High-Order Corrected Trapezoidal Quadrature Rules for Singular Functions
SIAM Journal on Numerical Analysis
Hybrid Gauss-Trapezoidal Quadrature Rules
SIAM Journal on Scientific Computing
Journal of Computational Physics
Locally corrected Nyström method for EM scattering by bodies of revolution
Journal of Computational Physics
A fast direct solver for boundary integral equations in two dimensions
Journal of Computational Physics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Numerical Methods for Special Functions
Numerical Methods for Special Functions
A fast direct solver for the integral equations of scattering theory on planar curves with corners
Journal of Computational Physics
On the numerical evaluation of the singular integrals of scattering theory
Journal of Computational Physics
Advances in Computational Mathematics
Hi-index | 31.45 |
A scheme for rapidly and accurately computing solutions to boundary integral equations (BIEs) on rotationally symmetric surfaces in R^3 is presented. The scheme uses the Fourier transform to reduce the original BIE defined on a surface to a sequence of BIEs defined on a generating curve for the surface. It can handle loads that are not necessarily rotationally symmetric. Nystrom discretization is used to discretize the BIEs on the generating curve. The quadrature is a high-order Gaussian rule that is modified near the diagonal to retain high-order accuracy for singular kernels. The reduction in dimensionality, along with the use of high-order accurate quadratures, leads to small linear systems that can be inverted directly via, e.g., Gaussian elimination. This makes the scheme particularly fast in environments involving multiple right hand sides. It is demonstrated that for BIEs associated with the Laplace and Helmholtz equations, the kernel in the reduced equations can be evaluated very rapidly by exploiting recursion relations for Legendre functions. Numerical examples illustrate the performance of the scheme; in particular, it is demonstrated that for a BIE associated with Laplace's equation on a surface discretized using 320,800 points, the set-up phase of the algorithm takes 1min on a standard laptop, and then solves can be executed in 0.5s.