Accurate Determination of Thousands of Eigenvalues for Large-Scale Eigenvalue Problems

In this paper, we address a fast approach for an accurate eigenfrequency determination, based on a finite-element computation of electromagnetic fields for a superconducting cavity and further employment of the Lanczos method for the eigenvalue determination. The major challenges posed by this paper are: 1) the ability of the approach to tackle the large-scale eigenvalue problem and 2) the capability to extract many, i.e., order of thousands, eigenfrequencies for the considered problem. In addition to the need to ensure high precision of the calculated eigenfrequencies, we compare them side by side with the reference data available from analytical expressions and CEM3D eigenmode solver. Furthermore, the simulations have shown high accuracy of this technique and good agreement with the reference data. Finally, all of the results show that the suggested technique can be used for precise determination of many eigenfrequencies.