Mesh-based multi-frontal solver with reuse of partial LU factorizations for antenna array

Abstract

There are a number of relevant physical problems in which their problem domains consist of the repetition of a given subdomain. The traditional multi-frontal solver implementations, like MUMPS or SuperLU, get on the input the global sparse linear system of equations. They are not aware of the structure of the computational mesh. They do not know that some parts of the mesh, i.e., some sub-domains are identical. In such a case, some sub-matrices of the global matrix are identical. However, when we assemble the matrices corresponding to identical sub-domains into a global sparse system, they overlap, and we ignore that they corresponded to identical sub-domains. In this paper we advocate another approach to this computational problem, based on the additional knowledge of the structure of the computational mesh. We propose a wrapper over a multi-frontal solver that partitions the computational problem into a cascade of sub-problems, for which a traditional multi-frontal solver is called and asked for the Schur complements. Such solver wrapper can massively reuse computations performed over identical sub-domains, as well as it can propagate this reuse technique towards further elimination steps. We test our reuse solver on a problem consisting of an arrays of antennas and compare it against the execution time of a traditional sparse matrix-based multi-frontal solver called for the entire domain.