A critical computational step in large-scale process simulation using rigorous equation-based models is the solution of a sparse linear equation system. Traditional sparse solvers based on indirect addressing are not effective on supercomputers because they do not vectorize well. By relying on vectorized dense matrix kernels, the multifrontal and frontal methods provide much better performance, as demonstrated using several examples. On problems with good initial matrix orderings the frontal method is most effective, while without good initial ordering the multifrontal method is attractive.

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