An adaptive multigrid on block-structured grids

Abstract

An implementation of the multigrid method on conformal block-structured grids is proposed. The algorithm is intended to solve a boundary-value problem for elliptic PDEs. Each block is discretized using a structured hexahedron grid.The set of multilevel grids are arranged in hierarchical levels. In each block the discrete finite volume scheme is constructed on the fine level grid. The coarse level equations are formed by the Galerkin procedure. The presence of the irregular block connections leads to irregular stencils in the nodes which adjoin of several blocks. Instead of a special irregular node treatment we propose to find the solution in these nodes in additive manner. Such an opportunity is provided by the use of the explicit iterative procedures for both the smoothers and the coarsest grid solver. We also present an adaptive technique which adjusts these procedures for achieving the prescribed multigrid convergence rate. The proposed approach enhances the potential of the multigrid method in ultra-parallel computing.