New Plane Wave Addition Theorems
Abstract
The Multilevel Fast Multipole Algorithm (MLFMA) is a well known and very successful method for accelerating the matrixvector products required for the iterative solution of Helmholtz problems. The MLFMA is based on an addition theorem which suffers from the socalled lowfrequency (LF) breakdown, due to numerical roundoff error. Here, a new addition theorem will be developed which does not suffer from an LF breakdown. Instead it suffers from a HighFrequency (HF) breakdown. The new addition theorem is based on a novel set of distributions, the so called pseudospherical harmonics, closely related to the spherical harmonics. The socalled translation operators can be calculated in closed form, which allows the easy implementation of an LFstable MLFMA.
 Publication:

Mathematical Modeling of Wave Phenomena: 3rd Conference on Mathematical Modeling of Wave Phenomena, 20th Nordic Conference on Radio Science and Communications
 Pub Date:
 March 2009
 DOI:
 10.1063/1.3117112
 Bibcode:
 2009AIPC.1106...46B
 Keywords:

 41.20.Cv;
 41.20.Jb;
 02.60.x;
 Electrostatics;
 Poisson and Laplace equations boundaryvalue problems;
 Electromagnetic wave propagation;
 radiowave propagation;
 Numerical approximation and analysis