Abstract
This paper addresses numerical procedures utilized to the accurate and robust calculation of thousands of eigenpairs for the Dirac billiard resonator. The main challenges posed by the present work are: first, the capability of the approaches to tackle the large-scale eigenvalue problem, second, the ability to accurately extract many, i.e. order of thousands, interior eigenfrequencies for the considered problem, and third, the efficient implementation of the underlying approaches. The eigenfield calculations are accomplished in two steps. Initially, the finite integration technique or the finite element method with higher order curvilinear elements is applied, and further, the (B-)Lanczos method with its variations is exploited for the eigenpair determination. The comparative assessment of the numerical results to the complementary measurements confirms the applicability of the approaches and points out the significant reductions of computational costs. Finally, all of the results indicate that the suggested techniques can be used for precise determination of many eigenfrequencies.
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This work was supported by the “Excellence Initiative” of the German Federal and State Governments and the Graduate School of Computational Engineering at TU Darmstadt.
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Banova, T., Ackermann, W., Weiland, T. (2016). Systematic Determination of Eigenfields in Frequency Domain. In: Bartel, A., Clemens, M., Günther, M., ter Maten, E. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry(), vol 23. Springer, Cham. https://doi.org/10.1007/978-3-319-30399-4_5
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DOI: https://doi.org/10.1007/978-3-319-30399-4_5
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