The relationship between Galerkin and collocation methods in statistical transmission line analysis

This paper discusses the relationship between two standard methods for the stochastic analysis of linear circuits, namely the stochastic Galerkin method (SGM) and the stochastic collocation method (SCM), based on a multidimensional Gaussian quadrature. It is established that the SCM corresponds to an approximate factorization of the SGM, involving matrix polynomials sharing the same coefficients as the pertinent polynomial chaos basis functions. Under certain assumptions, the two methods coincide. These findings are illustrated by means of a frequency-domain simulation of a transmission line circuit.

[1]  D. Xiu.  Fast numerical methods for stochastic computations: A review , 2009 .

[2]  Dries Vande Ginste,et al.  Uncertainty Assessment of Lossy and Dispersive Lines in SPICE-Type Environments , 2013, IEEE Transactions on Components, Packaging and Manufacturing Technology.

[3]  Majid Ahadi,et al.  Sparse Linear Regression (SPLINER) Approach for Efficient Multidimensional Uncertainty Quantification of High-Speed Circuits , 2016, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[4]  R. Tempone,et al.  Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison , 2011 .

[5]  T. Sarkar,et al.  Analysis of Multiconductor Transmission Lines , 1988, 31st ARFTG Conference Digest.

[7]  T. Dhaene,et al.  Variability Analysis of Multiport Systems Via Polynomial-Chaos Expansion , 2012, IEEE Transactions on Microwave Theory and Techniques.

[8]  Gene H. Golub,et al.  Calculation of Gauss quadrature rules , 1967, Milestones in Matrix Computation.

[9]  Andreas C. Cangellaris,et al.  Interconnect transient simulation in the presence of layout and routing uncertainty , 2011, 2011 IEEE 20th Conference on Electrical Performance of Electronic Packaging and Systems.

[10]  Roland Pulch,et al.  Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations , 2014, J. Comput. Appl. Math..

[11]  Luca Daniel,et al.  Stochastic Testing Method for Transistor-Level Uncertainty Quantification Based on Generalized Polynomial Chaos , 2013, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[12]  Michel S. Nakhla,et al.  Decoupled Polynomial Chaos and Its Applications to Statistical Analysis of High-Speed Interconnects , 2014, IEEE Transactions on Components, Packaging and Manufacturing Technology.

[13]  D. V. Ginste,et al.  On the relationship between the stochastic Galerkin method and the pseudo-spectral collocation method for linear differential algebraic equations , 2018 .