Iterative and direct sparse solvers on parallel computers

摘要: Solving large sparse systems of linear equations is required for a wide range of numerical applications. This paper addresses the main issues raised during the parallelization of iterative and direct solvers for such systems in distributed memory multiprocessors. If no preconditioning is considered, iterative solvers are simple to parallelize, as the most time-consuming computational structures are matrixvector products. Direct methods are much harder to parallelize, as new nonzero values may appear during computation and pivoting operations are usually accomplished due to numerical stability considerations. Suitable data structures and distributions for sparse solvers are discussed within the framework of a data-parallel environment, and experimentally evaluated and compared with existing solutions.