The Parallelization of an Adaptive Multigrid Eigenvalue Solver with LPARX

We have developed a parallel adaptive eigenvalue solver and applied it to a model problem in theoretical materials science. Our method combines adaptive mesh refinement techniques with a novel multigrid eigenvalue algorithm. By exploiting adaptivity, we have reduced computation time and memory consumption by more than two orders of magnitude. We have implemented our solver using the LPARX parallel programming system, which considerably simplified the programming and enabled us to run the same code on a diversity of high performance parallel architectures. 1 Introduction Many physical systems in science and engineering require the resolution of processes occurring at multiple length scales. Adaptivity is essential in resolving local phenomena. In collaboration with materials scientists and mathematicians, we are developing adaptive numerical techniques and the accompanying software infrastructure for resolving the multiple length scales present in materials science calculations. We hav..