Direct Solution of MoM Matrix Equation Using Sherman-Morrison-Woodbury Formula-Based Algorithm with Lagrange Interpolations

In this article, the Sherman-Morrison-Woodbury (SMW) formula is applied to accelerate the direct solution of electromagnetic scattering problem for three-dimensional (3D) perfect electric conducting (PEC) objects with the Lagrange interpolations. To speed up the direct solution of the matrix equation, the dense impedance matrix is transformed into products of several diagonal matrix blocks via the SMW formula. The Lagrange interpolation algorithm effectively compresses the matrices of far blocks interactions. The numerical results demonstrate the effectiveness and accuracy of the proposed algorithm.