Preconditioned Sparse Direct Solvers for Large-Scale Electromagnetic Modeling

Sparse solution methods are an essential enabling technology for high-fidelity modeling of engineering problems that involve electromagnetic (EM) field interactions on large, complex domains. In most cases, sparse iterative solution methods are used. However, there are many cases for which existing, preconditioned iterative solvers fail to provide adequate solution methods. Motivated by this limitation, significant effort has recently focused on developing sparse, direct solution methods. Such methods often provide solutions to problems for which iterative methods fail. Unfortunately, there remain many real-world applications where existing sparse direct solvers for electromagnetic applications become computationally prohibitive due to poor conditioning in the underlying matrix equation. This effort proposes to address this issue through the application of a new multilevel preconditioning strategy for sparse direct solvers. It is shown that this strategy enables the solution of problems for which both existing iterative solvers and an existing sparse, direct solver fail. In the proposed effort, this new computational technology will be incorporated into the University of Kentucky's MFDlib sparse direct solver library and tested on problems of interest to NASA"s computational electromagnetics team at the Johnson Space Center.