TY - JOUR
T1 - A High Frequency Boundary Element Method for Scattering by Convex Polygons with Impedance Boundary Conditions
AU - S. N. Chandler-Wilde, S. Langdon & M. Mokgolele
JO - Communications in Computational Physics
VL - 2
SP - 573
EP - 593
PY - 2012
DA - 2012/12
SN - 11
DO - http://doi.org/10.4208/cicp.231209.040111s
UR - https://global-sci.org/intro/article_detail/cicp/7379.html
KW - 
AB - <p style="text-align: justify;">We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions. Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy. Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem, we propose a novel Galerkin boundary element method, with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon. Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.</p>