A fast algorithm for particle simulations
Journal of Computational Physics
Rapid solution of integral equations of scattering theory in two dimensions
Journal of Computational Physics
Efficient algorithms for computing a strong rank-revealing QR factorization
SIAM Journal on Scientific Computing
A fast direct solver for boundary integral equations in two dimensions
Journal of Computational Physics
Journal of Computational Physics
Efficient discretization of Laplace boundary integral equations on polygonal domains
Journal of Computational Physics
Universal quadratures for boundary integral equations on two-dimensional domains with corners
Journal of Computational Physics
The effective conductivity of random checkerboards
Journal of Computational Physics
A Nonlinear Optimization Procedure for Generalized Gaussian Quadratures
SIAM Journal on Scientific Computing
A Fast and Stable Solver for Singular Integral Equations on Piecewise Smooth Curves
SIAM Journal on Scientific Computing
Journal of Computational Physics
A Nyström method for weakly singular integral operators on surfaces
Journal of Computational Physics
Advances in Computational Mathematics
Hi-index | 31.46 |
We describe an approach to the numerical solution of the integral equations of scattering theory on planar curves with corners. It is rather comprehensive in that it applies to a wide variety of boundary value problems; here, we treat the Neumann and Dirichlet problems as well as the boundary value problem arising from acoustic scattering at the interface of two fluids. It achieves high accuracy, is applicable to large-scale problems and, perhaps most importantly, does not require asymptotic estimates for solutions. Instead, the singularities of solutions are resolved numerically. The approach is efficient, however, only in the low- and mid-frequency regimes. Once the scatterer becomes more than several hundred wavelengths in size, the performance of the algorithm of this paper deteriorates significantly. We illustrate our method with several numerical experiments, including the solution of a Neumann problem for the Helmholtz equation given on a domain with nearly 10000 corner points.