Multigrid solution procedures for structural dynamics eigenvalue problems (Q1207277)

Three multigrid methods are described for solving the generalized symmetric eigenvalue problem encountered in structural dynamics. Two implicit algorithms are discussed that use a multigrid method to solve the linear matrix equations encountered in each iteration of the standard subspace and block Lanczos methods. An explicit method is also outlined which explicitly applies the basic multigrid philosophy of fine mesh relaxation and coarse mesh correction to the eigenvalue problem. The behavior of the methods is studied by examining the selection of convergence tolerances and the solutions of some ill-conditioned problems. A well-conditioned plate problem is solved to demonstrate the computational resources required by the algorithms.