FastSpice circuit partitioning to compute DC operating points preserving Spice-like simulators accuracy

Abstract FastSpice techniques are considered in this paper and in particular partitioning methods that split a large circuit in a set of smaller sub-circuits to quickly and accurately compute a dc solution. Each sub-circuit contributes to a set of Jacobian matrices with reduced dimensions that are more efficiently LU-factorised during the iterations of the solving methods. As a matter of fact, the numerical effort required by factorisation is a non linear (polynomial) function of the matrix dimension. We describe the use of voltage and current probes that can be inserted to “virtually” tear nodes and branches of the original circuit to further improve circuit splitting. The proposed techniques do not alter the accuracy of the simulation and thus we obtain FastSpice performances while keeping Spice accuracy. This can be a key issue in simulating circuits designed with deep-submicron technologies. Simulation performances of the proposed approach are compared with those of modern commercial full-chip FastSpice and Spice -like simulators.

[1]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[2]  Timothy A. Davis,et al.  Algorithm 907 , 2010 .

[3]  Federico Bizzarri,et al.  Probe Based Shooting Method to Find Stable and Unstable Limit Cycles of Strongly Nonlinear High- $Q$ Oscillators , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[4]  A. Sangiovanni-Vincentelli,et al.  A multilevel Newton algorithm with macromodeling and latency for the analysis of large-scale nonlinear circuits in the time domain , 1979 .

[5]  M. Honkala,et al.  Improving the convergence of combined Newton-Raphson and Gauss-Newton multilevel iteration method , 2002, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).

[6]  Sani R. Nassif,et al.  Hierarchical Multialgorithm Parallel Circuit Simulation , 2011, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[7]  Panos M. Pardalos,et al.  Algorithm 815: FORTRAN subroutines for computing approximate solutions of feedback set problems using GRASP , 2001, TOMS.

[8]  Kartikeya Mayaram,et al.  Frequency-Domain Simulation of Ring Oscillators With a Multiple-Probe Method , 2006, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[9]  Chung-Kuan Cheng,et al.  Parallel transistor level circuit simulation using domain decomposition methods , 2009, 2009 Asia and South Pacific Design Automation Conference.

[10]  James Hardy Wilkinson,et al.  Rounding errors in algebraic processes , 1964, IFIP Congress.

[11]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[12]  Leon O. Chua,et al.  Diakoptic and generalized hybrid analysis , 1976 .

[13]  Yu Wang,et al.  NICSLU: An Adaptive Sparse Matrix Solver for Parallel Circuit Simulation , 2013, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[14]  Almudena Suarez,et al.  Steady state analysis of free or forced oscillators by harmonic balance and stability investigation of periodic and quasi-periodic regimes , 1995 .

[15]  Danny C. Sorensen,et al.  Parallel domain decomposition for simulation of large-scale power grids , 2007, ICCAD 2007.

[16]  Leon O. Chua,et al.  An efficient heuristic cluster algorithm for tearing large-scale networks , 1977 .

[17]  Angelo Brambilla,et al.  Numerical Determination of Possible Multiple DC Solutions of Nonlinear Circuits , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[18]  C. W. Gear,et al.  Multirate linear multistep methods , 1984 .

[19]  Leon O. Chua,et al.  Linear and nonlinear circuits , 1987 .

[20]  Christophe Geuzaine,et al.  Relaxation methods for co-simulation of finite element and circuit solvers , 2016, 2016 IEEE Conference on Electromagnetic Field Computation (CEFC).

[21]  Kenneth S. Kundert,et al.  The designer's guide to SPICE and Spectre , 1995 .

[22]  A. Richard Newton,et al.  Mixed-mode simulation and analog multilevel simulation , 1994, The Kluwer international series in engineering and computer science.

[23]  Timothy A. Davis,et al.  Direct methods for sparse linear systems , 2006, Fundamentals of algorithms.

[24]  Eric R. Keiter,et al.  The Xyce Parallel Electronic Simulator - An Overview , 2000 .

[25]  Federico Bizzarri,et al.  The Probe-Insertion Technique for the Detection of Limit Cycles in Power Systems , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[26]  F. Wu,et al.  Solution of large-scale networks by tearing , 1976 .

[27]  Sani R. Nassif,et al.  MAPS: multi-algorithm parallel circuit simulation , 2008, ICCAD 2008.

[28]  Michal Rewienski,et al.  A Perspective on Fast-SPICE Simulation Technology , 2011 .

[29]  Giambattista Gruosso,et al.  Robust Harmonic-Probe Method for the Simulation of Oscillators , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[30]  Kishore Singhal,et al.  Computer Methods for Circuit Analysis and Design , 1983 .

[31]  Soumitro Banerjee,et al.  Simulation of Real World Circuits: Extending Conventional Analysis Methods to Circuits Described by Heterogeneous Languages , 2014, IEEE Circuits and Systems Magazine.