On Convergence of Iterative Matrix Solver Preconditioned with H-Matrix in Locally Corrected Nyström Discretization of CFIE

In the present study, we discuss a fast, parallel iterative solution of the Combined Field Integral Equation (CFIE) through the discretization with the Locally Corrected Nystrom (LCN) method. A less precise H-matrix, derived from the coefficient matrix, is employed as a preconditioner in the context of a linear iterative method such as GMRES. The employment of a less accurate preconditioner constructed with lower precision both at the stage of computing the H-matrix and its subsequent factorization is shown to effectively accelerate the iterative matrix equation solution. The effect of the numerical tolerance in formation of the preconditioner H-matrix and its factorization on the rate of convergence is studied.