AN ITERATIVE SOLVER FOR THE HPS DISCRETIZATION APPLIED TO THREE DIMENSIONAL HELMHOLTZ PROBLEMS

This manuscript presents an efficient solver for the linear system that arises from the hierarchical Poincare'--Steklov (HPS) discretization of three dimensional variable coefficient Helmholtz problems. Previous work on the HPS method has tied it with a direct solver. This work is the first efficient iterative solver for the linear system that results from the HPS discretization. The solution technique utilizes GMRES coupled with a locally homogenized block -Jacobi preconditioner. The local nature of the discretization and preconditioner naturally yield the matrix -free application of the linear system. Numerical results illustrate the performance of the solution technique. This includes an experiment where a problem approximately 100 wavelengths in each direction that requires more than a billion unknowns to achieve approximately 4 digits of accuracy takes less than 20 minutes to solve.