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
Solution of the Sylvester matrix equation AXBT + CXDT = E
ACM Transactions on Mathematical Software (TOMS)
Electrostatics and heat conduction in high contrast composite materials
Journal of Computational Physics
On the evaluation of layer potentials close to their sources
Journal of Computational Physics
Journal of Computational Physics
A Fast Direct Solver for a Class of Elliptic Partial Differential Equations
Journal of Scientific Computing
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
A fast direct solver for the integral equations of scattering theory on planar curves with corners
Journal of Computational Physics
| Hi-index | 31.46 |
An algorithm is presented for the fast and accurate solution of the electrostatic equation on multi-component random checkerboards. It relies on a particular choice of integral equation, extended as to separate ill-conditioning due to singular fields in corners from ill-conditioning due to interaction of clusters of well-conducting squares at large distances. Two separate preconditioners take care of the two separate phenomena. In a series of numerical examples, effective conductivities are computed for random checkerboards containing up to 10^4 squares with conductivity ratios of up to 10^6. The achievable relative precision in these examples is on the order of 10^-^1^1.