Porting an implicit method of lines solver to distributed-memory parallel processors

This thesis presents the design, implementation and evaluation of a strategy for the porting of a numerical method for solving partial differential equations from a sequential processor platform to a parallel processor platform while minimizing the rewriting of existing code. Two different architectures are used in the evaluation, the Intel iPSC/860 which is a distributed memory system and the Kendall Square Multiprocessor which is a virtual shared memory system.

This evaluation uses a numerical method called the implicit Method of Lines to approximate a partial differential equation by a system of ordinary differential equations and then uses an ordinary differential equation solver developed for a sequential processor to compute an approximation to the partial differential equation. The ordinary differential equation solver is used without modification, and the speed-up of the calculated solution is obtained by parallelizing the formation of a Jacobian matrix and the solution of the linear system of equations involving that matrix.

The results include the speed-up that is obtained for the solution of the partial differential equation and the performance rate that is obtained for the LU decomposition by the linear algebra routines in the solution of the system of equations. Also presented is the method of porting distributed-memory processor routines to a virtual shared-memory processors.