Parallel Reuse Methodologies for Elliptic Boundary Value Problems

We describe two parallel frameworks that allow the reuse of the discretization part of se-quential general elliptic PDE (partial differential equation) solvers. These parallel reuse meth-odologies are based on the "divide and conquer " computational paradigm. They have been integrated into the Parallel ELLPACI ( problem solving environment that supports PDE com-puting across many hardware platforms. Experimental results indicate the effectiveness of the reuse frameworks implemented. We also evaluate the performance of the Parallel ITPACK library of stationary iterative solvers. This package has been implemented using several message passing communication libraries. We consider the parallel solution of sparse algebraic equations obtained from the discretization of second order elliptic PDEs using finite difference and finite element techniques. The performance of the Parallel ITPACK solvers is measured on many distributed memory platforms including clusters of workstations. 1