ICCAP-a linear time sparsification and reordering algorithm for 3-D BEM capacitance extraction

• Published in: IEEE transactions on microwave theory and techniques Vol. 54; no. 7; pp. 3060 - 3068
• Main Authors: Rong Jiang, Yi-Hao Chang, Chen, C.C.-P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Acceleration; Algorithms; Applied sciences; Basis; boundary-element method (BEM); Capacitance; capacitance extraction; Circuit properties; Electric, optical and optoelectronic circuits; Electronics; Exact sciences and technology; Extraction; Frequency; hierarchical algorithm; interconnect; interconnect modeling; Iterative algorithms; Iterative methods; Linear systems; Mathematical analysis; Mathematical models; Matrix decomposition; Microwave circuits, microwave integrated circuits, microwave transmission lines, submillimeter wave circuits; Packaging; Panels; Parasitic capacitance; parasitic extraction; Preserves; reordering; Run time (computers); Sparse matrices; Studies; Very large scale integration; interconnect modeling; reordering; boundary-element method (BEM); parasitic extraction; Algorithm; interconnect; Parameter extraction; Basis; Three dimensional model; Experimental result; capacitance extraction; Algorithm performance; Interconnection; hierarchical algorithm; Algorithm complexity; Sparse matrix; Capacitance; Microwave circuit; Hierarchical system; Algorithm analysis; Comparative study; Boundary element method
• ISSN: 0018-9480; 1557-9670
• DOI: 10.1109/TMTT.2006.877046

This paper presents an efficient, simple, hierarchical, and sparse three-dimensional capacitance extraction algorithm, i.e., ICCAP. Most previous capacitance extraction algorithms, such as FastCap and HiCap, introduce intermediate variables to facilitate the hierarchical potential calculation, but still preserve the basic panels as basis. In this paper, we discover that those intermediate variables are a 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 and linear run time in comparison with the most recent hierarchical O(nlogn) approach in PHiCap. Furthermore, the explicit sparse formulation of a potential matrix not only enables the usage of preconditioned Krylov subspace iterative methods, but also the reordering technique. A new reordering technique, i.e., level-oriented reordering (LOR), is proposed to further reduce over 20% of memory consumption and run time compared with no reordering techniques applied. In fact, LOR is even better than the state-of-the-art minimum degree reordering and more efficient. Without complicated orthonormalization matrix computation, ICCAP is very simple, efficient, and accurate. Experimental results demonstrate the superior run time and memory consumption over previous approaches while achieving similar accuracy.