Enhanced Upward Translations for Systems with Clusters

Abstract

The paper is concerned with using boundary element methods (BEM) for the accurate evaluation of fields in structures with clusters. For large-scale problems, the BEM system is solved iteratively by speeding up matrix-to-vector multiplications by applying a kernel-independent fast multipole method. Multiplication starts with source-to-multipole (S2M) translations, whose accuracy predefines the overall accuracy. We aim to increase the accuracy of these translations. The intensities of sources are assembled into clusters by an algorithm suggested. Each of them is characterized by its representative source, whose intensity equals the sum of the intensities of cluster sources. Thus, with growing distance, its field tends toward the field of the cluster. The accuracy of S2M translations is increased by subtracting from and adding to the far field of the cluster the far field of its representative source, and by using the proposed modified kernel to evaluate the difference of the fields, which decreases faster than the field of the cluster itself. Numerical results for typical kernels show a notable increase in the accuracy provided by the modified S2M translations. Keeping in them merely the added field is acceptable for many practical applications. This simplifies the modified S2M translations by avoiding calculation and storing matrices specific to each of the clusters. The improved translations may be also used for multipole-to-multipole translations, performed on next, after leaves, levels in upward running a hierarchical tree.