Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
FastSies: a fast stochastic integral equation solver for modeling the rough surface effect
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Proceedings of the conference on Design, automation and test in Europe
Variational capacitance extraction of on-chip interconnects based on continuous surface model
Proceedings of the 46th Annual Design Automation Conference
PiCAP: a parallel and incremental capacitance extraction considering stochastic process variation
Proceedings of the 46th Annual Design Automation Conference
Robust simulation methodology for surface-roughness loss in interconnect and package modelings
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
Variation-aware interconnect extraction using statistical moment preserving model order reduction
Proceedings of the Conference on Design, Automation and Test in Europe
Proceedings of the 16th Asia and South Pacific Design Automation Conference
Uncertainty quantification for integrated circuits: stochastic spectral methods
Proceedings of the International Conference on Computer-Aided Design
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In this paper we present an efficient algorithm for extracting the complete statistical distribution of the input impedance of interconnect structures in the presence of a large number of random geometrical variations. The main contribution in this paper is the development of a new algorithm, which combines both Neumann expansion and Hermite expansion, to accurately and efficiently solve stochastic linear system of equations. The second contribution is a new theorem to efficiently obtain the coefficients of the Hermite expansion while computing only low order integrals. We establish the accuracy of the proposed algorithm by solving stochastic linear systems resulting from the discretization of the stochastic volume integral equation and comparing our results to those obtained from other techniques available in the literature, such as Monte Carlo and stochastic finite element analysis. We further prove the computational efficiency of our algorithm by solving large problems that are not solvable using the current state of the art.