A multigrid method for the generalized symmetric eigenvalue problem: Part I—algorithm and implementation

A multigrid method is described that can solve the generalized eigenvalue problem encountered in structural dynamics. The algorithm combines relaxation on a fine mesh with the solution of a singular equation on a coarse mesh. A sequence of coarser meshes may be used to quickly solve this singular equation using another multigrid method. The hierarchy of increasingly finer meshes can be further exploited using a nested iteration scheme, whereby initial approximations to the fine mesh eigenvectors are computed using interpolated coarse mesh eigenvectors. The solution of some simple plate problems on a Convex C240 demonstrates the efficiency of a vectorized version of the multigrid algorithm.