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  • 101.
    Engquist, Björn
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Runborg, O
    Wavelet-based numerical homogenisation with applications2001Ingår i: Lecture notes in computational science and engineering, Vol. 20, s. 97-148Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Classical homogenization is an analytic technique for approximating multiscale differential equations. The numbers of scales are reduced and the resulting equations are easier to analyze or numerically approximate. The class of problems that classical homogenization applies to is quite restricted. We shall describe a numerical procedure for homogenization, which starts from a discretization of the multiscale differential equation. In this procedure the discrete operator is represented in a wavelet space and projected onto a coarser subspace. The wavelet homogenization applies to a wider class of problems than classical homogenization. The projection procedure is general and we give a presentation of a framework in Hilbert space, which also applies to the differential equation directly. The wavelet based homogenization technique is applied to discretizations of the Helmholtz equation. In one problem from electromagnetic compatibility a subgrid scale geometrical detail is represented on a coarser grid. In another a wave-guide filter is efficiently approximated in a lower dimension. The technique is also applied to the derivation of effective equations for a nonlinear problem and to the derivation of coarse grid operators in multigrid. These multigrid methods work very well for equations with highly oscillatory or discontinuous coefficients

  • 102.
    Engquist, Björn
    et al.
    Department of Mathematics, The University of Texas at Austin, Austin, USA.
    Runborg, Olof
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Wavelet based numerical homogenization2009Ingår i: Highly Oscillatory Problems / [ed] Bjorn Engquist, Athanasios Fokas, Ernst Hairer, Arieh Iserles, Cambridge University Press, 2009, s. 98-126Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    We consider multiscale differential equations in which the operator varies rapidly over fine scales. Direct numerical simulation methods need to resolve the small scales and they therefore become very expensive for such problems when the computational domain is large. Inspired by classical homogenization theory, we describe a numerical procedure for homogenization, which starts from a fine discretization of a multiscale differential equation, and computes a discrete coarse grid operator which incorporates the influence of finer scales. In this procedure the discrete operator is represented in a wavelet space, projected onto a coarser subspace and approximated by a banded or block-banded matrix. This wavelet homogenization applies to a wider class of problems than classical homogenization. The projection procedure is general and we give a presentation of a framework in Hilbert spaces, which also applies to the differential equation directly. We show numerical results when the wavelet based homogenization technique is applied to discretizations of elliptic and hyperbolic equations, using different approximation strategies for the coarse grid operator.

  • 103.
    Engquist, Björn
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Runborg, Olof
    KTH, Tidigare Institutioner, Numerisk analys och datalogi, NADA.
    Tornberg, Anna Karin
    High-frequency wave propagation by the segment projection method2002Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 178, nr 2, s. 373-390Artikel i tidskrift (Refereegranskat)
    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.

  • 104.
    Engquist, Björn
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Schmidt, W
    Mathematics Unlimited: 2001 and Beyond2000Bok (Refereegranskat)
    Abstract [en]

    This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty. Limited collector's edition - an exclusive and timeless work. This special, numbered edition will be available until June 1, 2000. Firm orders only.

  • 105.
    Engquist, Björn
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Sjögreen, B
    High Order shock capturing methods1995Ingår i: Computational Fluid Dynamics Review, John Wiley & Sons, 1995, s. 210-233Kapitel i bok, del av antologi (Refereegranskat)
  • 106.
    Engquist, Björn
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Sjögreen, B
    The convergence rate of finite difference schemes in the presence of shocks1998Ingår i: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 35, nr 6, s. 2464-2485Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    : Finite difference approximations generically have O(1) pointwise errors close to a shock. We show that this local error may effect the smooth part of the solution such that only first order is achieved even for formally higher-order methods. Analytic and numerical examples of this form of accuracy are given. We also show that a converging method will have the formal order of accuracy in domains where no characteristics have passed through a shock.

  • 107.
    Engquist, Björn
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Smedsaas, T
    A system for automatic code generation for hyperbolic problems1975Ingår i: Signum Newsletter, Vol. 10, s. 20-22Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    DCG is a program which generates FORTRAN code for difference approximations from a mathematical specification of a hyperbolic system. In our system the user presents his problem in a mathematical notation. DCG analyses the problem, chooses algorithms and generates a complete program for the numerical integration. The main parts of DCG are a program for symbolic analysis, “the analyser”, a library of FORTRAN-code and a program, “the synthesiser” that composes a complete FORTRAN program using code from the library.

  • 108.
    Engquist, Björn
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Smedsaas, T
    Automatic analysis in PDE software1984Konferensbidrag (Refereegranskat)
  • 109.
    Engquist, Björn
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Smedsaas, T
    Automatic computer code generation for hyperbolic and parabolic differential equations1980Ingår i: SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, ISSN 0196-5204, Vol. 1, nr 2, s. 249-259Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A program system which generates computer code for the numerical solution of systems of hyperbolic and parabolic differential equations is described. The input to the program is a mathematical formulation of a hyperbolic or parabolic initial boundary value problem in one space dimension. The differential equations and boundary conditions are analyzed by the program system, and a finite difference algorithm is designed for the given problem. The output is an executable FORTRAN program.

