Article ID Journal Published Year Pages File Type
519268 Journal of Computational Physics 2011 13 Pages PDF
Abstract

Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace–Beltrami operator on rather general curved surfaces. Our algorithm, which is based on the Closest Point Method, relies on an embedding of the surface in a higher-dimensional space, where standard Cartesian finite difference and interpolation schemes can be easily applied. We show that there is a one-to-one correspondence between a problem defined in the embedding space and the original surface problem. For open surfaces, we present a simple way to impose Dirichlet and Neumann boundary conditions while maintaining second-order accuracy. Convergence studies and a series of examples demonstrate the effectiveness and generality of our approach.

► A simple algorithm for solving eigenvalue problems on a general curved surfaces. ► Implicit representation of the geometry allows for open or non-orientable surfaces. ► A simple way to impose Dirichlet and Neumann boundary conditions. ► Includes Laplace–Beltrami example computations and convergence studies.

Related Topics
Physical Sciences and Engineering Computer Science Computer Science Applications
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