Preconditioners for large dense matrices in a low-rank format

Abstract In this paper, we apply low rank approximations to a large dense matrix in the solution of an integral equation in the problems of electromagnetic wave diffraction on a perfectly conductive object. In the case of a large wave number, the matrix of the system becomes ill-conditioned, therefore, we propose to use a preconditioner to solve the system with such a matrix by an iterative method. Based on block-sparse matrices, two types of preconditioners are constructed in this paper. Low-rank approximations are used to store the factors of the LU decomposition of the preconditioner matrix. The preconditioners make it possible to obtain a solution to the diffraction problem on a perfectly conductive object of 120 wavelengths.