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

Schweitzer Marc Alexander

ISBN 10: 3540003517 ISBN 13: 9783540003519

Editorial: Springer, 2003

Idioma: Ingl�s

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Print on Demand pp. v + 194.

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T�tulo: A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations
Editor: Springer
Fecha de publicaci�n: 2003
Idioma: Ingl�s
ISBN 10: 3540003517
ISBN 13: 9783540003519
Encuadernaci�n: Encuadernaci�n de tapa blanda
Estado: New

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Sinopsis

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.

De la contraportada

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.

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