Multigrid and cyclic reduction applied to the Helmholtz equation

Kenneth Brackenridge

Oxford University Computing Laboratory, Oxford OX1 3QD, U.K.


We consider the Helmholtz equation with a discontinuous complex parameter and inhomogeneous Dirichlet boundary conditions in a rectangular domain. A variant of the direct method of cyclic reduction is employed to facilitate the design of improved multigrid components, resulting in the method of CR-MG. We demonstrate the improved convergence properties of this method.