Modelling and Discretization of Circuit Problems

Günther, Michael; Feldmann, U.; Maten, ter Ejw Jan

doi:10.1016/s1570-8659(04)13006-8

Cited by 57 publications

(79 citation statements)

References 161 publications

(212 reference statements)

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“…It is obvious that none of the approximations (8), (11) and (13) change the eigenvalues of λC + G. With Lemma 1 and the assumption that (12) is stability preserving it directly follows that the ESVDMOR approach is stability preserving.…”

Section: Theorem 1 Consider An Asymptotically Stable System (1) Withmentioning

confidence: 91%

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On Stability, Passivity and Reciprocity Preservation of ESVDMOR

Benner

Schneider

2011

Lecture Notes in Electrical Engineering

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The reduction of parasitic linear subcircuits is one of many issues in model order reduction (MOR) for VLSI design. This issue is well explored, but recently the incorporation of subcircuits from different modelling sources into the circuit model has led to new structural aspects: so far, the number of elements in the subcircuits was significantly larger than the number of connections to the whole circuit, the so called pins or terminals. This assumption is no longer valid in all cases such that the simulation of these circuits or rather the reduction of the model requires new methods. In [6,15,17], the extended singular value decomposition based model order reduction (ESVDMOR) algorithm is introduced as a way to handle this kind of circuits with a massive number of terminals. Unfortunately, the ESVDMOR approach has some drawbacks because it uses the SVD for matrix factorizations. In [5,22] the truncated SVD (TSVD) as an alternative to the SVD within the ESVDMOR is introduced. In this paper we show that ESVDMOR as well as the modified approach is stability, passivity, and reciprocity preserving under reasonable assumptions.

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Section: Theorem 1 Consider An Asymptotically Stable System (1) Withmentioning

confidence: 91%

“…The original model which results from the mathematical modeling with the help of, e. g., modified nodal analysis [11] has to be simplified due to its complexity. One special part of this simplification for VLSI design is the MOR of parasitic linear interconnect circuits [7].…”

Section: Introductionmentioning

confidence: 99%

On Stability, Passivity and Reciprocity Preservation of ESVDMOR

Benner

Schneider

2011

Lecture Notes in Electrical Engineering

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“…For example, modified nodal analysis yields matrices with a linear dependence on the parameters in case of linear electric networks, cf. [10]. Otherwise, a redefinition of parameters often enables to meet this assumption (for example, 1/p is replaced by p * := 1/p and a random distribution is considered for p * ).…”

Section: Intrusive Methodsmentioning

confidence: 99%

“…Examples are models of electric circuits or multibody dynamics, see [10,20]. We consider linear dynamical systems, which represent DAEs or ordinary differential equations (ODEs).…”

Section: Introductionmentioning

confidence: 99%

Sensitivity analysis and model order reduction for random linear dynamical systems

Pulch

Maten

Augustin

2015

Mathematics and Computers in Simulation

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“…For simplicitly, to reduce notation and the amount of partial derivatives further on, we use p, both in (3) and in (4). Fault Analysis consists of simulations for a large number of pairs of vectors (u, v), or (a, b) and various values of p, and compare the result x p (t) of (1) at specific time points with the "golden" solution x(t) of the faultfree circuit (corresponding with p = 0).…”

Section: Fault Simulationmentioning

confidence: 99%