Parallel Multilevel Methods
Subtitle: Adaptive Mesh Refinement and Loadbalancing
By: by Gerhard Zumbusch
Series: Advances in Numerical Mathematics, 1616-2994; Wiley-Teubner series, advances in numerial mathematics
Publisher: Vieweg+Teubner Verlag
Published: 2003
Place of publication: Wiesbaden
Language: eng
Format: [electronic resource] :
Number of pages: 216
ISBN-13: 9783322800633
Subjects: Mathematics; Global analysis (Mathematics); Computer science
Description: 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.