  • 110.
    Engquist, Björn
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Smedsaas, T
    PDE software: modules, interfaces and systems: Proceedings of the third IFIP TC2 working conference held in Soderkoping1984Bok (Refereegranskat)
  • 111.
    Engquist, Björn
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Tornberg, Anna Karin
    A finite element based level-set method for multi-phase flow, Proceedings of Conference on Progress in Numerical Solutions of Partial Differential Equations2002Ingår i: Scientific World Journal, ISSN 1537-744X, E-ISSN 1537-744X, s. 86-110Artikel i tidskrift (Refereegranskat)
  • 112.
    Engquist, Björn
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Weinan, E
    Large time behavior and homogenization of solutions of two-dimensional conservation laws1993Ingår i: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312, Vol. 46, nr 1, s. 1-26Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the large time behavior of solutions of scalar conservation laws in one and two space dimensions with periodic initial data. Under a very weak nonlinearity condition, we prove that the solutions converge to constants as time goes to infinity. Even in one space dimension our results improve the earlier ones since we only require the fluxes to be nonlinear in a neighborhood of the mean value of the initial data. We then use these results to study the homogenization problem for scalar conservation laws with oscillatory initial data.

  • 113.
    Engquist, Björn
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Ying, Lexing
    Fast directional multilevel computation for problems with oscillatory kernels2007Ingår i: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, s. 1710-1737Artikel i tidskrift (Refereegranskat)
  • 114.
    Engquist, Björn
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Ying, Lexing
    Fast directional multilevel computation for problems with oscillatory kernels2007Ingår i: Proceeding in Appl. Math. And Mech., 2007Konferensbidrag (Refereegranskat)
  • 115.
    Engquist, Björn
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Zhao, H-K
    Absorbing boundary conditions for domain decomposition1998Ingår i: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 27, nr 4, s. 315-324Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we would like to point out some similarities between two artificial boundary conditions. One is the far field or absorbing boundary conditions for computations over unbounded domain. The other is the boundary conditions used at the boundary between subdomains in domain decomposition. We show some convergence result for the generalized Schwarz alternating method (GSAM), in which a convex combination of Dirichlet data and Neumann data is exchanged at the artificial boundary. We can see clearly how the mixed boundary condition and the relative size of overlap will affect the convergence rate. These results can be extended to more general coercive elliptic partial differential equations using the equivalence of elliptic operators. Numerically first- and second-order approximations of the Dirichlet-to-Neumann operator are constructed using local operators, where information tangential to the boundary is included. Some other possible extensions and applications are pointed out. Finally numerical results are presented.

  • 116.
    Engquist, Björn
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Zhao, H-K
    Absorbing boundary conditions for domain decomposition1998Ingår i: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 27, nr 4, s. 341-365Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we would like to point out some similarities between two artificial boundary conditions. One is the far field or absorbing boundary conditions for computations over unbounded domain. The other is the boundary conditions used at the boundary between subdomains in domain decomposition. We show some convergence result for the generalized Schwarz alternating method (GSAM), in which a convex combination of Dirichlet data and Neumann data is exchanged at the artificial boundary. We can see clearly how the mixed boundary condition and the relative size of overlap will affect the convergence rate. These results can be extended to more general coercive elliptic partial differential equations using the equivalence of elliptic operators. Numerically first- and second-order approximations of the Dirichlet-to-Neumann operator are constructed using local operators, where information tangential to the boundary is included. Some other possible extensions and applications are pointed out. Finally numerical results are presented.

  • 117. Fatemi, E
    et al.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Osher, S
    Finite difference methods for the nonlinear equations of perturbed geometrical optics1996Ingår i: ACES J, Vol. 11, s. 90-98Artikel i tidskrift (Refereegranskat)
  • 118. Fatemi, E
    et al.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Osher, S
    Numerical solution of the high frequency asymptotic expansion for the scalar wave equation1995Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 120, nr 1, s. 145-155Artikel i tidskrift (Refereegranskat)
    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.

  • 119.
    Gallouët, Thierry
    et al.
    Université de Provence.
    Larcher, Aurélien
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Latché, Jean-Claude
    Institut de Sûreté et de Radioprotection Nucléaire.
    Convergence of a finite volume scheme for the convection-diffusion equation with L1 data2012Ingår i: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 81, nr 279, s. 1429-1454Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we prove the convergence of a finite-volume schemefor the time-dependent convection–diffusion equation with an L1 right-handside. To this purpose, we first prove estimates for the discrete solution andfor its discrete time and space derivatives. Then we show the convergence of asequence of discrete solutions obtained with more and more refined discretiza-tions, possibly up to the extraction of a subsequence, to a function which metsthe regularity requirements of the weak formulation of the problem; to thispurpose, we prove a compactness result, which may be seen as a discrete ana-logue to Aubin-Simon’s lemma. Finally, such a limit is shown to be indeed aweak solution.

