A new row ordering strategy for frontal solvers

The frontal method is a variant of Gaussian elimination that has been widely used since the mid 1970s. In the innermost loop of the computation the method exploits dense linear algebra kernels, which are straightforward to vectorize and parallelize. This makes the method attractive for modern computer architectures. However, unless the matrix can be ordered so that the front is never very large, frontal methods can require many more floating-point operations for factorization than other approaches. We are interested in matrices that have a highly asymmetric structure. We use the idea of a row graph of an unsymmetric matrix combined with a variant of Sloan’s profile reduction algorithm to reorder the rows. We also look at applying the spectral method to the row graph. Numerical experiments performed on a range of practical problems illustrate that our proposed MSRO and hybrid MSRO row ordering algorithms yield substantial reductions in the front sizes and, when used with a frontal solver, significantly enhance its performance both in terms of the factorization time and storage requirements. Copyright © 1999 John Wiley & Sons, Ltd.