A Level-Set Method for Computing the Eigenvalues of Elliptic Operators Defined on Compact Hypersurfaces

@article{Brandman2008ALM,
  title={A Level-Set Method for Computing the Eigenvalues of Elliptic Operators Defined on Compact Hypersurfaces},
  author={Jeremy Brandman},
  journal={J. Sci. Comput.},
  year={2008},
  volume={37},
  pages={282-315}
}
Abstract We demonstrate, through separation of variables and estimates from the semiclassical analysis of the Schrödinger operator, that the eigenvalues of an elliptic operator defined on a compact hypersurface in Rn can be found by solving an elliptic eigenvalue problem in a bounded domain Ω ⊂ Rn. The latter problem is solved using standard finite element methods on the Cartesian grid. We also discuss the application of these ideas to solving evolution equations on surfaces, including a new… CONTINUE READING
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