An efficient finite element method applied to quantum billiard systems

Woo-Sik Son; Sunghwan Rim; Chil-Min Kim

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arXiv · 0902.0499

An efficient finite element method applied to quantum billiard systems

Woo-Sik Son·Sunghwan Rim·Chil-Min Kim

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Abstract

An efficient finite element method (FEM) for calculating eigenvalues and eigenfunctions of quantum billiard systems is presented. We consider the FEM based on triangular $C_1$ continuity quartic interpolation. Various shapes of quantum billiards including an integrable unit circle are treated. The numerical results show that the applied method provides accurate set of eigenvalues exceeding a thousand levels for any shape of quantum billiards on a personal computer. Comparison with the results from the FEM based on well-known $C_0$ continuity quadratic interpolation proves the efficiency of the method.

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Woo-Sik Son, Sunghwan Rim, Chil-Min Kim. 2009-02-25. An efficient finite element method applied to quantum billiard systems. https://arxiv.org/abs/0902.0499

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