For the analysis and solution of discretized ordinary or partial differential equations it
is necessary to solve systems of equations or eigenproblems with coefficient matrices
of different sparsity patterns, depending on the discretization method. In many cases,
the use of the finite element method (FE) results in largely unstructured systems of
equations. The main computational cost in iterative methods for solving these problems
consists of matrix-vector products and vector-vector operations; usually the main
work in each iteration is the computation of matrix-vector products. When iterative
solvers are parallelized on a multiprocessor system with distributed memory, the data
distribution and the communication scheme { depending on the data structures used for
sparse matrices { are of the greatest importance for an efficient execution. Here, data
distribution and communication schemes are presented that are based on the analysis
of the column indices of the non-zero matrix elements. Performance tests, using the
conjugate gradient method (CG) and the Lanczos algorithm for the symmetric eigenproblem,
were carried out on the distributed memory systems INTEL iPSC/860 and
PARAGON XP/S 10 of the Research Centre J?ulich with sparse matrices from FE models.
The parallel variants of the algorithms showed good scaling behavior for matrices
with very different sparsity patterns.