A Fast Propagation Method for the Helmholtz Equation

A fast method is proposed for solving the high frequency Helmholtz equation. The building block of the new fast method is an overlapping domain decomposition method for layered medium. In the new fast method, the computation domain is?rstly decomposed hierarchically into many subdomains on different levels. Then the mapping from incident waves to out-going waves on all the subdomains are set up. Finally, the wave propagates on the subdomain boundaries on different levels to reach the solution to the Helmholtz equation. The new fast method is of low complexity, and suitable for parallel computing. Numerical experiments show that with the new fast method, 2D Helmholtz equations with half billion unknowns could be solved efficiently on massively parallel machines.