SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Characterizing DAE circuit models via mixed determinantal expansions

I. García de la Vega and R. Riaza

Abstract
An index characterization is essential to make a correct numerical treatment of any kind of DAE and, in particular, of DAE-based circuit models. Beyond the passive setting, an index characterization has been achieved for nodal models by performing a Maxwell-type determinantal expansion of the nodal admittance matrix. Nevertheless, this characterization precludes current-controlled resistors and topological degeneracies. Overcoming these restrictions entails studying matrices with a more complex structure: in this communication we enlarge the scope of former results by extending Maxwell's determinantal expansions to these so-called mixed matrices. As a byproduct, we address other related problems in circuit theory. Research supported by Project MTM2010-15102 of Ministerio de Ciencia e Innovación, Spain, and by SisDAC Research Group and Depto. de Matemática Aplicada a las Tecnologías de la Información, ETSI Telecomunicación, Universidad Politécnica de Madrid.

Organized by         Universidad de Valladolid     IMUVA