arXiv subjects

Caren Tischendorf

Publications and source records attributed to Caren Tischendorf.

3 recordsLinked to original sources

arXiv2024

Index concepts for linear differential-algebraic equations in finite and infinite dimensions

Different index concepts for linear differential-algebraic equations are defined in the general Banach space setting, and compared. For regular finite-dimensional linear differential-algebraic equations, all these indices exist and are equivalent. For infinite-dimensional systems, the situation is more complex. It is proven that although some indices imply others, in general they are not equivalent. The situation is illustrated with a number of examples.

math.DS↗

arXiv2020

Waveform relaxation for low frequency coupled field/circuit differential-algebraic models of index 2

Motivated by the task to design quench protection systems for superconducting magnets in particle accelerators we address a coupled field/circuit simulation based on a magneto-quasistatic field modeling. We investigate how a waveform relaxation of Gauß-Seidel type performs for a coupled simulation when circuit solving packages are used that describe the circuit by the modified nodal analysis. We present sufficient convergence criteria for the coupled simulation of FEM discretised field models and circuit models formed by a differential-algebraic equation (DAE) system of index 2. In particular, we demonstrate by a simple benchmark system the drastic influence of the circuit topology on the convergence behavior of the coupled simulation.

math.NA↗

arXiv2019

Generalized Circuit Elements

The structural analysis, i.e., the investigation of the differential-algebraic nature, of circuits containing simple elements, i.e., resistances, inductances and capacitances is well established. However, nowadays circuits contain all sorts of elements, e.g. behavioral models or partial differential equations stemming from refined device modelling. This paper proposes the definition of generalized circuit elements which may for example contain additional internal degrees of freedom, such that those elements still behave structurally like resistances, inductances and capacitances. Several complex examples demonstrate the relevance of those definitions.

math.NA↗