Wave-ray algorithms for Helmholtz equations with variable wave numbers: a one-dimensional implementation of two-dimensional ideas

The subject of this paper is multigrid solvers for Helmholtz operators with large wave numbers. Algorithms presented here are variations of the wave-ray solver which is modified to allow efficient solutions for operators with constant, continuous, and discontinuous wave numbers. Both geometric and algebraic frameworks are employed, all yielding efficient and scalable solvers at very little additional costs, compared to standard multigrid techniques. The algorithms are implemented in one dimension, but with a clear extension to higher dimensions.