Efficient Methods for Large Resistor Networks

Rommes, Joost; Schilders, W.H.A.

doi:10.1109/tcad.2009.2034402

Cited by 73 publications

(72 citation statements)

References 14 publications

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“…IfB = [b ij ] is an incidence matrix withb ij ∈ {−1, 0, 1}, which has maximally two non-zeros ( −1 and/or 1) in each column [30,35], then one can obtain an m × m row permutation matrix P r and an n × n column permutation matrix P c such that P r TB P c = B is a lower trapezoidal form. Thus T in (3) is an (n + m) × (n + m) permutation matrix with P = P c and Q = P r .…”

Section: Determination Of Transformation Matrix Tmentioning

confidence: 99%

“…Thus T in (3) is an (n + m) × (n + m) permutation matrix with P = P c and Q = P r . Systems of the form (1) with incidence matrixB evolve in resistor network modeling [30], the Stokes equations [9], and many other applications with network topology.…”

Section: Determination Of Transformation Matrix Tmentioning

confidence: 99%

“…The row related to the ground node is deleted from the incidence matrixB, which makes the system stable [30]. As a result,B has at most two nonzero elements in each column, which is permuted into a lower trapezoidal form.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Systems of the form (1) are known as saddle point problems, which are resulted from discretization of PDEs or coupled PDEs such as the Stokes and mixed finite element methods. Saddle point systems also arise in electronic circuit simulations [30,35], Maxwell's equations [26], economic models and constrained optimization problems [1,10,15,16,18,33]. For example consider the equality-constrained quadratic programming problem: min x f (x) = 1 2x TÅx −x Tf subject toBx =g.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Sparse block factorization of saddle point matrices

Lungten

Schilders

Maubach

2016

Linear Algebra and its Applications

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The factorization method presented in this paper takes advantage of the special structures and properties of saddle point matrices. A variant of Gaussian elimination equivalent to the Cholesky's factorization is suggested and implemented for factorizing the saddle point matrices block-wise with small blocks of order 1 and 2. The Gaussian elimination applied to these small blocks on block level also induces a block 3 × 3 structured factorization of which the blocks have special properties. We compare the new block factorization with the Schilders' factorization in terms of the sparsity of their factors and computational efficiency. The factorization can be used as a direct method, and also anticipate for preconditioning techniques.

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Section: Determination Of Transformation Matrix Tmentioning

confidence: 99%

Section: Determination Of Transformation Matrix Tmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Sparse block factorization of saddle point matrices

Lungten

Schilders

Maubach

2016

Linear Algebra and its Applications

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“…Indeed, one may always identify the resistive subnetwork of any circuit, interconnected to other elements through terminals. The recent paper [9] describes how large resistive circuits occur in the design of very-large-scale integration chips, and how this leads to issues of efficient computation and of the replacement of a large resistive circuit by an equivalent circuit with the same terminals.…”

Section: E-mail Addressmentioning

confidence: 99%

Characterization and partial synthesis of the behavior of resistive circuits at their terminals

Schaft

2010

Systems & Control Letters

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Error bounds for reduction of multi‐port resistor networks

Ugryumova

Rommes

Schilders

2013

Int J Numerical Modelling

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SUMMARYThe interconnect layouts of chips can be modeled by large resistor networks. In order to be able to speed up simulations of such large networks, reduction techniques are applied to reduce the size of the networks. For some class of networks, an existing reduction strategy does not provide sufficient reduction in terms of the number of resistors appearing in the final network. In this paper we propose an approach for obtaining a further reduction in the amount of resistors. The suggested approach improves sparsity of the conductance matrix by neglecting resistors which do not contribute significantly to the behavior of the circuit. Explicit error bounds, which give an opportunity to control the errors due to approximation, have been derived. Numerical examples show that the suggested approach appears promising for multi-terminal resistor networks and, in combination with the existing reduction strategy, leads to better reduction.

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Efficient Methods for Large Resistor Networks

Cited by 73 publications

References 14 publications

Sparse block factorization of saddle point matrices

Sparse block factorization of saddle point matrices

Characterization and partial synthesis of the behavior of resistive circuits at their terminals

Error bounds for reduction of multi‐port resistor networks

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