The Mathematical Institute, University of Oxford, Eprints Archive

Reviving the Method of Particular Solutions

Betcke, Timo and Trefethen, Lloyd N. (2003) Reviving the Method of Particular Solutions. Technical Report. Unspecified. (Submitted)

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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.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1196
Deposited By:Lotti Ekert
Deposited On:18 May 2011 08:12
Last Modified:18 May 2011 08:12

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