Parallel multilevel methods with adaptivity on unstructured grids

We present two parallel multilevel methods for solving large-scale discretized partial differential equations on unstructured 2D/3D grids. The presented methods combine three powerful numerical algorithms: overlapping domain decomposition, multigrid method and adaptivity. As the foundation of the methods we propose an algorithm for generating and partitioning a hierarchy of adaptively refined unstructured grids, so that adaptivity can be incorporated up to a certain grid level. We ensure that the resulting subgrid hierarchies are well balanced and no inter-processor communication is needed across different grid levels, thus obtaining high parallel efficiency. Numerical experiments show that the parallel multilevel methods offer almost equally fast convergence as their sequential multigrid counterpart. And the resulting implementation has reasonably good scalability. Received: 4 December 1998 / Accepted: 12 January 2000