A Near-Field Preconditioner for Surface Integral Equations Based on Nested Dissection Reordering

An effective preconditioner is presented for a surface integral equation (SIE) in the electromagnetic wave scattering problem. To alleviate the effect of the strong near field, a sparse matrix is extracted from the SIE matrix within a predetermined distance. Nested dissection reordering based on geometrical information is used to minimize the nonzeros after factorization of the extracted sparse matrix. In addition, a low-rank approximation of
off
-diagonal terms successfully further reduces the computational resources. Moreover, numerical validation is exhibited, including eigenspectrum and complexity estimation. Finally, the ill-conditioned scattering problem of a mock-up F-16 jet fighter is considered, an application to show the robustness of the proposed method.