A quasi-Newton preconditioned Newton-Krylov method for robust and efficient time-domain simulation of integrated circuits with strong parasitic couplings

In this paper, the Newton-Krylov method is explored for robust and efficient time-domain VLSI circuit simulation. Different from the LU-factorization based direct method, the Newton-Krylov method uses a preconditioned Krylov-subspace iterative method for linear system solving. Our key contribution is to introduce an effective quasi-Newton preconditioning scheme for Krylov-subspace methods to reduce the number and cost of LU factorizations during time-domain circuit simulation. Experimental results on a collection of digital, analog and RF circuits have shown that the quasi-Newton preconditioned Krylov-subspace method is as robust and accurate as SPICE3. The proposed Newton-Krylov method is especially attractive for simulating circuits with a large amount of parasitic RLC elements for post-layout verification

[1]  Charlie Chung-Ping Chen,et al.  Efficient large-scale power grid analysis based on preconditioned Krylov-subspace iterative methods , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[2]  A. Richard Newton,et al.  Iterated Timing Analysis , 1990 .

[3]  Jacob K. White,et al.  Relaxation Techniques for the Simulation of VLSI Circuits , 1986 .

[4]  Fabrice Veersé.  Efficient Iterative Time Preconditioners for Harmonic Balance RF Circuit Simulation , 2003, ICCAD 2003.

[5]  A.L. Sangiovanni-Vincentelli,et al.  Relaxation-Based Electrical Simulation , 1983, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[6]  David E. Long,et al.  Efficient frequency domain analysis of large nonlinear analog circuits , 1996, Proceedings of Custom Integrated Circuits Conference.

[7]  Joel R. Phillips,et al.  Simulation approaches for strongly coupled interconnect systems , 2001, ICCAD 2001.

[8]  Jeng-Liang Tsai,et al.  HiSIM: hierarchical interconnect-centric circuit simulator , 2004, ICCAD 2004.

[9]  Ernest S. Kuh,et al.  A sparse matrix method for analysis of piecewise-linear resistive networks , 1972 .

[10]  Yousef Saad,et al.  A Flexible Inner-Outer Preconditioned GMRES Algorithm , 1993, SIAM J. Sci. Comput..

[11]  Valeria Simoncini,et al.  Flexible Inner-Outer Krylov Subspace Methods , 2002, SIAM J. Numer. Anal..

[12]  C. Shi,et al.  Tree relaxation: a new iterative solution method for linear equations , 1988, 1988., IEEE International Symposium on Circuits and Systems.

[13]  Zhao Li,et al.  An efficiently preconditioned GMRES method for fast parasitic-sensitive deep-submicron VLSI circuit simulation , 2005, Design, Automation and Test in Europe.

[14]  D. Keyes,et al.  Jacobian-free Newton-Krylov methods: a survey of approaches and applications , 2004 .

[15]  A. Sangiovanni-Vincentelli,et al.  RELAX: A New Circuit Simulator for Large Scale MOS Integrated Circuits , 1982, 19th Design Automation Conference.

[16]  Ron Sacks-Davis,et al.  An Alternative Implementation of Variable Step-Size Multistep Formulas for Stiff ODEs , 1980, TOMS.

[17]  Kartikeya Mayaram,et al.  A new matrix solution technique for general circuit simulation , 1993, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[18]  Lawrence T. Pileggi,et al.  PRIMA: passive reduced-order interconnect macromodeling algorithm , 1997, ICCAD 1997.

[19]  J. J. Moré,et al.  Quasi-Newton Methods, Motivation and Theory , 1974 .

[20]  Jacob K. White,et al.  Fast simulation algorithms for RF circuits , 1996, Proceedings of Custom Integrated Circuits Conference.

[21]  Andrew T. Yang,et al.  Stable and efficient reduction of substrate model networks using congruence transforms , 1995, Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[22]  Bo Wan,et al.  MCAST: an abstract-syntax-tree based model compiler for circuit simulation , 2003, Proceedings of the IEEE 2003 Custom Integrated Circuits Conference, 2003..

[23]  C.-J.R. Shi,et al.  A Quasi-Newton Preconditioned Newton-Krylov Method for Robust and Efficient Time-Domain Simulation of Integrated Circuits With Strong Parasitic Couplings , 2006, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[24]  Lawrence T. Pileggi,et al.  TETA: transistor-level waveform evaluation for timing analysis , 2002, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[25]  Kartikeya Mayaram,et al.  PGS and PLUCGS-two new matrix solution techniques for general circuit simulation , 1989, 1989 IEEE International Conference on Computer-Aided Design. Digest of Technical Papers.

[26]  Charlie Chung-Ping Chen,et al.  Power grid transient simulation in linear time based on transmission-line-modeling alternating-direction-implicit method , 2001, IEEE/ACM International Conference on Computer Aided Design. ICCAD 2001. IEEE/ACM Digest of Technical Papers (Cat. No.01CH37281).

[27]  Ping Yang,et al.  New implicit integration method for efficient latency exploitation in circuit simulation , 1989, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[28]  C.-J.R. Shi,et al.  SILCA: Fast-Yet-Accurate Time-Domain Simulation of VLSI Circuits with Strong Parasitic Coupling Effects , 2003, ICCAD 2003.

[29]  Zhao Li,et al.  SILCA: SPICE-accurate iterative linear-centric analysis for efficient time-domain Simulation of VLSI circuits with strong parasitic couplings , 2006, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[30]  William J. McCalla.  Fundamentals of Computer-Aided Circuit Simulation , 1987 .

[31]  Bo Hu,et al.  Fast-yet-accurate PVT simulation by combined direct and iterative methods , 2005, ICCAD-2005. IEEE/ACM International Conference on Computer-Aided Design, 2005..

[32]  A. Yajima,et al.  Complete LU decomposition conjugate residual method and its performance for large-scale circuit simulation , 1988, 1988., IEEE International Symposium on Circuits and Systems.

[33]  Resve Saleh,et al.  Iterated timing analysis and splice1 , 1984 .

[34]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[35]  Peng Li,et al.  Efficient harmonic balance simulation using multi-level frequency decomposition , 2004, ICCAD 2004.