Parallel Multilevel Methods

Adaptive Mesh Refinement and Loadbalancing

  • Gerhard Zumbusch
Part of the Advances in Numerical Mathematics book series (ANUM)

Table of contents

  1. Front Matter
    Pages 1-9
  2. Gerhard Zumbusch
    Pages 11-18
  3. Gerhard Zumbusch
    Pages 19-58
  4. Gerhard Zumbusch
    Pages 59-89
  5. Gerhard Zumbusch
    Pages 90-143
  6. Gerhard Zumbusch
    Pages 144-168
  7. Gerhard Zumbusch
    Pages 169-193
  8. Gerhard Zumbusch
    Pages 194-196
  9. Back Matter
    Pages 197-216

About this book

Introduction

Main aspects of the efficient treatment of partial differential equations are discretisation, multilevel/multigrid solution and parallelisation. These distinct topics are coverd from the historical background to modern developments. It is demonstrated how the ingredients can be put together to give an adaptive and parallel multilevel approach for the solution of elliptic boundary value problems. Error estimators and adaptive grid refinement techniques for ordinary and for sparse grid discretisations are presented. Different types of additive and multiplicative multilevel solvers are discussed with respect to parallel implementation and application to adaptive refined grids. Efficiency issues are treated both for the sequential multilevel methods and for the parallel version by hash table storage techniques. Finally, space-filling curve enumeration for parallel load balancing and processor cache efficiency are discussed.

Keywords

Adaptive Parallel Multilevel Methods Adaptively Refined Grids Multilevel Iterative Solver Numerical Applications Space-Filling Curves differential equation

Authors and affiliations

  • Gerhard Zumbusch
    • 1
    • 2
    • 3
    • 4
    • 5
    • 6
    • 7
  1. 1.TU MünchenDeutschland
  2. 2.Konrad-Zuse-Zentrum für Informationstechnik BerlinDeutschland
  3. 3.FU BerlinDeutschland
  4. 4.SINTEF Anvendt Matematikk OsloNorway
  5. 5.Universität BonnDeutschland
  6. 6.Wissenschaftliches Rechnen/Numerische MathematikFriedrich-Schiller-Universität JenaDeutschland
  7. 7.Instituts für Angewandte MathematikDeutschland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-322-80063-3
  • Copyright Information Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 2003
  • Publisher Name Vieweg+Teubner Verlag
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-519-00451-6
  • Online ISBN 978-3-322-80063-3
  • Series Print ISSN 1616-2994
  • About this book