Vladimir Rokhlin

A fast algorithm for particle simulations

An algorithm is presented for the rapid evaluation of the potential and force fields in systems involving large numbers of particles whose interactions are Coulombic or gravitational in nature. For a system ofNparticles, an amount of work of the orderO(N2) has traditionally been required to evaluate all pairwise interactions, unless some approximation or truncation method is used. The algorithm of the present paper requires an amount of work proportional toNto evaluate all interactions to within roundoff error, making it considerably more practical for large-scale problems encountered in plasma physics, fluid dynamics, molecular dynamics, and celestial mechanics.

The fast multipole method for the wave equation: a pedestrian prescription

A practical and complete, but not rigorous, exposition of the fact multiple method (FMM) is provided. The FMM provides an efficient mechanism for the numerical convolution of the Greens function for the Helmholtz equation with a source distribution and can be used to radically accelerate the iterative solution of boundary-integral equations. In the simple single-stage form presented here, it reduces the computational complexity of the convolution from O(N/sup 2/) to O(N/sup 3/2/), where N is the dimensionality of the problems discretization.<<ETX>>

Rapid solution of integral equations of classical potential theory

An algorithm is described for rapid solution of classical boundary value problems (Dirichlet an Neumann) for the Laplace equation based on iteratively solving integral equations of potential theory. CPU time requirements for previously published algorithms of this type are proportional to n2, where n is the number of nodes in the discretization of the boundary of the region. The CPU time requirements for the algorithm of the present paper are proportional to n, making it considerably more practical for large scale problems.

Rapid solution of integral equations of scattering theory in two dimensions

Abstract The present paper describes an algorithm for rapid solution of boundary value problems for the Helmholtz equation in two dimensions based on iteratively solving integral equations of scattering theory. CPU time requirements of previously published algorithms of this type are of the order n 2 , where n is the number of nodes in the discretization of the boundary of the scatterer. The CPU time requirements of the algorithm of the present paper are n 4 3 , and can be further reduced, making it considerably more practical for large scale problems.

A New Version of the Fast Multipole Method for the Laplace Equation in Three Dimensions.

Abstract : We introduce a new version of the Fast Multipole Method for the evaluation of potential fields in three dimensions. It is based on a new diagonal form for translation operators and yields high accuracy at a reasonable cost.

Fast Fourier transforms for nonequispaced data

A group of algorithms is presented generalizing the fast Fourier transform to the case of noninteger frequencies and nonequispaced nodes on the interval

A Fast Adaptive Multipole Algorithm for Particle Simulations

[ - \pi ,\pi ]

The fast multipole method (FMM) for electromagnetic scattering problems

. The schemes of this paper are based on a combination of certain analytical considerations with the classical fast Fourier transform and generalize both the forward and backward FFTs. Each of the algorithms requires

Wavelet-like bases for the fast solutions of second-kind integral equations

O(N\cdot \log N + N\cdot \log (1/\varepsilon ))

Randomized algorithms for the low-rank approximation of matrices

arithmetic operations, where