ICCAP: a linear time sparse transformation and reordering algorithm for 3D BEM capacitance extraction

This paper presents an efficient hierarchical 3D capacitance extraction algorithm - ICCAP. Most previous capacitance extraction algorithms introduce intermediate variables to facilitate the hierarchical potential calculation but still preserve the leaf panels as the basis. In this paper, we discover that those intermediate variables are fundamentally much better basis than leaf panels. As a result, we are able to explicitly construct the sparse potential coefficient matrix and solve it with linear memory in linear runtime. Furthermore, the explicit sparse formulation not only enables the usage of preconditioned iterative Krylov subspace methods but also the reordering technique. A new reordering technique is proposed to further reduce over 20% of memory consumption and runtime in comparison to no reordering techniques applied. Experimental results demonstrate the superior runtime and memory consumption of ICCAP over previous approaches while achieving similar accuracy.