Abstract
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.
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