Some Variants of the Bank-Holst Parallel Adaptive Meshing Paradigm

The Bank-Holst adaptive meshing paradigm is an efficient approach for parallel adaptive meshing of elliptic partial differential equations. It is designed to keep communication costs low and to take advantage of existing sequential adaptive software. While in principle the procedure could be used in any parallel environment, it was mainly conceived for use on small Beowulf clusters with a relatively small number of processors and a slow communication network. A typical calculation on such a machine might involve, say p = 32 processors, an adaptive fine mesh with a few million vertices, and use 2–3 minutes of computational time. In this work we, discuss a variant of the original scheme that could be used in situations where a much larger number of processors, say p > 100 is available. In this case the problem size could be much larger, say 10–100 million, with still a low to moderate computation time.