  • 120. Gottschling, Peter
    et al.
    Lindbo, Dag
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Generic compressed sparse matrix insertion: algorithms and implementations in MTL4 and FEniCS2009Ingår i: Proceedings of the 8th workshop on Parallel/High-Performance Object-Oriented Scientific Computing, 2009, s. 2-1Konferensbidrag (Refereegranskat)
    Abstract [en]

    Sparse matrices are indispensable components of most scientific applications. Nevertheless, there is very little general-purpose software support. With the Matrix Template Library 4 (MTL4) we provide a generic library support for dense and compressed sparse matrices. The first challenge in working with compressed matrices is how to set the nonzero entries in an efficient manner. The implementation in MTL4 does not need any pre-allocation or pre-sorting phase, uses a minimal amount of memory and was in all measures as fast or faster than comparable libraries. We demonstrate the performance on well-defined benchmarks.

  • 121. Guermond, Jean-Luc
    et al.
    Nazarov, Murtazo
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Popov, Bojan
    Implementation of the entropy viscosity method2011Rapport (Övrigt vetenskapligt)
  • 122.
    Gustavsson, Katarina
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Oppelstrup, Jesper
    Consolidation of concentrated suspensions - numerical simulations using a two-phase fluid model2000Ingår i: Computing and Visualization in Science, ISSN 1432-9360, E-ISSN 1433-0369, Vol. 3, s. 39-45Artikel i tidskrift (Refereegranskat)
  • 123.
    Gustavsson, Katarina
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Oppelstrup, Jesper
    Eiken, Jon
    Consolidation of concentrated suspensions - shear and irreversible floc structure rearrangement2001Ingår i: Computing and Visualization in Science, ISSN 1432-9360, E-ISSN 1433-0369, Vol. 4, s. 61-66Artikel i tidskrift (Refereegranskat)
  • 124.
    Gustavsson, Katarina
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Tornberg, Anna Karin
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Numerical Simulations of Rigid Fiber Suspensions2008Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, we present a numerical method designed to simulate the

    challenging problem of the dynamics of slender fibers immersed in an incompressible

    fluid. Specifically, we consider microscopic, rigid fibers, that

    sediment due to gravity. Such fibers make up the micro-structure of many

    suspensions for which the macroscopic dynamics are not well understood.

    Our numerical algorithm is based on a non-local slender body approximation

    that yields a system of coupled integral equations, relating the forces

    exerted on the fibers to their velocities, which takes into account the hydrodynamic

    interactions of the fluid and the fibers. The system is closed by

    imposing the constraints of rigid body motions.

    The fact that the fibers are straight have been further exploited in the

    design of the numerical method, expanding the force on Legendre polynomials

    to take advantage of the specific mathematical structure of a finite-part

    integral operator, as well as introducing analytical quadrature in a manner

    possible only for straight fibers.

    We have carefully treated issues of accuracy, and present convergence

    results for all numerical parameters before we finally discuss the results from

    simulations including a larger number of fibers.

  • 125.
    Gustavsson, Katarina
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW.
    Tornberg, Anna-Karin
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW.
    Gravity induced sedimentation of slender fibers2009Ingår i: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 21, nr 12Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Gravity induced sedimentation of slender, rigid fibers in a highly viscous fluid is investigated by large scale numerical simulations. The fiber suspension is considered on a microscopic level and the flow is described by the Stokes equations in a three dimensional periodic domain. Numerical simulations are performed to study in great detail the complex dynamics of a cluster of fibers. A repeating cycle is identified. It consists of two main phases: a densification phase, where the cluster densifies and grows, and a coarsening phase, during which the cluster becomes smaller and less dense. The dynamics of these phases and their relation to fluctuations in the sedimentation velocity are analyzed. Data from the simulations are also used to investigate how average fiber orientations and sedimentation velocities are influenced by the microstructure in the suspension. The dynamical behavior of the fiber suspension is very sensitive to small random differences in the initial configuration and a number of realizations of each numerical experiment are performed. Ensemble averages of the sedimentation velocity and fiber orientation are presented for different values of the effective concentration of fibers and the results are compared to experimental data. The numerical code is parallelized using the Message Passing Instructions (MPI) library and numerical simulations with up 800 fibers can be run for very long times which is crucial to reach steady levels of the averaged quantities. The influence of the periodic boundary conditions on the process is also carefully investigated.

