Parallel Sparse Matrix Computations in Iterative Solvers on Distributed Memory Machines

Sparse matrix computations play an important role in iterative methods to solve systems of equations or eigenvalue problems that are applied during the solution of discretized partial differential equations. The large size of many technical or physical applications in this area results in the need for parallel execution of sparse operations, in particular sparse matrix-vector multiplication, on distributed memory computers. In this report, a data distribution and a communication scheme are presented for parallel sparse iterative solvers. Performance tests, using the conjugate gradient method, the QMR and the TFQMR algorithm for solving systems of equations, and the Lanczos method for the symmetric eigenvalue problem, were carried out on a PARAGON XP/S 10 with 140 processors. The parallel variants of the algorithms show good scaling behavior for matrices with different sparsity patterns