Preconditioned multi-zone boundary element analysis for fast 3D electric simulation. (English) Zbl 1069.78012
Summary: For fast 3D electric simulation, the multi-zone collocation boundary element analysis (BEA) with iterative solver like GMRES algorithm is required. In this paper, we present a scheme of equation assembly with ordering unknowns and collocation points, and a matrix storing structure. A group of easily computed preconditioners based on the mesh neighbor method are then proposed to remarkably quicken the convergence of GMRES iteration, and demonstrate at least 30% time reduction than using the diagonal preconditioner. Compared with the equation assembly in M. Merkel, V. Bulgakov, R. Bialecki and G. Kuhn [Eng. Anal. Bound. Elem. 22, No. 3, 183–197 (1998; Zbl 0963.74563)], where two unknowns on same interfacial node are arranged subsequently, and two storing schemes in Li et al. and Araujo et al. [Syst. Eng. Electron. 21, 10 (1999); J. Chin. Inst. Eng. 23, 269 (2000)], the proposed method generates fewest non-zero blocks and facilitates the matrix-vector multiplication remarkably. Numerical experiments verify the analysis and show a fast iterative multi-zone BEA simulator for actual very large-scale integration interconnects with a large amount of zones.
MSC:
| 78M15 | Boundary element methods applied to problems in optics and electromagnetic theory |
| 65F10 | Iterative numerical methods for linear systems |
Keywords:
Boundary element method; Multi-zone collocation; Equation assembly; Iterative solution; Preconditioner; Electric simulation; GMRES algorithmCitations:
Zbl 0963.74563References:
| [1] | Brebbia, C. A.; Telles, J. C.F.; Wrobel, L. C., Boundary element techniques: theory and applications in engineering (1984), Springer: Springer Berlin · Zbl 0556.73086 |
| [2] | Crotty, J. M., A block equation solver for large unsymmetric matrices arising in the boundary element method, Int J Numer Meth Engng, 18, 997-1017 (1982) · Zbl 0485.73068 |
| [3] | Kane, J. H., Boundary element analysis in engineering continuum mechanics (1994), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ |
| [4] | Kane, J. H.; Kashava, B. L.K., An arbitrary condensing, noncondensing solution strategy for large scale, multi-zone boundary element analysis, Comput Meth Appl Mech Engng, 79, 219-244 (1990) |
| [5] | Rigby, R. H.; Aliabadi, M. H., Out-of-core solver for large, multi-zone boundary element matrices, Int J Numer Meth Engng, 38, 1507-1533 (1995) · Zbl 0830.73076 |
| [6] | Kane, J. H.; Keyes, D. E.; Prasad Guru, K., Iterative solution techniques in boundary element analysis, Int J Numer Meth Engng, 31, 1511-1536 (1991) · Zbl 0825.73901 |
| [7] | Prasad Guru, K.; Kane, J. H., Preconditioned Krylov solvers for BEA, Int J Numer Meth Engng, 37, 1651-1672 (1994) · Zbl 0800.73504 |
| [8] | Walker, M. G., Modeling the wiring of deep submicron ICs, IEEE Spectrum, 37, 3, 65-71 (2000) |
| [9] | Nabors, K.; White, J., Multipole accelerated capacitance extraction algorithm for 3-D structures with multiple dielectrics, IEEE Trans Circuits Sys I, 39, 11, 946-954 (1992) · Zbl 0775.94136 |
| [10] | Bachtold, M.; Korvink, J. G.; Baltes, H., Enhanced multipole acceleration technique for the solution of large Poisson computations, IEEE Trans Comput-Aided Des, 15, 12, 1541-1546 (1996) |
| [11] | Yu, W.; Wang, Z.; Gu, J., Fast capacitance extraction of actual 3-D VLSI interconnects using quasi-multiple medium accelerated BEM, IEEE Trans Microwave Theory Tech, 51, 1, 109-119 (2003) |
| [12] | Yu, W.; Wang, Z., A fast quasi-multiple medium method for 3-D BEM calculation of parasitic capacitance, Comput Math Appl, 45, 12, 1883-1894 (2003) · Zbl 1049.65137 |
| [13] | Merkel, M.; Bulgakov, V.; Bialecki, R.; Kuhn, G., Iterative solution of large-scale 3D-BEM industrial problems, Engng Anal Bound Elem, 22, 183-197 (1998) · Zbl 0963.74563 |
| [14] | Li, Y.; Hou, J.; Wang, Z., Calculating capacitance with the multiple dielectrics using the direct BEM and accelerating with single dielectric, Syst Engng Electron, 21, 6, 10-15 (1999), in Chinese |
| [15] | Araujo, F. C.; Belmonte, G. J.; Freitas, M. S.R., Efficiency increment in 3D multi-zone boundary element algorithms by use of iterative solvers, J Chin Inst Engrs, 23, 3, 269-274 (2000) |
| [16] | Saad, Y.; Schultz, M. H., GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM, J. Sci Stat Comput, 7, 3, 856-869 (1986) · Zbl 0599.65018 |
| [17] | Vavasis, S. A., Preconditioning for boundary integral equations, SIAM, J Matrix Anal Appl, 13, 3, 905-925 (1992) · Zbl 0755.65109 |
| [18] | Nachtigal, N. M.; Reddy, S.; Trefethen, N., How fast are nonsysmmetric matrix iterations, SIAM J Matrix Anal Appl, 13, 3, 778-795 (1992) · Zbl 0754.65036 |
| [19] | Chen, K., On a class of preconditioning methods for dense linear systems from boundary element, SIAM, J Sci Comput, 20, 2, 684-698 (1998) · Zbl 0924.65037 |
| [20] | Chen, K., An analysis of sparse approximate inverse preconditioners for boundary integral equations, SIAM, J Matrix Anal Appl, 22, 4, 1058-1078 (2001) · Zbl 0985.65038 |
| [21] | Wang, Z.; Wu, Q., A two-dimensional resistance simulator using the boundary element method, IEEE Trans Comput-Aided Des, 11, 4, 497-504 (1992) |
| [22] | Barrett, R.; Berry, M.; Chan, T. F., Templates for the solution of linear systems: Building blocks for iterative methods (1994), SIAM: SIAM Philadelphia, PA, . Available at http://www.netlib.org/ |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
