GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A fast algorithm for particle simulations
Journal of Computational Physics
Implementation of the GMRES method using householder transformations
SIAM Journal on Scientific and Statistical Computing - Telecommunication Programs at U.S. Universities
Laplace's equation and the Dirichlet-Neumann map in multiply connected domains
Journal of Computational Physics
Thin bridges in isotropic electrostatics
Journal of Computational Physics
Integral equation methods for Stokes flow and isotropic elasticity in the plane
Journal of Computational Physics
Fast algorithms for polynomial interpolation, integration, and differentiation
SIAM Journal on Numerical Analysis
Microstructural evolution in inhomogeneous elastic media
Journal of Computational Physics
On the numerical evaluation of electrostatic fields in dense random dispersions of cylinders
Journal of Computational Physics
Algorithm 788: automatic boundary integral equation programs for the planar Laplace equation
ACM Transactions on Mathematical Software (TOMS)
Generalized Gaussian Quadratures and Singular Value Decompositions of Integral Operators
SIAM Journal on Scientific Computing
Scientific Computing
The use of rational functions in numerical quadrature
Journal of Computational and Applied Mathematics - Special issue on orthogonal polynomials, special functions and their applications
Evaluation of Single Layer Potentials over Curved Surfaces
SIAM Journal on Scientific Computing
A Method for Computing Nearly Singular Integrals
SIAM Journal on Numerical Analysis
A numerical model of stress driven grain boundary diffusion
Journal of Computational Physics
A fast solver for the Stokes equations with distributed forces in complex geometries
Journal of Computational Physics
Laplace's equation and the Dirichlet-Neumann map: a new mode for Mikhlin's method
Journal of Computational Physics
Electrostatics and heat conduction in high contrast composite materials
Journal of Computational Physics
Fast evaluation of electro-static interactions in multi-phase dielectric media
Journal of Computational Physics
Fourth order accurate evaluation of integrals in potential theory on exterior 3D regions
Journal of Computational Physics
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
Journal of Computational Physics
Journal of Computational Physics
Faster convergence and higher accuracy for the Dirichlet-Neumann map
Journal of Computational Physics
Integral equation methods for elliptic problems with boundary conditions of mixed type
Journal of Computational Physics
Stokes-Darcy boundary integral solutions using preconditioners
Journal of Computational Physics
Journal of Computational Physics
The effective conductivity of random checkerboards
Journal of Computational Physics
A Fast and Stable Solver for Singular Integral Equations on Piecewise Smooth Curves
SIAM Journal on Scientific Computing
Stability of the Nyström Method for the Sherman-Lauricella Equation
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Quadrature by expansion: A new method for the evaluation of layer potentials
Journal of Computational Physics
Hi-index | 31.49 |
When solving elliptic boundary value problems using integral equation methods one may need to evaluate potentials represented by a convolution of discretized layer density sources against a kernel. Standard quadrature accelerated with a fast hierarchical method for potential field evaluation gives accurate results far away from the sources. Close to the sources this is not so. Cancellation and nearly singular kernels may cause serious degradation. This paper presents a new scheme based on a mix of composite polynomial quadrature, layer density interpolation, kernel approximation, rational quadrature, high polynomial order corrected interpolation and differentiation, temporary panel mergers and splits, and a particular implementation of the GMRES solver. Criteria for which mix is fastest and most accurate in various situations are also supplied. The paper focuses on the solution of the Dirichlet problem for Laplace's equation in the plane. In a series of examples we demonstrate the efficiency of the new scheme for interior domains and domains exterior to up to 2000 close-to-touching contours. Densities are computed and potentials are evaluated, rapidly and accurate to almost machine precision, at points that lie arbitrarily close to the boundaries.