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
On the numerical evaluation of electrostatic fields in dense random dispersions of cylinders
Journal of Computational Physics
SIAM Journal on Applied Mathematics
Nonlinear Optimization, Quadrature, and Interpolation
SIAM Journal on Optimization
A numerical model of stress driven grain boundary diffusion
Journal of Computational Physics
A fast direct solver for boundary integral equations in two dimensions
Journal of Computational Physics
Electrostatics and heat conduction in high contrast composite materials
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
On the evaluation of layer potentials close to their sources
Journal of Computational Physics
Integral equation methods for elliptic problems with boundary conditions of mixed type
Journal of Computational Physics
Efficient discretization of Laplace boundary integral equations on polygonal domains
Journal of Computational Physics
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 Fast and Stable Solver for Singular Integral Equations on Piecewise Smooth Curves
SIAM Journal on Scientific Computing
A fast direct solver for the integral equations of scattering theory on planar curves with corners
Journal of Computational Physics
Journal of Computational Physics
Quadrature by expansion: A new method for the evaluation of layer potentials
Journal of Computational Physics
Journal of Computational Physics
Advances in Computational Mathematics
Hi-index | 31.50 |
We take a fairly comprehensive approach to the problem of solving elliptic partial differential equations numerically using integral equation methods on domains where the boundary has a large number of corners and branching points. Use of non-standard integral equations, graded meshes, interpolatory quadrature, and compressed inverse preconditioning are techniques that are explored, developed, mixed, and tested on some familiar problems in materials science. The recursive compressed inverse preconditioning, the major novelty of the paper, turns out to be particularly powerful and, when it applies, eliminates the need for mesh grading completely. In an electrostatic example for a multiphase granular material with about two thousand corners and triple junctions and a conductivity ratio between phases up to a million we compute a common functional of the solution with an estimated relative error of 10^-^1^2. In another example, five times as large but with a conductivity ratio of only a hundred, we achieve an estimated relative error of 10^-^1^4.