Block Preconditioned Conjugate Gradient Methods on a Distributed Virtual Shared Memory Multiprocessor

We study both shared and distributed approaches for the parallel implementation of the SSOR and Jacobi block preconditioned Krylov methods on a distributed virtual shared memory computer: a BBN TC2000. We consider the solution of block tridiagonal systems arising from the discretization of 3D partial differential equations, which diagonal blocks correspond to the discretization of 2D partial differential equations. The solution of the diagonal subproblems required for the preconditionings are performed using a domain decomposition method with overlapped subdomains: a variant of the Schwarz alternating method.