An algebraic multigrid wave–ray algorithm to solve eigenvalue problems for the helmholtz operator.

Helmholtz equations with variable coefficients are known to be hard to solve both analytically and numerically. In this paper, we introduce a numerical multigrid solver for one-dimensional Helmholtz eigenvalue problems with periodic potentials and solutions. The solvers employ wave–ray methodology suggested by Brandt, Livshits for Helmholtz equations with constant coefficients. The paper concludes with numerical experiments and the discussion of future efforts for solving two-dimensional problems. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]