow and outflow boundaries and lead to a divergence free solution. Moreover, the specific form of the boundary condition makes it possible derive a symmetric positive definite equation system for the internal pressure. Numerical experiments support the theoretical conclusions.

  • 49. Noullez, A.
    et al.
    Fanelli, D.
    Aurell, Erik
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    A heap-based algorithm for the study of one-dimensional particle systems2003In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 186, no 2, p. 697-703Article in journal (Refereed)
  • 50. Nourgaliev, R. R.
    et al.
    Dinh, Truc-Nam
    KTH, School of Engineering Sciences (SCI), Physics, Nuclear Power Safety.
    Theofanous, T. G.
    Adaptive characteristics-based matching for compressible multifluid dynamics2006In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 213, no 2, p. 500-529Article in journal (Refereed)
    Abstract [en]

    This paper presents an evolutionary step in sharp capturing of shocked, high acoustic impedance mismatch (AIM) interfaces in an adaptive mesh refinement (AMR) environment. The central theme which guides the present development addresses the need to optimize between the algorithmic complexities in advanced front capturing and front tracking methods developed recently for high AIM interfaces with the simplicity requirements imposed by the AMR multi-level dynamic solutions implementation. The paper shows that we have achieved this objective by means of relaxing the strict conservative treatment of AMR prolongation/restriction operators in the interfacial region and by using a natural-neighbor-interpolation (NNI) algorithm to eliminate the need for ghost cell extrapolation into the other fluid in a characteristics-based matching (CBM) scheme. The later is based on a two-fluid Riemann solver, which brings the accuracy and robustness of front-tracking approach into the fast local level set front-capturing implementation of the CBM method. A broad set of test problems (including shocked multi-gaseous media, bubble collapse, underwater explosion and shock passing over a liquid drop suspended in a gaseous medium) was performed and the results demonstrate that the fundamental assumptions/approximations made in modifying the AMR prolongation/restriction operators and in using the NNI algorithm for interfacial treatment are acceptable from the accuracy point of view, while they enable an effective implementation and utility of the structured AMR technology for solving complex multiphase problems in a highly compressible setting.

12 1 - 50 of 80
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf