Abstract
A Gaussian point-adaptive grouping scheme for the multilevel fast multipole algorithm (MLFMA) has been proposed in this communication to significantly reduce the heavy memory cost resulted from using the basis functions defined on large patches without sacrificing the accuracy of the numerical solutions. The grouping process in the MLFMA has been considered as a single-objective optimization problem and is solved by using the clustering algorithm for Gaussian quadrature points on each patch. Meanwhile, the constraint of the addition theorem for MLFMA is still satisfied. As a result, the presented scheme is able to acquire an optimal number of multipoles for each basis function. Compared to the conventional octree grouping scheme or other grouping schemes used in the past, the method in this communication is advantageous in terms of the memory efficiency and the solution accuracy. Numerical examples have been given to demonstrate the validity and effectiveness of the proposed scheme.
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