A linear time implicit congruence sparsification technique for BEM capacitance extraction

This paper presents an efficient methodology for generating sparsified potential coefficient matrices for three-dimensional capacitance extraction. Previous capacitance extraction algorithms based on boundary element method (BEM) formulate the potential coefficient matrix in terms of surface potentials and charges on those most delicate panels (leaf panels). By introducing the concept of basis charges, we discover that leaf panel charges compose the worst basis which leads to the densest linear system. Therefore, we propose a linear time basis panel selection algorithm to choose a new basis. It is provable that the n × n potential coefficient matrix constructed in terms of the new basis contains O(n) non-zero entries and hence the sparse system can be solved much more efficiently by preconditioned Krylov subspace iterative methods. Experimental results demonstrate the superior runtime and memory consumption over previous approaches while achieving similar accuracy.