Limited resource scheduling in multifrontal algorithms for sparse linear systems

We present analytic models and simulation techniques that describe the performance of the multifrontal method on distributed memory architectures. We focus on particular strategies for partitioning, clustering, and mapping of task nodes to processors in order to minimize the overall parallel execution time and minimize communication costs. The performance model has been used to obtain estimates for the speedups of various engineering and scientific problems, on several distributed architectures. The result is that the available speedup of these problems is strongly dependent on the sparsity structure and reordering of the input matrices