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2010

An Exponentially Convergent Nonpolynomial Finite Element Method for Time-Harmonic Scattering from Polygons

9 years 9 months ago
An Exponentially Convergent Nonpolynomial Finite Element Method for Time-Harmonic Scattering from Polygons
In recent years nonpolynomial finite element methods have received increasing attention for the efficient solution of wave problems. As with their close cousin the method of particular solutions, high efficiency comes from using solutions to the Helmholtz equation as basis functions. We present and analyze such a method for the scattering of two-dimensional scalar waves from a polygonal domain that achieves exponential convergence purely by increasing the number of basis functions in each element. Key ingredients are the use of basis functions that capture the singularities at corners, and representing the scattered field towards infinity by a combination of fundamental solutions. The solution is obtained by minimizing a least-squares functional, which we discretize in such a way that a matrix least-squares problem is obtained. We give computable exponential bounds on the rate of convergence of the least-squares functional that are in very good agreement with the observed numerical ...
A. H. Barnett, Timo Betcke
Added 30 Jan 2011
Updated 30 Jan 2011
Type Journal
Year 2010
Where SIAMSC
Authors A. H. Barnett, Timo Betcke
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