A HIERARCHICAL 2-LEVEL MULTIGRID SOLVER

In this paper we present a fast, inherently parallel, two-level multigrid (TLMG) algorithm for solving quadratic finite element models containing tetrahedral meshes. The basic idea is to integrate a TLMG algorithm with hierarchical octree structure based on Recursive Spatial Decomposition (RSD). The new hierarchical TLMG (HTLMG) algorithm combines direct substructuring and static condensation with a new algorithm for performing hierarchically the SOR iteration. The hierarchical SOR (HSOR) iteration is designed to operate independently on each subdomain in the octree structure. The time and space complexities of the HSOR and the HTLMG iterations are derived for a regular domain. Two test problems are used to compare the computational cost of the HTLMG algorithm with that of a direct solver.