  • 126. Hagdahl, Stefan
    et al.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Numerical techniques for mixed high-low frequency EM-problems2002Konferensbidrag (Refereegranskat)
    Abstract [en]

    Our poster present numerical methods to be used for wave propagation problems where both relatively short and long wavelengths, λ , are present. Short and long wavelengths is referred to the characteristic sizes of the scales in the boundary conditions (BC) and material properties (MP). We propose that, depending on properties of the BC, one of three different Boundary Element Methods (BEM) are hybridised with a wave front, as opposed to a ray, implementation of Geometrical Theory of Diffraction (GTD). We will only consider the scattering problem in the presentation. Sometimes the electromagnetic engineer needs to know how a small size feature, e.g. a small perturbation of the BC, affects scattering parameters. We indicate the original Scatterer by an upper case S and the small scatterer, i.e. the perturbation, with lower case s . If the perturbation together with the Scatterer is small, BEM will serve as an excellent tool for numerical computations. However, when the complexity of the problem overcome the computer resources, other methods must be used. We propose that either of the three following boundary element methods are hybridised with GTD. If the perturbation only consist in an addition of a geometrical detail, i.e. the Scatterer’s BC and MP is unaffected by the perturbation, the perturbation can be discretized with local boundary elements and the impact on scattering parameters can be taken into account with GTD. If a boundary element is close to the scatterer, hence does not illuminate the scatterer with a ray field, we propose to use a linear combination of the image solution and the GTD to model the illumination. From an implementation point of view the interaction between the perturbation and the scattering is preferably done out-of-core and iteratively thereby leaving the GTD-solver and the BEM-solver separated. If the perturbation actually consist of a modifications of the Scatterer we propose that, at least in the two dimensional case, edge diffraction is applied to the artificial edges that indicate the points separating the perturbed and unperturbed parts of the Scatterer. No iteration needs to be done in this case since we assume that all scattered waves are outgoing. The third BEM is to be used when the perturbation actually changes the scatterer and the shape of the Scatterer close to the perturbation is crucial and needs to be rigorously taken into account. We then need to have mixed local and global boundary elements in the BEM-domain to model the interaction properly. We discuss how to formulate the boundary integral problem for a small change in a infinite electric perfect conducting ground plane. To take into account features that are far away from the perturbation can, as mentioned above, GTD be used. GTD has its origin in the method of characteristics. The characteristics are typically found with two types of methods in CEM-software.By using analytical or numerical methods applied to a variational problem with constraints. The method will fail in caustics since we then have infinite many solutions.By using the so-called shooting method. The shooting method succeed in caustics but may produce bad resolution for certain problems. We propose that our implementation of GTD, which we call the Wave Front method (WF-method), is used instead of the two methods presented above since we then will avoid the problems with efficiency and accuracy. It can be used in a CAD-setting and also be applied to smooth surface diffraction and inhomogeneousan isotropic materials. We will present numerical results from the presented methods in future publications.

  • 127. Halpern, L
    et al.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Open boundary conditions for long time computations1990Ingår i: Journal of Computational Acoustics, ISSN 0218-396X, Vol. 3, s. 77-88Artikel i tidskrift (Refereegranskat)
  • 128.
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    A note on the consistent initialization for nonlinear index-2 differential-algebraic equations in Hessenberg form2004Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In a previous paper, we developed a new algorithm for the consistent initialization of general index-2 differential-algebraic equations arising within the method of lines for solving partial differential equations. In the case of Hessenberg systems, the structural information allows for a lot of simplifications thus allowing for much larger systems to be solved. The crucial point consists of providing sparse projections by the use of sparse approximations to the inverse of the mass matrix. We obtain almost linear computational complexity with respect to the number of degrees of freedom.

  • 129.
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Benchmarking Femlab 3.0a: Laminar Flows in 2D2004Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Recently, version 3.0a of the software package FEMLAB for solving multiphysics partialdifferential equations was released. In the present project we compared its performance with the previous release 2.3 and the package Fluent 6.1 in stationary laminar flow benchmarkproblems in two and three dimensions. It turns out that the new version is an essential improvement over the old version. It is much faster than Fluent in 2D.

  • 130.
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Benchmarking Femlab 3.1i: Solid Structural Mechanics2005Rapport (Övrigt vetenskapligt)
    Abstract [en]

    The software package FEMLAB is an environment for modelling and solving multiphysics applications which are described in terms of partial differential differential equations.

    In this project we tested the performance of the structural mechanics toolbox version 3.1. This version of the toolbox represents a considerable enhancement over previous releases with respect to modelling capabilities. We compare the performance of version 3.1 to that of the older version 2.3 and a state-of-the-art finite element package for solving structural mechanics problems, namely, ANSYS 9.0.

