Multilevel Fast Multipole Algorithm With Global and Local Interpolators

In this paper a new version of the multilevel fast multipole algorithm (MLFMA), based on an interpolator that utilizes trigonometric polynomial expansion, is presented. This novel version allows in levels, where the cube size is large, the use of the local interpolator that utilizes the Lagrange interpolating polynomial. The accuracy of aggregation and disaggregation is improved by choosing the sample rates for each cube according to the distribution of the basis functions inside the cube in question. Additionally an algorithm for an efficient evaluation of the translator is presented. Further some optimizations and good compromises, both in terms of memory and CPU-time, are suggested. Hierarchical matrices are employed to reduce the memory requirements of the sparse block system matrix. The provided numerical results demonstrate that the presented version is able to maintain good accuracy provided that the local interpolator is only utilized in levels where cube size is large enough.