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

被引：12

作者：

Brandman, Jeremy ^{[1
]}

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2008年 / 37卷 / 03期

基金：

美国国家科学基金会;

关键词：

Level-set method; Eigenvalues; Elliptic operator; Finite element method; Semi-classical analysis of the Schrodinger equation;

D O I：

10.1007/s10915-008-9210-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We demonstrate, through separation of variables and estimates from the semi-classical analysis of the Schrodinger 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 Omega Cn. 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 proof of a result due to Greer (J. Sci. Comput. 29(3):321-351, 2006).

引用

页码：282 / 315

页数：34

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