Reviving the Method of Particular Solutions

Betcke, Timo and Trefethen, Lloyd N. (2005) Reviving the Method of Particular Solutions. SIAM Review, 47 (3). pp. 469-491. ISSN 0036-1445

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Abstract

Fox, Henrici, and Moler made famous a "method of particular solutions" for computing eigenvalues and eigenmodes of the Laplacian in planar regions such as polygons. We explain why their formulation of this method breaks down when applied to regions that are insufficiently simple and propose a modification that avoids these difficulties. The crucial changes are to introduce points in the interior of the region as well as on the boundary and to minimize a subspace angle rather than just a singular value or a determinant. Similar methods may be used to improve other "mesh-free" algorithms for a variety of computational problems.

Item Type: Article
Uncontrolled Keywords: eigenvalues, method of particular solutions, subspace angles
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Dr. Timo Betcke
Date Deposited: 14 Sep 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/589

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