Six-Color Procedure for the Parallel Solution of Elliptic Systems Using the Finite Quadtree Structures.

摘要

We consider the parallel assembly and solution on shared-memory computers of linear algebraic systems arising from the finite element discretization of two-dimensional linear self-adjoint elliptic problems. Stiffness matrix assembly and conjugate gradient solution of the linear system using element-by-element and symmetric successive over-relaxation preconditioners are processed in parallel with computations scheduled on noncontiguous regions in order to minimize process synchronization. An underlying quadtree structure, used for automatic mesh generation and solution-based mesh refinement, is separated into disjoint regions called quadrants using six-color procedure having linear time complexity.