The Multilevel Fast Multipole Algorithm (MLFMA) is a well known and very successful method for accelerating the matrix-vector products required for the iterative solution of Helmholtz problems. The MLFMA is based on an addition theorem which suffers from the so-called low-frequency (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 High-Frequency (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 so-called translation operators can be calculated in closed form, which allows the easy implementation of an LF-stable MLFMA.
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
- Poisson and Laplace equations boundary-value problems;
- Electromagnetic wave propagation;
- radiowave propagation;
- Numerical approximation and analysis