Parallel multigrid in an adaptive PDE solver based on hashing and space-filling curves

Abstract

Partial differential equations can be solved efficiently by adaptive multigrid methods on a parallel computer. We report on the concept of hash-table storage techniques to set up such a program. The code requires substantial less amount of memory than implementations based on tree type data structures and is easier to program in the sequential case. The parallelization takes place by a space-filling curve domain decomposition intimately connected to the hash table. The new data structure simplifies the parallelization of the code substantially and introduces a cheap way to solve the load balancing and mapping problem. We report on the main features of the method and give the results of numerical experiments with the new parallel solver on a cluster of 64 Pentium II/400MHz connected by a Myrinet in a fat tree topology.