TEMF, TU Darmstadt, Darmstadt, Germany
Efficient and accurate computation of eigenvalues and eigenvectors is of fundamental importance in the accelerator physics community. Moreover, the eigensystem analysis is generally used for the identifications of many physical phenomena connected to vibrations. Therefore, various types of algorithms such that Arnoldi, Lanczos, Krylov-Schur, Jacobi-Davidson etc. were implemented to solve the eigenvalue problem efficiently. In this direction, we investigate the performance of selected commercial and freely available software tools for the solution of a generalized eigenvalue problem. We choose two setups by considering spherical and billiard resonators in order to test the robustness, accuracy, and computational speed and memory consumption issues of the recent versions of CST, Matlab, Pysparse, SLEPc and CEM3D. Simulations were performed on a standard personal computer as well as on a cluster computer to enable the handling of large sparse matrices in the order of hundreds of thousands up to several millions degrees of freedom. We obtain interesting comparison results with the examined solvers which is useful for choosing the appropriate solvers for a given practical application.
