216 IGPM216.pdf        June 2002
TITLE On a Multigrid Method for Solving Partial Eigenproblems
AUTHORS Maxim Larin
ABSTRACT In the early eighties the direct application of a multigrid technique for solving the partial eigenvalue problem of computing few of the smallest eigenvalues and their corresponding eigenvectors of a large symmetric positive definite matrix A was proposed by Brandt, McCormick and Ruge [4]. This method solves the eigenvalue problems on the sequence of nested grids using an interpolant of the solution on each grid as the initial guess for the next one and improving it by the Full Approximation Scheme (FAS) [3] applied as an inner nonlinear multigrid method. In the present paper an experimental study of the method for model elliptic and linear elasticity problems is carried out. Based on these results the quality of the method is improved by using the nonlinear Gauss-Seidel iteration as pre- and postsmoothing steps. Finally, we give some practical advice for a good choice of multigrid-related parameters.
KEYWORDS multigrid methods, eigenvalue problems, sparse matrices