Iterative convergence of boundary-volume integral equation method

The boundary-volume integral equation numerical technique can be a powerful tool for piecewise heterogeneous media, but it is limited to small problems or low frequencies because of great computational cost. Therefore, a restarted GMRES method is applied to solve large-scale boundary-volume scattering problems in this paper to overcome the computational barrier. The iterative method is firstly applied to responses of dimensionless frequency to a semicircular alluvial valley filled with sediments, compared with the standard Gaussian elimination method. Then the method is tested by a heterogeneous multilayered model to show its applicability. Numerical experiments indicate that the preconditioned GMRES method can significantly improve computational efficiency especially for large Earth models and high frequencies, but with a faster convergence for the left diagonal preconditioning.