Objective:

The Multilevel Fast Multipole Method, when used in combination with the Boundary Element Method (BEM), is a tool to significantly speed up the simulation of large objects almost without loss in accuracy.

Method:

The Fast Multipole Method subdivides the Boundary Element mesh into different clusters. If two clusters are sufficiently far away from each other (i.e. they are in each other's far field), all calculations that would have to be made for every pair of nodes can be reduced to the midpoints of the clusters with almost no loss of accuracy. For clusters not in the far field, the traditional BEM has to be applied. The Multilevel Fast Multipole Method introduces different levels of clustering (clusters made out of smaller clusters) to additionally enhance computation speed.

Application:

The MLFFM is used for the simulation of head related transfer functions. The diagram above compares the result of a classical BEM with the MLFMM.