A fast algorithm for particle simulations
Journal of Computational Physics
Approximation of integrals for boundary element methods
SIAM Journal on Scientific and Statistical Computing
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
The rapid evaluation of volume integrals of potential theory on general regions
Journal of Computational Physics
Numerical quadratures for layer potentials over curved domains in R3
SIAM Journal on Numerical Analysis
Laplace's equation and the Dirichlet-Neumann map in multiply connected domains
Journal of Computational Physics
A fast Poisson solver for complex geometries
Journal of Computational Physics
Electrostatic fields without singularities: theory and algorithms
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
An {\it bf O(N)} Algorithm for Three-Dimensional N-body Simulations
An {\'it bf O(N)} Algorithm for Three-Dimensional N-body Simulations
A geometric approach to computing higher order form factors
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Rendering equation revisited: how to avoid explicit visibility computations
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
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The following problems that arise in the computation of electrostatic forces and in the Boundary Element Method are considered. Given two convex interior-disjoint polyhedra in 3-space endowed with a volume charge density which is a polynomial in the Cartesian coordinates of R3, compute the Coulomb force acting on them. Given two interior-disjoint polygons in 3-space endowed with a surface charge density which is polynomial in the Cartesian coordinates of R3, compute the normal component of the Coulomb force acting on them. For both problems adaptive Gaussian approximation algorithms are given, which, for n Gaussian points, in time O(n), achieve absolute error Oc-n for a constant c 1. Such a result improves upon previously known best asymptotic bounds. This result is achieved by blending techniques from integral geometry, computational geometry and numerical analysis. In particular, integral geometry is used in order to represent the forces as integrals whose kernal is free from singularities.