CST2013: Multi Level Fast Multipole Method

The integral equation solver with surface mesh is of special interest for electrically large models. The discretization of the calculation area is reduced to the object boundaries and thus leads to a linear equation system with less unknowns than volume methods. The system matrix is dense. For calculation efficiency the equation system is solved by the Multi Level Fast Multipole Method (MLFMM).

The MLFMM speeds up the matrix vector multiplication for an iterative solver and also enhances the memory efficiency. It scales very good for large problems (geometry >> wavelength). The complexity is O(n log n). The MLFMM is an approximate.

The system matrix is dense because every element couples to all other elements. The single level fast multipole method (FMM) uses boxes to combine the couplings. A recursive scheme is used for the MLFMM to increase the efficiency.

For electrically small problems a direct linear equation solver is available in Special Integral Equation Solver Parameters .