Name
Abstract | ||
|---|---|---|
In this paper we propose and analyze a hybrid hp boundary element method for the solution of problems of high frequency acoustic scattering by sound-soft convex polygons, in which the approximation space is enriched with oscillatory basis functions which efficiently capture the high frequency asymptotics of the solution. We demonstrate, both theoretically and via numerical examples, exponential convergence with respect to the order of the polynomials, moreover providing rigorous error estimates for our approximations to the solution and to the far field pattern, in which the dependence on the frequency of all constants is explicit. Importantly, these estimates prove that, to achieve any desired accuracy in the computation of these quantities, it is sufficient to increase the number of degrees of freedom in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1137/110856812 | SIAM JOURNAL ON NUMERICAL ANALYSIS |
Keywords | Field | DocType |
high frequency scattering,boundary element method,hp-method | Discretization,Polygon,Mathematical optimization,Polynomial,Mathematical analysis,Regular polygon,Basis function,Boundary element method,Logarithm,Asymptotic analysis,Mathematics | Journal |
Volume | Issue | ISSN |
51 | 1 | 0036-1429 |
Citations | PageRank | References |
3 | 0.43 | 11 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| D. P. Hewett | 1 | 9 | 2.40 |
| Steve Langdon | 2 | 63 | 12.10 |
| Jens Markus Melenk | 3 | 133 | 24.18 |