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
Variational interconnect analysis via PMTBR
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
Recycling Krylov Subspaces for Sequences of Linear Systems
SIAM Journal on Scientific Computing
Proceedings of the conference on Design, automation and test in Europe
Stochastic integral equation solver for efficient variation-aware interconnect extraction
Proceedings of the 45th annual Design Automation Conference
Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space
SIAM Journal on Scientific Computing
ARMS - automatic residue-minimization based sampling for multi-point modeling techniques
Proceedings of the 46th Annual Design Automation Conference
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Automated compact dynamical modeling: an enabling tool for analog designers
Proceedings of the 47th Design Automation Conference
Stochastic dominant singular vectors method for variation-aware extraction
Proceedings of the 47th Design Automation Conference
Model order reduction of fully parameterized systems by recursive least square optimization
Proceedings of the International Conference on Computer-Aided Design
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In this paper we present a stochastic model order reduction technique for interconnect extraction in the presence of process variabilities, i.e. variation-aware extraction. It is becoming increasingly evident that sampling based methods for variation-aware extraction are more efficient than more computationally complex techniques such as stochastic Galerkin method or the Neumann expansion. However, one of the remaining computational challenges of sampling based methods is how to simultaneously and efficiently solve the large number of linear systems corresponding to each different sample point. In this paper, we present a stochastic model reduction technique that exploits the similarity among the different solves to reduce the computational complexity of subsequent solves. We first suggest how to build a projection matrix such that the statistical moments and/or the coefficients of the projection of the stochastic vector on some orthogonal polynomials are preserved. We further introduce a proximity measure, which we use to determine apriori if a given system needs to be solved, or if it is instead properly represented using the currently available basis. Finally, in order to reduce the time required for the system assembly, we use the multivariate Hermite expansion to represent the system matrix. We verify our method by solving a variety of variation-aware capacitance extraction problems ranging from on-chip capacitance extraction in the presence of width and thickness variations, to off-chip capacitance extraction in the presence of surface roughness. We further solve very large scale problems that cannot be handled by any other state of the art technique.