A comparison of solvers for large eigenvalue problems occuring in the design of resonant cavities (Q2760335)

Four solvers for large sparse generalized eigenvalue problems are compared with respect to their execution time. The goal is to compute a few of the lowest eigenfrequencies of standing electromagnetic waves in a resonant cavity. Linear as well as quadratic Lagrange and Nédélec finite elements are used to discretize a penalty and mixed formulation, respectively. The solvers investigated are (a) subspace iteration, (b) block Lanczos and (c) implicitly restarted Lanczos algorithm, (d) Jacobi-Davidson algorithm. NEWLINENEWLINENEWLINEOn the basis of a model 3D problem with known eigenvalues, the authors come to the conclusion that the penalty method yields a better price-performance rate than the mixed method, and that quadratic elements should be preferred over linear elements. As for the solvers, (b) is by far the fastest but its memory requirements put rather strict limits on a problem size. For large problems, (c) and (d) perform best. NEWLINENEWLINENEWLINEBefore presenting the numerical experiments, the authors introduce the tested methods in a brief but well-informed way. Among references, the Technical Report 275, ETH Zürich, October 1997, published by the authors and \textit{S.~Adam} gives further details and reports on multiple processors experiments. It is available at the URL \url{http://www.inf.ethz.ch/publications/}.