Parallel Multilevel Methods: Adaptive Mesh Refinement and Loadbalancing

✍ Scribed by Prof. Dr. Gerhard Zumbusch Diplom, Promotion (auth.)

• Publisher: Vieweg+Teubner Verlag
• Year: 2003
• Tongue: English
• Leaves: 214
• Series: Advances in Numerical Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages 1-9
Introduction....Pages 11-18
Multilevel Iterative Solvers....Pages 19-58
Adaptively Refined Meshes....Pages 59-89
Space-Filling Curves....Pages 90-143
Adaptive Parallel Multilevel Methods....Pages 144-168
Numerical Applications....Pages 169-193
Concluding Remarks and Outlook....Pages 194-196
Back Matter....Pages 197-216

✦ Subjects

Computational Mathematics and Numerical Analysis; Analysis