Directional Preconditioner for 2D High Frequency Obstacle Scattering

The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems from bounded scatterers. This paper presents the directional preconditioner for the linear systems of the boundary integral method in two dimensions. This new preconditioner builds a data-sparse approximation of the integral operator, transforms it into a sparse linear system, and computes an approximate inverse with efficient sparse linear algebra algorithms. This preconditioner is efficient and results in small and almost frequency-independent iteration counts for nonresonant scatterers when combined with standard iterative solvers. Numerical results are provided to demonstrate the effectiveness of the new preconditioner.