Conjugate gradient and Lanczos methods for sparse matrices on distributed memory multiprocessors

Conjugate gradient methods for solving sparse systems of linear equations and Lanczos algorithms for sparse symmetric eigenvalue problems play an important role in numerical methods for solving discretized partial differential equations, When these 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 the sparse coefficient matrices-are crucial for efficient execution. Here, data distribution and communication schemes are presented that are based on the analysis of the indices of the nonzero matrix elements, On an Intel PARAGON XP/S 10 with 140 processors, the developed parallel variants of the solvers show good scaling behavior for matrices with different sparsity patterns stemming from real finite element applications. (C) 1997 Academic Press.