Elliptic boundary value problems occur in many disciplines. In cases where the boundaries are complex and irregular, these problems are recast as integral equations and solved by boundary integral equation methods. This technique requires the solution of a linear system. In many problems of practical interest these systems are large enough that the computational effort required for their solution is prohibitive. In recent years, vector supercomputers have expanded the range of problems which may be solved numerically but there remains a significant number of problems which lie beyond current capabilities. The combination of parallel supercomputers and powerful iterative methods holds the promise of expanding the territory of solvable problems. This SGER project addresses both aspects of this combination. An O(N) algorithm which was recently implemented on serial and vector machines will be implemented on a parallel architecture, and the existing repertoire of iterative methods will be expanded to uniquely augment the power of the O(N) algorithm.