  • 131.
    Hanke, Michael
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Cabauatan-Villanueva, Marry-Chriz
    Chalmers University of Technology, Math. Dept.
    Analytical And Numerical Approximation of Effective Diffusivities in The Cytoplasm of Biological Cells2007Rapport (Övrigt vetenskapligt)
    Abstract [en]

    The simulation of the metabolism in mammalian cells becomes a severe problem if spatial distributions must be taken into account. Especially the cytoplsma has a very complex geometric structure which cannot be handled by standard discretization techniques. In the present paper we propose a homogenization technique for computing effective diffusion constants. This is accomplished by using a two-step strategy. The first step consists of an analytic homogenization from the smallest to an intermediate scale. The homogenization error is estimated by comparing the analytic diffusion constant with a numerical estimate obtained by using real cell geometries. The second step consists of a random homogenization. Since no analytical solution is known to this homogenization problem, a numerical approximation algorithm is proposed. Although rather expensive this algorithm provides a reasonable estimate of the homogenized diffusion constant.

  • 132.
    Hanke, Michael
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Cabauatan-Villanueva, Marry-Chriz
    Chalmers University of Technology, Math Dept..
    On the simulation of the metabolism in mammalian cells using homogenization methods2007Ingår i: European Comsol Conference 2007 / [ed] Petit, Jean-Marc; Squalli, Oumnia, 2007, s. 40-46Konferensbidrag (Övrigt vetenskapligt)
  • 133.
    Hanke, Michael
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Loubenets, Alexei
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    An immersed finite element method and its convergence for elliptic interface problems with discontinuous coefficients and singular sources2007Rapport (Övrigt vetenskapligt)
    Abstract [en]

    This paper is concerned with the analysis of an immersed ginite element method for two dimensional elliptic interface problems. The main idea of the method is to use specifically designed macro elements in the vicinity of the interface, such that the jump conditions are well approximated. In general, the resulting immersed finite element space is non-conforming. It is shown that the presented method is second order accurate in L² norm. The provided numerical results agree with the theoretical estimates.

  • 134.
    Hanke, Michael
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Olsson, K. Henrik A.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Strömgren, Magnus
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Stability Analysis of a Reduced Heat Exchanger Model2005Ingår i: Proceedings in Applied Mathematics and Mechanics: PAMM, ISSN 1617-7061, E-ISSN 1617-7061, Vol. 5, nr 1, s. 805-806Artikel i tidskrift (Refereegranskat)
  • 135.
    Hanke, Michael
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Reis, Timo
    The Perturbation and ADAE Index of a Degenerated Hyperbolic System2009Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider a linear version of the zero Mach-number limit of the Euler equations of compressible fluid flow. This system turns out to be a coupled hyperbolic/parabolic equation with coupled, time-dependent boundary conditions. Using the theory of abstract differential-algebraic equations it is shown that the frozen coefficient system has ADAE index 1. Moreover, the much stronger result is proven that the system has time-perturbation index one and space-perturbation index two even in the case of time-dependent boundary conditions. The results are stated in terms of the original physical variables. The estimates agree well with numerical experiments.

  • 136. Hansbo, P
    et al.
    Szepessy, Anders
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    A velocity pressure streamline diffusion finite element method for Navier-Stokes equations1990Ingår i: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 84, nr 2, s. 175-192Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A streamline diffusion finite-element method is introduced for the time-dependent incompressible Navier-Stokes equations in a bounded domain in R squared and R cubed in the case of a flow with a high Reynolds number. An error estimate is proved and numerical results are given. The method is based on a mixed velocity-pressure formulation using the same finite-element discretization of space-time for the velocity and the pressure spaces, which consist of piecewise linear functions, together with certain least-squares modifications of the Galerkin variational formulation giving added stability without sacrificing accuracy.

  • 137. Harten, A
    et al.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Osher, S
    Chakravarthy, S.R.
    Uniformly High Order Accurate Essentially Non-oscillatory Schemes, III1997Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 131, nr 1, s. 3-47Artikel i tidskrift (Refereegranskat)
    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.

  • 138. Harten, A
    et al.
    Osher, S
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Chakravarthy, Sukumar R
    Some results on uniformly high-order accurate essentially nonoscillatory schemes1986Ingår i: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 2, nr 3-5, s. 347-377Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We continue the construction and the analysis of essentially nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first-order accuracy in the sense of truncation error, at extrema of the solution. In this paper we construct an hierarchy of uniformly high-order accurate approximations of any desired order of accuracy which are tailored to be essentially nonoscillatory. This means that, for piecewise smooth solutions, the variation of the numerical approximation is bounded by that of the true solution up to O(hR - 1), for 0 <R and h sufficiently small. The design involves an essentially nonoscillatory 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. To solve this reconstruction problem we use 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.

  • 139.
    Henningson, Dan Stefan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Kreiss, Gunilla
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Threshold amplitudes in subcritical shear flows - Non-linear stability bonds2005Ingår i: IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions / [ed] Mullin, T; Kerswell, R, DORDRECHT: SPRINGER , 2005, Vol. 77, s. 233-249Konferensbidrag (Refereegranskat)
    Abstract [en]

    Non-linear stability bounds are derived for subcritical shear flows. First the methodology is exemplified using a model problem and then it is applied to plane Couette flow. The result is a lower bound which scales as Re-4. Upper bounds based on numerical simulations are found to be about Re-1, depending slightly on the transition scenario investigated. Bounds for plane Poiseuille flow are also presented.

