This dissertation reports the implementation of a boundary element method (BEM) application on the massively parallel MasPar MP-1 and MP-2 computers. That implementation provides a case study to demonstrate several techniques for parallelization of sequential algorithms and for optimization of parallel programs;An existing formal technique for transforming a sequential algorithm into a systolic architecture is presented. This dissertation then discusses how a parallel systolic algorithm on a mesh-connected computer can be derived from such a systolic Architecture; The matrix multiplication algorithm used in the BEM implementation is derived in this way;As part of the BEM implementation, this dissertation covers a novel method of solving a system of linear equations, using matrix inversion and LU decomposition. This method is shown to be less expensive than LU decomposition alone. Several parallelizations of matrix inversion are considered;Finally, this dissertation presents techniques for transforming parallel program source code to increase performance. The transformation improves performance by decreasing processor local memory access cost and by increasing processor utilization.