Adaptive Multigrid Methods in MPI

Adaptive multigrid methods solve partial differential equations through a discrete representation of the domain that introduces more points in those zones where the equation behavior is highly irregular. The distribution of the points changes at run time in a way that cannot be foreseen in advance. We propose a methodology to develop a highly parallel solution based upon a load balancing strategy that respects the locality property of adaptive multigrid method, where the value of a point p depends on the points that are ”close” to p according to a neighborhood stencil. We also describe the update of the mapping at run time to recover an unbalancing, together with strategies to acquire data mapped onto other processing nodes. A MPI implementation is presented together with some experimental results.