A New Organization of Sparse Gauss Elimination for Solving PDEs
Mo Mu, John R. Rice · Purdue e-Pubs (Purdue University System) · 1990
A new Gauss elimination algorithm is presented for solving sparse, nonsymmetric linear systems arising from partial differential equation (PDE) problems.It is particularly suitable for use on distributed memory message passing (DMMP) multiprocessor computers and it is presented and analyzed in this context.The objective of the algorithm is to exploit the sparsity (Le., reducing both computational and memory requirements) and sharply reduce the data structure manipulation overhead of standard sparse matrix algorithms.The algorithm is based on the nested dissection approach, which starts with a large set of very sparse, completely independent subsystems and progresses in stages to a single.nearly dense system at the last stage.The computational efforts of each stage are roughly equal (almost exactly equal for model problems), yet the data structures appropriate for the first and last stages are quite different.Thus we use different types of data structures and algorithm components at different stages of the solution...