Fast Direct Solution of Composite Conducting-Dielectric Arrays Using Sherman-Morrison-Woodbury Algorithm

Abstract

Abstract-In this paper, the Sherman-Morrison-Woodbury (SMW) Formula-based algorithm (SMWA) is used to enable the fast direct solution of conducting-dielectric arrays. To speed up the direct solution of the matrix equation, the dense impedance matrix is transformed into a product of several block diagonal matrices via the SMW formula. In the grouping process, the situation that the elements of an array simultaneously belong to two different subgroups at peer level is avoided in order to promote the efficiency. The SMWA conducts the calculation with a respectable reduction in the computational time as well as memory.

Diagonal Factorization of Integral Equation Matrices via Localizing Sources and Orthogonally Matched Receivers

“…Multiple strategies have been used to develop sparse direct solvers, e.g., [1][2][3][4][5][6][7]. The set of approaches considered here are based on the use of localizing functions [8][9][10][11][12][13].…”