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GMRES with new preconditioning for solving BEM-type linear system

A linear system solver has been proposed by adopting the product-type method as a preconditioner to the generalized minimal residual method (GMRES). When applied to the boundary-element method (BEM)-type linear system arising from the two-dimensional Laplace problem, the solver has a faster speed than the Gaussian elimination. In order to compare the proposed solver with the variable preconditioned conjugate gradient method, the operation count for both methods are estimated. As a result, it is found that the proposed solver is a powerful tool for solving the BEM-type linear system.