The fast multipole method (FMM) for electromagnetic scattering problems

A convergence theorem for the fast multipole method for 2 dimensional scattering problems

The Fast Multipole Method (FMM) designed by V. Rokhlin rapidly computes the field scattered from an obstacle. This computation consists of solving an integral equation on the boundary of the obstacle. The main result of this paper shows the convergence of the FMM for the two dimensional Helmholtz equation. Before giving the theorem, we give an overview of the main ideas of the FMM. This is done...

Experiments on Iterative Methods and the Fast Multipole Method in Electromagnetic Scattering Calculations

We describe the iterative solution of dense linear systems arising from a surface integral equation of electromagnetic scattering. The complex symmetric version of QMR has been used as an iterative solver together with a sparse approximate inverse preconditioner. The preconditioner is computed using the topological information from the computational mesh. The matrix-vector products are computed...

Revision of FMM-Yukawa: An adaptive fast multipole method for screened Coulomb interactions

FMM-Yukawa: An adaptive fast multipole method for screened Coulomb interactions

Article history: Received 30 April 2009 Received in revised form 25 June 2009 Accepted 29 June 2009 Available online 2 July 2009 PACS: 02.30.Em 02.30.Rz 02.60.Dc 24.10.Cn

Efficient fast multipole method for low-frequency scattering

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 vecto...