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

  • Marc Alexander Schweitzer

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 29)

Table of contents

  1. Front Matter
    Pages i-v
  2. Marc Alexander Schweitzer
    Pages 1-11
  3. Marc Alexander Schweitzer
    Pages 13-22
  4. Marc Alexander Schweitzer
    Pages 23-49
  5. Marc Alexander Schweitzer
    Pages 51-96
  6. Marc Alexander Schweitzer
    Pages 97-126
  7. Marc Alexander Schweitzer
    Pages 127-153
  8. Marc Alexander Schweitzer
    Pages 155-159
  9. Back Matter
    Pages 161-199

About this book

Introduction

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.


Keywords

Numerical integration Transformation construction differential equation hyperbolic equation meshfree method multilevel method numerical quadrature parallel computation partial differential equation partition of unity tree code

Authors and affiliations

  • Marc Alexander Schweitzer
    • 1
  1. 1.Institut für Angewandte MathematikUniversität BonnBonnGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-59325-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-00351-9
  • Online ISBN 978-3-642-59325-3
  • Series Print ISSN 1439-7358
  • Buy this book on publisher's site
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