On the existence of mosaic-skeleton approximations for discrete analogues of integral operators (Q1687794)

The authors are concerned with the 3D exterior Dirichlet boundary value problem attached to the Laplace and Helmholtz equations. The problems are reduced to some Fredholm integral equations of the first kind. It seems that the integral equations are discretized by a Galerkin-type method. The linear algebraic system provided is solved using the mosaic-skeleton algorithm. This algorithm reduces the computational cost and the complexity of iterative methods for solving dense linear algebraic systems, mainly the matrix-vector multiplication effort. Two numerical examples are carried out in order to illustrate the capabilities of the algorithm.