Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
SPICE (3rd ed.): a guide to circuit simulation and analysis using PSpice
SPICE (3rd ed.): a guide to circuit simulation and analysis using PSpice
Efficient steady-state analysis based on matrix-free Krylov-subspace methods
DAC '95 Proceedings of the 32nd annual ACM/IEEE Design Automation Conference
The Designer's Guide to Spice and Spectre
The Designer's Guide to Spice and Spectre
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure
SIAM Journal on Scientific Computing
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
Stochastic analysis of interconnect performance in the presence of process variations
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Statistical model order reduction for interconnect circuits considering spatial correlations
Proceedings of the conference on Design, automation and test in Europe
Proceedings of the conference on Design, automation and test in Europe
ASP-DAC '07 Proceedings of the 2007 Asia and South Pacific Design Automation Conference
ASP-DAC '07 Proceedings of the 2007 Asia and South Pacific Design Automation Conference
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
Is Gauss Quadrature Better than Clenshaw-Curtis?
SIAM Review
Stochastic integral equation solver for efficient variation-aware interconnect extraction
Proceedings of the 45th annual Design Automation Conference
Stochastic formulation of SPICE-type electronic circuit simulation with polynomial chaos
ACM Transactions on Modeling and Computer Simulation (TOMACS)
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Polynomial chaos for multirate partial differential algebraic equations with random parameters
Applied Numerical Mathematics
Variational capacitance extraction of on-chip interconnects based on continuous surface model
Proceedings of the 46th Annual Design Automation Conference
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Stochastic dominant singular vectors method for variation-aware extraction
Proceedings of the 47th Design Automation Conference
Numerical Methods for Stochastic Computations: A Spectral Method Approach
Numerical Methods for Stochastic Computations: A Spectral Method Approach
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Modelling and simulation of autonomous oscillators with random parameters
Mathematics and Computers in Simulation
Variational capacitance extraction and modeling based on orthogonal polynomial method
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Model order reduction of fully parameterized systems by recursive least square optimization
Proceedings of the International Conference on Computer-Aided Design
IEEE Transactions on Information Theory
First-Order Incremental Block-Based Statistical Timing Analysis
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Sensitivity Analysis for Oscillators
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A parallel and incremental extraction of variational capacitance with stochastic geometric moments
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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Due to significant manufacturing process variations, the performance of integrated circuits (ICs) has become increasingly uncertain. Such uncertainties must be carefully quantified with efficient stochastic circuit simulators. This paper discusses the recent advances of stochastic spectral circuit simulators based on generalized polynomial chaos (gPC). Such techniques can handle both Gaussian and non-Gaussian random parameters, showing remarkable speedup over Monte Carlo for circuits with a small or medium number of parameters. We focus on the recently developed stochastic testing and the application of conventional stochastic Galerkin and stochastic collocation schemes to nonlinear circuit problems. The uncertainty quantification algorithms for static, transient and periodic steady-state simulations are presented along with some practical simulation results. Some open problems in this field are discussed.