Rapid solution of integral equations of scattering theory in two dimensions
Journal of Computational Physics
Multipole translation theory for the three-dimensional Laplace and Helmholtz equations
SIAM Journal on Scientific Computing
Fast Fourier Transform Accelerated Fast Multipole Algorithm
SIAM Journal on Scientific Computing
Analysis of the truncation errors in the fast multipole method for scattering problems
Journal of Computational and Applied Mathematics - Proceedings of the 8th international congress on computational and applied mathematics
The fast multipole method: numerical implementation
Journal of Computational Physics
SIAM Journal on Numerical Analysis
The Fast Multipole Method I: Error Analysis and Asymptotic Complexity
SIAM Journal on Numerical Analysis
Accelerating Fast Multipole Methods for the Helmholtz Equation at Low Frequencies
IEEE Computational Science & Engineering
The Accuracy of Fast Multipole Methods for Maxwell's Equations
IEEE Computational Science & Engineering
A faster aggregation for 3D fast evanescent wave solvers using rotations
Journal of Computational Physics
Journal of Computational Physics
High performance BLAS formulation of the multipole-to-local operator in the fast multipole method
Journal of Computational Physics
Fast electrostatic force calculation on parallel computer clusters
Journal of Computational Physics
A low frequency stable plane wave addition theorem
Journal of Computational Physics
Multistep and Multistage Convolution Quadrature for the Wave Equation: Algorithms and Experiments
SIAM Journal on Scientific Computing
Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation
Journal of Computational Physics
A new Fast Multipole formulation for the elastodynamic half-space Green's tensor
Journal of Computational Physics
Hi-index | 31.48 |
The solution of the Helmholtz and Maxwell equations using integral formulations requires to solve large complex linear systems. A direct solution of those problems using a Gauss elimination is practical only for very small systems with few unknowns. The use of an iterative method such as GMRES can reduce the computational expense. Most of the expense is then computing large complex matrix vector products. The cost can be further reduced by using the fast multipole method which accelerates the matrix vector product. For a linear system of size N, the use of an iterative method combined with the fast multipole method reduces the total expense of the computation to N log N. There exist two versions of the fast multipole method: one which is based on a multipole expansion of the interaction kernel exp ikr/r and which was first proposed by V. Rokhlin and another based on a plane wave expansion of the kernel, first proposed by W.C. Chew. In this paper, we propose a third approach, the stable plane wave expansion (SPW-FMM), which has a lower computational expense than the multipole expansion and does not have the accuracy and stability problems of the plane wave expansion. The computational complexity is N log N as with the other methods.