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An introduction to hierarchical matrices

Wolfgang Hackbusch, Lars Grasedyck, Steffen Börm (2002)

Mathematica Bohemica

We give a short introduction to a method for the data-sparse approximation of matrices resulting from the discretisation of non-local operators occurring in boundary integral methods or as the inverses of partial differential operators. The result of the approximation will be the so-called hierarchical matrices (or short ℋ -matrices). These matrices form a subset of the set of all matrices and have a data-sparse representation. The essential operations for these matrices (matrix-vector and matrix-matrix...

An iterative method of alternating type for systems with special block matrices

Milan Práger (1991)

Applications of Mathematics

An iterative procedure for systems with matrices originalting from the domain decomposition technique is proposed. The procedure introduces one iteration parameter. The convergence and optimization of the method with respect to the parameter is investigated. The method is intended not as a preconditioner for the CG method but for the independent use.

An unconditionally stable finite element-finite volume pressure correction scheme for the drift-flux model

Laura Gastaldo, Raphaèle Herbin, Jean-Claude Latché (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present in this paper a pressure correction scheme for the drift-flux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the continuous problem: the scheme is conservative, the unknowns are kept within their physical bounds and, in the homogeneous case (i.e. when the drift velocity vanishes), the discrete entropy of the system decreases; in addition, when using for the drift velocity a closure law which takes the form of...

An unconditionally stable pressure correction scheme for the compressible barotropic Navier-Stokes equations

Thierry Gallouët, Laura Gastaldo, Raphaele Herbin, Jean-Claude Latché (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We present in this paper a pressure correction scheme for the barotropic compressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the continuous problem also hold for the discrete solution. The stability proof is based on two independent results for general finite volume discretizations, both interesting for their own sake: the L2-stability of the discrete advection operator provided it...

An upwinding mixed finite element method for a mean field model of superconducting vortices

Zhiming Chen, Qiang Du (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we construct a combined upwinding and mixed finite element method for the numerical solution of a two-dimensional mean field model of superconducting vortices. An advantage of our method is that it works for any unstructured regular triangulation. A simple convergence analysis is given without resorting to the discrete maximum principle. Numerical examples are also presented.

An XFEM/DG approach for fluid-structure interaction problems with contact

Luca Formaggia, Federico Gatti, Stefano Zonca (2021)

Applications of Mathematics

In this work, we address the problem of fluid-structure interaction (FSI) with moving structures that may come into contact. We propose a penalization contact algorithm implemented in an unfitted numerical framework designed to treat large displacements. In the proposed method, the fluid mesh is fixed and the structure meshes are superimposed to it without any constraint on the conformity. Thanks to the Extended Finite Element Method (XFEM), we can treat discontinuities of the fluid solution on...

Currently displaying 421 – 440 of 540