A Schwarz splitting variant of cubic spline collocation methods for elliptic PDEs

We consider the formulation of the Schwarz alternating method for a new class of elliptic cubic spline collocation discretization schemes. The convergence of the method is studied using Jacobi and Gauss-Seidel iterative methods for implementing the interaction among subdomains. The Schwarz Cubic Spline Collocation (SCSC) method is formulated for hypercube architectures and implemented on the NCUBE (128 processors) machine. The performance and convergence of the hypercube SCSC algorithm is studied with respect to domain partition and subdomain overlapping area. The numerical results indicate that the partition and mapping of the SCSC on the NCUBE is almost optimal while the speedup obtained is similar to other domain decomposition techniques.