The stationary semiconductor device equations
The stationary semiconductor device equations
A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
Computer Methods for Circuit Analysis and Design
Computer Methods for Circuit Analysis and Design
SPRIM: structure-preserving reduced-order interconnect macromodeling
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Sparse and efficient reduced order modeling of linear subcircuits with large number of terminals
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Numerical analysis of DAEs from coupled circuit and semiconductor simulation
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
deal.II—A general-purpose object-oriented finite element library
ACM Transactions on Mathematical Software (TOMS)
An efficient terminal and model order reduction algorithm
Integration, the VLSI Journal
$\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
SIAM Journal on Matrix Analysis and Applications
Circuit synthesis of passive descriptor systems—a modified nodal approach
International Journal of Circuit Theory and Applications
PABTEC: passivity-preserving balanced truncation for electrical circuits
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Nonlinear Model Reduction via Discrete Empirical Interpolation
SIAM Journal on Scientific Computing
PRIMA: passive reduced-order interconnect macromodeling algorithm
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Guaranteed passive balancing transformations for model order reduction
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Positivity of discrete singular systems and their stability: An LP-based approach
Automatica (Journal of IFAC)
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We consider model order reduction of integrated circuits with semiconductor devices. Such circuits are modeled using modified nodal analysis by differential-algebraic equations coupled with the nonlinear drift-diffusion equations. A spatial discretization of these equations with a mixed finite element method yields a high dimensional nonlinear system of differential-algebraic equations. Balancing-related model reduction is used to reduce the dimension of the decoupled linear network equations, whereas the semidiscretized semiconductor model is reduced using proper orthogonal decomposition. Because the computational complexity of the reduced-order model through the nonlinearity of the drift-diffusion equations still depends on the number of variables of the full model, we apply the discrete empirical interpolation method to further reduce the computational complexity. We provide numerical comparisons that demonstrate the performance of the presented model reduction approach. Copyright © 2012 John Wiley & Sons, Ltd.