A parallel implementation of an OL-LOGOS sparse direct solver

Data sparse direct solution methods for electromagnetic simulation problems have proven to be useful for a number of situations, both as standalone direct solvers and as general purpose preconditioners for use with iterative solvers. One set of such direct methods is provided by the LOGOS framework, which is based on expanding the underlying system matrix in a basis of local solutions that satisfy global boundary conditions. A particular subset of the LOGOS-based solution methods is referred to as the overlapped, localizing (OL) LOGOS method. This approach to factoring the system matrix is based on expanding the system matrix in a basis of overlapping sources that localize the scattered field to a spatial region that is also covered by the source functions. It has previously been shown that the computational complexity of such factorizations can scale as well as O(N log N) for low to moderate frequencies when used as a direct solver. The OL-LOGOS method has also been shown to provide an effective, O(N log N) general purpose preconditioner when used to factor the near-neighbor matrix obtained from the multilevel fast multipole method algorithm.