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arXiv · 1812.03006

Modal Tracking Based on Group Theory

Michal Masek·Miloslav Capek·Lukas Jelinek·Kurt Schab
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Abstract

Issues in modal tracking in the presence of crossings and crossing avoidances between eigenvalue traces are solved via the theory of point groups. The von Neumann-Wigner theorem is used as a key factor in predictively determining mode behavior over arbitrary frequency ranges. The implementation and capabilities of the proposed procedure are demonstrated using characteristic mode decomposition as a motivating example. The procedure is, nevertheless, general and can be applied to an arbitrarily parametrized eigenvalue problems. A treatment of modal degeneracies is included and several examples are presented to illustrate modal tracking improvements and the immediate consequences of improper modal tracking. An approach leveraging a symmetry-adapted basis to accelerate computation is also discussed. A relationship between geometrical and physical symmetries is demonstrated on a practical example.

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Michal Masek, Miloslav Capek, Lukas Jelinek, Kurt Schab. 2018-12-07. Modal Tracking Based on Group Theory. https://doi.org/10.1109/tap.2019.2943354

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