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
Rapid solution of integral equations of scattering theory in two dimensions
Journal of Computational Physics
SIAM Journal on Scientific and Statistical Computing
Fast and Efficient Algorithms in Computational Electromagnetics
Fast and Efficient Algorithms in Computational Electromagnetics
Journal of Computational Physics
Reduced-rank approximations to the far-field transform in the gridded fast multipole method
Journal of Computational Physics
Hi-index | 31.45 |
The fast multipole method (FMM) is applied to the solution of large-scale, three-dimensional acoustic scattering problems involving inhomogeneous objects defined on a regular grid. The grid arrangement is especially well suited to applications in which the scattering geometry is not known a priori and is reconstructed on a regular grid using iterative inverse scattering algorithms or other imaging techniques. The regular structure of unknown scattering elements facilitates a dramatic reduction in the amount of storage and computation required for the FMM, both of which scale linearly with the number of scattering elements. In particular, the use of fast Fourier transforms to compute Green's function convolutions required for neighboring interactions lowers the often-significant cost of finest-level FMM computations and helps mitigate the dependence of FMM cost on finest-level box size. Numerical results demonstrate the efficiency of the composite method as the number of scattering elements in each finest-level box is increased.