  • 140.
    Hoel, Håkon
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Coarse Graining Monte Carlo Methods for Wireless Channels and Stochastic Differential Equations2010Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis consists of two papers considering different aspects of stochastic process modelling and the minimisation of computational cost.

    In the first paper, we analyse statistical signal properties and develop a Gaussian pro- cess model for scenarios with a moving receiver in a scattering environment, as in Clarke’s model, with the generalisation that noise is introduced through scatterers randomly flip- ping on and off as a function of time. The Gaussian process model is developed by extracting mean and covariance properties from the Multipath Fading Channel model (MFC) through coarse graining. That is, we verify that under certain assumptions, signal realisations of the MFC model converge to a Gaussian process and thereafter compute the Gaussian process’ covariance matrix, which is needed to construct Gaussian process signal realisations. The obtained Gaussian process model is under certain assumptions less computationally costly, containing more channel information and having very similar signal properties to its corresponding MFC model. We also study the problem of fitting our model’s flip rate and scatterer density to measured signal data.

    The second paper generalises a multilevel Forward Euler Monte Carlo method intro- duced by Giles [1] for the approximation of expected values depending on the solution to an Ito stochastic differential equation. Giles work [1] proposed and analysed a Forward Euler Multilevel Monte Carlo method based on realsiations on a hierarchy of uniform time discretisations and a coarse graining based control variates idea to reduce the computa- tional effort required by a standard single level Forward Euler Monte Carlo method. This work introduces an adaptive hierarchy of non uniform time discretisations generated by adaptive algorithms developed by Moon et al. [3, 2]. These adaptive algorithms apply either deterministic time steps or stochastic time steps and are based on a posteriori error expansions first developed by Szepessy et al. [4]. Under sufficient regularity conditions, our numerical results, which include one case with singular drift and one with stopped dif- fusion, exhibit savings in the computational cost to achieve an accuracy of O(T ol), from O(T ol−3 ) to O (log (T ol) /T ol)2 . We also include an analysis of a simplified version of the adaptive algorithm for which we prove similar accuracy and computational cost results.

     

  • 141.
    Hoel, Håkon
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Complexity and Error Analysis of Numerical Methods for Wireless Channels, SDE, Random Variables and Quantum Mechanics2012Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis consists of the four papers which consider different aspects of stochastic process modeling, error analysis, and minimization of computational cost.

         In Paper I, we construct a Multipath Fading Channel (MFC) model for wireless channels with noise introduced through scatterers flipping on and off. By coarse graining the MFC model a Gaussian process channel model is developed. Complexity and accuracy comparisons of the models are conducted.

         In Paper II, we generalize a multilevel Forward Euler Monte Carlo method introduced by Mike Giles for the approximation of expected values depending on solutions of Ito stochastic differential equations. Giles' work proposed and analyzed a Forward Euler Multilevel Monte Carlo (MLMC) method based on realizations on a hierarchy of uniform time discretizations and a coarse graining based control variates idea to reduce the computational cost required by a standard single level Forward Euler Monte Carlo method. This work is an extension of Giles' MLMC method from uniform to adaptive time grids. It has the same improvement in computational cost and is applicable to a larger set of problems.

         In paper III, we consider the problem to estimate the mean of a random variable by a sequential stopping rule Monte Carlo method. The performance of a typical second moment based sequential stopping rule is shown to be unreliable both by numerical examples and by analytical arguments. Based on analysis and approximation of error bounds we construct a higher moment based stopping rule which performs more reliably.

         In paper IV, Born-Oppenheimer dynamics is shown to provide an accurate approximation of time-independent Schrödinger observables for a molecular system with an electron spectral gap, in the limit of large ratio of nuclei and electron masses, without assuming that the nuclei are localized to vanishing domains. The derivation, based on a Hamiltonian system interpretation of the Schrödinger equation and stability of the corresponding hitting time Hamilton-Jacobi equation for non ergodic dynamics, bypasses the usual separation of nuclei and electron wave functions, includes caustic states and gives a different perspective on the Born-Oppenheimer approximation, Schrödinger Hamiltonian systems and numerical simulation in molecular dynamics modeling at constant energy.

