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Discrete empirical interpolation in POD model order reduction of drift-diffusion equations in electrical networks. (English) Zbl 1247.78039
Michielsen, Bastiaan (ed.) et al., Scientific computing in electrical engineering SCEE 2010. Selected papers based on the presentations at the 8th conference, Toulouse, France, September 2010. Berlin: Springer (ISBN 978-3-642-22452-2/hbk; 978-3-642-22453-9/ebook). Mathematics in Industry 16, 423-431 (2012).
Summary: We consider model order reduction of integrated circuits with semiconductors modeled by modified nodal analysis and drift-diffusion (DD) equations. The DD-equations are discretized in space using a mixed finite element method. This discretization yields a higher-dimensional, nonlinear system of differential-algebraic equations. Proper orthogonal decomposition is used to reduce the dimension of this model. Since the computational complexity of the reduced-order model still depends through the nonlinearity of the DD equations 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 which demonstrate the performance of this approach.
For the entire collection see [Zbl 1234.65015].

MSC:
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78M34 Model reduction in optics and electromagnetic theory
65L80 Numerical methods for differential-algebraic equations
65F50 Computational methods for sparse matrices
Software:
DASSL; deal.ii; rbMIT
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