Rapid methods for the conformal mapping of multiply connected regions
Journal of Computational and Applied Mathematics
A computational model of aquatic animal locomotion
Journal of Computational Physics
Computer simulation using particles
Computer simulation using particles
Journal of Computational Physics
Rapid solution of integral equations of scattering theory in two dimensions
Journal of Computational Physics
Fast parallel iterative solution of Poisson's and the biharmonic equations on irregular regions
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
On the difficulty of triangulating three-dimensional nonconvex polyhedra.
Discrete & Computational Geometry
The rapid evaluation of volume integrals of potential theory on general regions
Journal of Computational Physics
On the numerical solution of the biharmonic equation in the plane
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Wavelet-like bases for the fast solutions of second-kind integral equations
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
A fast Poisson solver for complex geometries
Journal of Computational Physics
Integral equation methods for Stokes flow and isotropic elasticity in the plane
Journal of Computational Physics
A direct adaptive Poisson solver of arbitrary order accuracy
Journal of Computational Physics
Asymptotic Expansion of the Free-space Green's Function for the Discrete 3-D Poisson Equation
SIAM Journal on Scientific Computing
Rapid parallel evaluation of integrals in potential theory on general three-dimensional regions
Journal of Computational Physics
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
A Fast Direct Solution of Poisson's Equation Using Fourier Analysis
Journal of the ACM (JACM)
The immersed interface method for the Navier-Stokes equations with singular forces
Journal of Computational Physics
A New Fast-Multipole Accelerated Poisson Solver in Two Dimensions
SIAM Journal on Scientific Computing
A fast solver for the Stokes equations with distributed forces in complex geometries
Journal of Computational Physics
Journal of Computational Physics
Note: Analytic inversion of the five-point poisson operator
Journal of Computational Physics
Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
Journal of Computational Physics
On the evaluation of layer potentials close to their sources
Journal of Computational Physics
Journal of Computational Physics
MIB method for elliptic equations with multi-material interfaces
Journal of Computational Physics
Fast integral equation methods for Rothe's method applied to the isotropic heat equation
Computers & Mathematics with Applications
A kernel-free boundary integral method for implicitly defined surfaces
Journal of Computational Physics
Hi-index | 31.47 |
We present two methods for the rapid, high order accurate evaluation of integrals in potential theory on general, unbounded 3D regions. Our methods allow for direct calculation of derivatives of the integrals as well. One of the methods uses a fourth order compact stencil, and the other uses a nonstandard variant of Richardson extrapolation. Both methods involve calculation of discontinuities in high order derivatives of the integrals across the boundary of the integration region. The extrapolation method, in addition, involves correction for the discontinuities in truncation error. The number of operations required for the methods is essentially equal to twice the number of operations needed to solve Poisson's equation on a regular grid. Both methods avoid problems associated with using quadrature methods to evaluate integrals with singular kernels. Numerical results are presented for experiments on a variety of geometries in free space.