  • 142.
    Hoel, Håkon
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Gaussian Coarse Graining of a Master Equation GeneralisationManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    Abstract. In this report, statistical signal properties are analysed and aGaussian process model is developed for scenarios with a moving receiver ina scattering environment, as in Clarke’s model, with the generalisation thatnoise is introduced through scatterers randomly flipping on and off as a functionof time. The Gaussian process model is developed by extracting meanand covariance properties from the Multipath Fading Channel model (MFC).That is, we verify that under certain assumptions, signal realisations of theMFC model converge to a Gaussian process and thereafter compute the Gaussianprocess’ covariance matrix, which is needed to construct Gaussian processsignal realisations. The obtained Gaussian process model is, under certainassumptions, less computationally costly, contains more channel informationand has very similar signal properties to its corresponding MFC model. Theproblem of fitting our model’s flip rate and scatterer density to measured signaldata is also studied.

  • 143.
    Hoel, Håkon
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Nyberg, Henrik
    Ericsson Research.
    Gaussian Coarse Graining of a Master Equation Extension of Clarke's Model2012Rapport (Övrigt vetenskapligt)
    Abstract [en]

    We study the error and computational cost of generating outputsignal realizations for the channel model of a moving receiver in a scatteringenvironment, as in Clarke’s model, with the extension that scatterers randomlyflip on and off. At micro scale, the channel is modeled by a Multipath FadingChannel (MFC) model, and by coarse graining the micro scale model we derivea macro scale Gaussian process model. Four algorithms are presented for gen-erating stochastic signal realizations, one for the MFC model and three for theGaussian process model. A computational cost comparison of the presentedalgorithms indicates that Gaussian process algorithms generate signal realiza-tions more efficiently than the MFC algorithm does. Numerical examples ofgenerating signal realizations in time independent and time dependent scatter-ing environments are given, and the problem of estimating model parametersfrom real life signal measurements is also studied.

  • 144.
    Hoel, Håkon
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Von Schwerin, Erik
    Applied Mathematics and Computational Sciences, KAUST, Thuwal, Saudi Arabia.
    Szepessy, Anders
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Tempone, Raul
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Adaptive Multi Level Monte Carlo Simulation2012Ingår i: Numerical Analysis of Multiscale Computations: Proceedings of a Winter Workshop at the Banff International Research Station 2009, Springer, 2012, Vol. 82, s. 217-234Konferensbidrag (Refereegranskat)
    Abstract [en]

    This work generalizes a multilevel Forward Euler Monte Carlo methodintroduced in [5] for the approximation of expected values depending onthe solution to an Itˆo stochastic differential equation. The work [5] proposedand analyzed a Forward Euler Multilevel Monte Carlo method basedon a hierarchy of uniform time discretizations and control variates to reducethe computational effort required by a standard, single level, ForwardEuler Monte Carlo method. This work introduces an adaptive hierarchyof non uniform time discretizations, generated by adaptive algorithms introducedin [11, 10]. These adaptive algorithms apply either deterministictime steps or stochastic time steps and are based on a posteriori error expansionsfirst developed in [14]. Under sufficient regularity conditions, ournumerical results, which include one case with singular drift and one withstopped diffusion, exhibit savings in the computational cost to achieve anaccuracy of O(TOL), from O`TOL−3´to O“`TOL−1 log (TOL)´2”. Wealso include an analysis of a simplified version of the adaptive algorithmfor which we prove similar accuracy and computational cost results.

  • 145.
    Hoel, Håkon
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    von Schwerin, Erik
    King Abdullah University of Science and Technology.
    Szepessy, Anders
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Tempone, Raul
    King Abdullah University of Science and Technology.
    Implementation and Analysis of an Adaptive Multilevel Monte Carlo Algorithm2012Rapport (Övrigt vetenskapligt)
    Abstract [en]

    This work generalizes a multilevel Monte Carlo (MLMC) method in-troduced in [7] for the approximation of expected values of functions depending on the solution to an Ito stochastic differential equation. The work [7] proposed and analyzed a forward Euler MLMC method based on a hierarchy of uniform time discretizations and control variates to reduce the computational effort required by a standard, single level, forward Euler Monte Carlo method from O( TOL^(−3) ) to O( TOL^(−2) log( TOL^(−1))^2 ) for a meansquare error of size 2 . This work uses instead a hierarchy of adaptivelyrefined, non uniform, time discretizations, generated by an adaptive algo-rithm introduced in [20, 19, 5]. Given a prescribed accuracy TOL in theweak error, this adaptive algorithm generates time discretizations basedon a posteriori expansions of the weak error first developed in [24]. Atheoretical analysis gives results on the stopping, the accuracy, and thecomplexity of the resulting adaptive MLMC algorithm. In particular, it isshown that: the adaptive refinements stop after a finite number of steps;the probability of the error being smaller than TOL is under certain as-sumptions controlled by a given confidence parameter, asymptotically asTOL → 0; the complexity is essentially the expected for MLMC methods,but with better control of the constant factors. We also show that themultilevel estimator is asymptotically normal using the Lindeberg-FellerCentral Limit Theorem. These theoretical results are based on previouslydeveloped single level estimates, and results on Monte Carlo stoppingfrom [3]. Our numerical tests include cases, one with singular drift andone with stopped diffusion, where the complexity of uniform single levelmethod is O TOL−4 . In both these cases the results confirm the theoryby exhibiting savings in the computational cost to achieve an accuracy of O(TOL), from O( TOL^(−3) )for the adaptive single level algorithm toessentially O( TOL^(−2) log(TOL−1)^2 ) for the adaptive MLMC.

