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Solving eigenvalue problems on curved surfaces using the Closest Point Method

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 ...

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Publication status:
Published

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Publisher copy:
10.1016/j.jcp.2011.06.021

Authors


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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
JOURNAL OF COMPUTATIONAL PHYSICS
Volume:
230
Issue:
22
Pages:
7944-7956
Publication date:
2011-09-10
DOI:
EISSN:
1090-2716
ISSN:
0021-9991
URN:
uuid:b8618849-eb6f-44ab-b3ae-ff0b5ed4b1e9
Source identifiers:
190670
Local pid:
pubs:190670

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