A new row ordering strategy for frontal solvers

A new row ordering strategy for frontal solvers. Abstract 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 oating-point operations for factorization than other approaches. We use the idea of a row graph of an unsymmetric matrix combined with a variant of Sloan's proole reduction algorithm to reorder the rows. We also look at using the spectral method applied to the row graph. Numerical experiments are performed on a range of practical problems. Our new row ordering algorithm is shown to produce orderings that are a signiicant improvement on those obtained with existing algorithms. Numerical results also compare the performance of the frontal solver MA42 on the reordered matrix with other direct solvers for large sparse unsymmetric linear systems.