Accessibility navigation

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

Banett, A.H. and Betcke, T. (2010) An Exponentially Convergent Nonpolynomial Finite Element Method for Time-Harmonic Scattering from Polygons. Siam Journal on Scientific Computing, 32 (3). pp. 1417-1441. ISSN 1064-8275

Text - Published Version
· Please see our End User Agreement before downloading.


It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

To link to this item DOI: 10.1137/090768667


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 the representation of 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 convergence. Challenging numerical examples, including a nonconvex polygon with several corner singularities, and a cavity domain, are solved to around 10 digits of accuracy with a few seconds of CPU time. The examples are implemented concisely with MPSpack, a MATLAB toolbox for wave computations with nonpolynomial basis functions, developed by the authors. A code example is included.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:17191
Publisher:Society for Industrial and Applied Mathematics


Downloads per month over past year

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation