Charalampos Antoniadis
ABSTRACT
The integration of more components into ICs due to the ever increasing technology scaling has led to very large parasitic networks consisting of million of nodes, which have to be simulated in many times or frequencies to verify the proper operation of the chip. Model Order Reduction techniques have been employed routinely to substitute the large scale parasitic model by a model of lower order with similar response at the input/output ports. However, all established MOR techniques result in dense system matrices that render their simulation impractical. To this end, in this paper we propose a methodology for the sparsification of the dense circuit matrices resulting from Model Order Reduction, which employs a sequence of algorithms based on the computation of the nearest diagonally dominant matrix and the sparsification of the corresponding graph. Experimental results indicate that a high sparsity ratio of the reduced system matrices can be achieved with very small loss of accuracy.
- Z. Ye, D. Vasilyev, Z. Zhu and J. R. Phillips, Sparse Implicit Projection (SIP) for reduction of general many-terminal networks, IEEE/ACM International Conference on Computer-Aided Design, 2008. Google Scholar
Digital Library
- R. Ionutiu, J. Rommes and W. H. A. Schilders, SparseRC: Sparsity Preserving Model Reduction for RC Circuits With Many Terminals, IEEE Trans. on CAD of Integrated Circuits and Systems, vol. 30, pp. 1828--1841, 2011. Google ScholarDigital Library
- D. Oyaro and P. Triverio, TurboMOR: an Efficient Model Order Reduction Technique for RC Networks with Many Ports, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 35, pp. 1695--1706, 2016. Google ScholarDigital Library
- A. E. Ruehli, Circuit Analysis, Simulation and Design, Part 1, New York: North-Holland, 1986. Google ScholarDigital Library
- R. Horn and C. Johnson, Matrix Analysis, Cambridge University Press, 1985. Google ScholarDigital Library
- R. Merris, Laplacian matrices of a graph: A survey, Linear Algebra and its Applications, vol. 197, pp. 143--176, 1994.Google ScholarCross Ref
- M. Mendoza, M. Raydan and P. Tarazaga, Computing the nearest diagonally dominant matrix, Numerical Linear Algebra with Applications, vol. 5, pp. 461--474, 1998.Google ScholarCross Ref
- J.P. Boyle and R.L. Dykstra, A Method for Finding Projections onto the Intersection of Convex Sets in Hilbert Spaces, Springer, 1986.Google ScholarCross Ref
- M. Monsalve, J. Moreno, R. Escalante and M. Raydan, Selective alternating projections to find the nearest SDD+ matrix, Applied Mathematics and Computation, vol. 145, pp. 205--220, 2003. Google ScholarDigital Library
- K.D. Gremban, Combinatorial Preconditioners for Sparse, Symmetric, Diagonally Dominant Linear Systems, Ph.D. thesis, Carnegie-Mellon University, Department of Computer Science, 1996.Google Scholar
- D. Spielman and N. Srivastava, Graph Sparsification by Effective Resistances, SIAM Journal on Computing, vol. 40, pp. 1913--1926, 2011. Google ScholarDigital Library
- D. Achlioptas, Database-friendly Random Projections, ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, 2001. Google ScholarDigital Library
- D. Spielman and S.H. Teng, Nearly-linear Time Algorithms for Graph Partitioning, Graph Sparsification, and Solving Linear Systems, ACM Symposium on Theory of Computing, 2004. Google ScholarDigital Library
- I. Koutis, G.L. Miller and R. Peng, A nearly-m logn solver for SDD linear systems, IEEE Symposium on Foundations of Computer Science, 2011. Google ScholarDigital Library
- A. Odabasioglu, M. Celik and L.T. Pileggi, PRIMA: passive reduced-order interconnect macromodeling algorithm, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 17, pp. 645--654, 1998. Google ScholarDigital Library
Recommendations
A Rigorous Approach for the Sparsification of Dense Matrices in Model Order Reduction of RLC Circuits
DAC '19: Proceedings of the 56th Annual Design Automation Conference 2019The integration of more components into modern Systems-on-Chip (SoCs) has led to very large RLC parasitic networks consisting of million of nodes, which have to be simulated in many times or frequencies to verify the proper operation of the chip. Model ...
Determinant-Preserving Sparsification of SDDM Matrices
We show that variants of spectral sparsification routines can preserve the total spanning tree counts of graphs. By Kirchhoff's matrix-tree theorem, this is equivalent to preserving the determinant of a graph Laplacian minor or, equivalently, of any symmetric ...
Robust model order reduction technique for MIMO systems via ANN-LMI-based state residualization
Even though model order reduction (MOR) techniques for linear dynamical systems are developed rather properly, there are still quite a lot of issues to be considered. This paper addresses a novel MOR technique for multi-input multi-output system with ...
Comments