A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations

Marc Alexandre Schweitzer

194 pages, parution le 10/03/2003

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Résumé

The numerical treatment of partial differential equations with meshfree discretization techniques has been a very active research area in recent years. Up to now, however, meshfree methods have been in an early experimental stage and were not competitive due to the lack of efficient iterative solvers and numerical quadrature. This volume now presents an efficient parallel implementation of a meshfree method, namely the partition of unity method (PUM). A general numerical integration scheme is presented for the efficient assembly of the stiffness matrix as well as an optimal multilevel solver for the arising linear system. Furthermore, detailed information on the parallel implementation of the method on distributed memory computers is provided and numerical results are presented in two and three space dimensions with linear, higher order and augmented approximation spaces with up to 42 million degrees of freedom.

Contents

Introduction
Partition of Unity Method
Treatment of Elliptic Equations
Multilevel Solution of the Resulting Linear System
Tree Partition of Unity Method
Parallelization and Implementational Details
Concluding Remarks

L'auteur - Marc Alexandre Schweitzer

University of Bonn, Germany

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Marc Alexandre Schweitzer
Parution	10/03/2003
Nb. de pages	194
Format	15,5 x 23,5
Couverture	Broché
Poids	392g
Intérieur	Noir et Blanc
EAN13	9783540003519