Data-sparse LU-decomposition preconditioning combined with multilevel fast multipole method for electromagnetic scattering problems

Abstract

Owing to the robust of the multilevel fast multipole method (MLFMM), large dense linear systems, arising from discretised electric field integral equations of electromagnetic scattering problems, are generally solved by a Krylov iterative solver. An efficient preconditioning technique based on hierarchical LU-decomposition (ℋ-LU) is proposed to accelerate the convergence rate of the Krylov iterations. The ℋ-LU preconditioner is constructed from the available sparse near-field matrix and provides a data-sparse way to approximate its LU-factors, which can be computed and stored in ℋ-matrix arithmetic with almost linear complexity. The accuracy of the approximation is adjustable that will guarantee a bounded number of iterations. Some means are introduced to further lower the computational cost of the ℋ-LU. Numerical examples are provided to illustrate that the resulting ℋ-LU preconditioner is effective and flexible with MLFMM to reduce both the iteration number and the overall simulation time significantly.