  • 146.
    Hoffman, Claes
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Johnson, Claes
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Adaptive finite element methods for incompressible flow2003Ingår i: Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics / [ed] Barth, Timothy J.; Deconinck, Herman, Springer , 2003Kapitel i bok, del av antologi (Refereegranskat)
  • 147.
    Hoffman, Johan
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Adaptive simulation of the subcritical flow past a sphere2006Ingår i: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 568, s. 77-88Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Adaptive DNS/LES (direct numerical simulation/large-eddy simulation) is used to compute the drag coefficient CD for the flow past a sphere at Reynolds number Re = 10(4). Using less than 10(5) mesh points, CD is computed to an accuracy of a few percent, corresponding to experimental precision, which is at least an order of magnitude cheaper than standard non-adaptive LES computations in the literature. Adaptive DNS/LES is a General Galerkin G2 method for turbulent flow, where a stabilized Galerkin finite element method is used to compute approximate solutions to the Navier-Stokes equations, with the mesh being adaptively refined until a stopping criterion is reached with respect to the error in a chosen output of interest, in this paper CD. Both the stopping criterion and the mesh refinement strategy are based on a posteriori error estimates, in the form of a space-time integral of residuals multiplied by derivatives of the solution of an associated dual problem, linearized at the approximate solution, and with data coupling to the output of interest. There is no filtering of the equations, and thus no Reynolds stresses are introduced that need modelling. The stabilization in the numerical method is acting as a simple turbulence model.

  • 148.
    Hoffman, Johan
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Adaptive Turbulence Computation Based on Weak Solutions and Weak Uniqueness2008Ingår i: QUALITY AND RELIABILITY OF LARGE-EDDY SIMULATIONS / [ed] Meyers J, Geurts BJ, Sagaut P, Springer , 2008, Vol. 12, s. 21-35Konferensbidrag (Refereegranskat)
    Abstract [en]

    We review our work oil adaptivity and error control for turbulent, flow, and we present, recent. development's oil turbulent, boundary layer flow. The computational method G2 is not based oil filtering of the Navier-Stokes (NS) equations, and thus no Reynolds (subgrid) stresses are introduced. Instead the mathematical basis is E-weak solutions to the NS equations and weak uniqueness of such epsilon-weak solutions. Based oil this mathematical framework we construct adaptive finite element methods for the computation of (mean value) Output ill turbulent HOW. Where the mesh is refined with respect to it posteriori estimates of the error in the out put of interest. The a posteriori error estimates are based oil stability information front the numerical solution of an associated dual (adjoint) problem with data given by the output, of interest. To model turbulent, boundary layer separation we use, it skill friction boundary layer model, and we also consider the case of zero skin friction corresponding to solving the inviscid Euler equations with slip boundary conditions, which we refer to as an EG2 method. The results of EG2 a new resolution to the d'Alembert paradox, and it new scenario for turbulent boundary layer separation.

  • 149.
    Hoffman, Johan
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Computation of mean drag for bluff body problems using adaptive DNS/LES2005Ingår i: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 27, nr 1, s. 184-207Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We compute the time average of the drag in two benchmark bluff body problems: a surface mounted cube at Reynolds number 40000, and a square cylinder at Reynolds number 22000, using adaptive DNS/LES. In adaptive DNS/LES the Galerkin least-squares finite element method is used, with adaptive mesh refinement until a given stopping criterion is satisfied. Both the mesh refinement criterion and the stopping criterion are based on a posteriori error estimates of a given output of interest, in the form of a space-time integral of a computable residual multiplied by a dual weight, where the dual weight is obtained from solving an associated dual problem computationally, with the data of the dual problem coupling to the output of interest. No filtering is used, and in particular no Reynolds stresses are introduced. We thus circumvent the problem of closure, and instead we estimate the error contribution from subgrid modeling a posteriori, which we find to be small. We are able to predict the mean drag with an estimated tolerance of a few percent using about 105 mesh points in space, with the computational power of a PC.

  • 150.
    Hoffman, Johan
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Dynamic subgrid modeling for scalar convection-diffusion-reaction equations with fractal coefficients2001Ingår i: Lecture notes in computational science and engineeringArtikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we propose and study a subgrid model for linear convection-diffusion-reaction problems with fractal rough coefficients. The subgrid model is based on extrapolation model of a modeling residual from coarser scales using a computed solution without subgrid model on a finest scale as reference. We present a priori and a posteriori error estimates, and we show in experiments that a solution with subgrid model on a scale h corresponds to a solution without subgrid model on a scale less than h/4

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