Parallel solution of the multidimensional Helmholtz/Schroedinger equation using high order methods Original Research Article

We show that high order methods are useful in deriving fast and efficient parallel algorithms for solving multidimensional inhomogeneous Helmholtz/Schroedinger equations. Using high order methods we represent one-dimensional operators by small size matrices that serve together to construct an efficiently parallelizable preconditioner. The coupled multidimensional sparse system of equations is then solved iteratively on massively parallel systems with linear speedup. As an example, we demonstrate linear speed up in performance on the IBM SP2 massively parallel machine.