An efficient finite element method applied to quantum billiard systems

Details An efficient finite element method applied to quantum billiard systems An efficient finite element method applied to quantum billiard systems

2009-02-03

arxiv.org/abs/0902.0499v2

Nonlinear Sciences

Chaotic Dynamics

submitted to Phys. Rev. E

Scientific paper

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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