Multi-Level Multipole Research Articles

Acceleration of Multilevel Characteristic Basis Function Method by Multilevel Multipole Approach

Multilevel characteristic basis function (CBF) method (MLCBFM) accelerated by multilevel multipoles will be presented in this article. The proposed algorithm starts from the conventional MLCBFM, rearrange CBFs for each level as multilevel aggregated CBFs. The algorithm not only reduces degrees of freedom of problems but also exploits hierarchical characteristics of divided geometries such as different truncation coefficients or sampling rates in each level of multipole expansions, which results in dramatic acceleration in analyzing electrically large structure. The results of the proposed method agree very well with exact solutions.

Multilevel multipole and local operators for potentials of the form [formula omitted

This paper presents multilevel multipole and local operators for potentials of the form r − λ . A new addition theorem which enables the construction of the multilevel operators is stated and proved. Simulations of the new operators are presented that indicate the reduction of error with increasing number of multipoles and O ( N ) complexity of the method.

A multipole Galerkin boundary element method for acoustics

A fast multilevel multipole (FMM) algorithm is derived for the Helmholtz equation and adopted to the symmetric Galerkin boundary element method (BEM) for acoustics. The FMM allows to evaluate a matrix–vector product of the BEM with a computational cost of O(N log 2N), thus leading to a significant reduction of computation time and memory requirements compared to standard BEM formulations. This allows the simulation of large scale acoustic models. The performance of the algorithm is demonstrated on the example of sound radiation from an L-shaped domain with BE discretizations of up to 45,000 elements.