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Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case

Paola F. Antonietti, Blanca Ayuso (2007)

ESAIM: Mathematical Modelling and Numerical Analysis


We propose and study some new additive, two-level non-overlapping Schwarz preconditioners for the solution of the algebraic linear systems arising from a wide class of discontinuous Galerkin approximations of elliptic problems that have been proposed up to now. In particular, two-level methods for both symmetric and non-symmetric schemes are introduced and some interesting features, which have no analog in the conforming case, are discussed. Both the construction and analysis of the proposed domain...

s∗-compressibility of the discrete Hartree-Fock equation

Heinz-Jürgen Flad, Reinhold Schneider (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown...

s∗-compressibility of the discrete Hartree-Fock equation

Heinz-Jürgen Flad, Reinhold Schneider (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown...

Seasonal Forcing Drives Spatio-Temporal Pattern Formation in Rabies Epidemics

N. V. Festenberg, T. Gross, B. Blasius (2010)

Mathematical Modelling of Natural Phenomena

Seasonal forcing is identified as a key pattern generating mechanism in an epidemic model of rabies dispersal. We reduce an established individual-based high-detail model down to a deterministic conceptual model. The characteristic wave pattern characterized by high densities of infected individuals is maintained throughout the reduction process. In our model it is evident that seasonal forcing is the dominant factor that drives pattern formation. In particular we show that seasonal forcing can...

Second-order MUSCL schemes based on Dual Mesh Gradient Reconstruction (DMGR)

Christophe Berthon, Yves Coudière, Vivien Desveaux (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We discuss new MUSCL reconstructions to approximate the solutions of hyperbolic systems of conservations laws on 2D unstructured meshes. To address such an issue, we write two MUSCL schemes on two overlapping meshes. A gradient reconstruction procedure is next defined by involving both approximations coming from each MUSCL scheme. This process increases the number of numerical unknowns, but it allows to reconstruct very accurate gradients. Moreover a particular attention is paid on the limitation...

Self-correcting iterative methods for computing 2 -inverses

Stanimirović, Predrag S. (2003)

Archivum Mathematicum

In this paper we construct a few iterative processes for computing { 2 } -inverses of a linear bounded operator. These algorithms are extensions of the corresponding algorithms introduced in [11] and a method from [8]. A few error estimates are derived.

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