Progress in Industrial Mathematics at ECMI 2010 by Kai Bittner, Emira Dautbegovic (auth.), Michael Günther,

By Kai Bittner, Emira Dautbegovic (auth.), Michael Günther, Andreas Bartel, Markus Brunk, Sebastian Schöps, Michael Striebel (eds.)

ECMI, the ecu Consortium for arithmetic in undefined, is the eu model linked to utilized arithmetic for and organizes hugely profitable biannual meetings. during this sequence, the ECMI 2010, the sixteenth ecu convention on arithmetic for undefined, used to be held within the old urban corridor of Wuppertal in Germany. It coated the maths of a variety of functions and strategies, from circuit and electromagnetic gadget simulation to version order relief for chip layout, uncertainties and stochastics, creation, fluids, existence and environmental sciences, and devoted and flexible methods.

These court cases of ECMI 2010 emphasize arithmetic as an innovation enabler for and enterprise, and as a fully crucial pre-requiste for Europe on its method to changing into the top knowledge-based financial system within the world.

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We first study the network equations (using the Modified Nodal Analysis) without the nonlinear coupling term describing the device currents, and we assume these equations to be of tractability index 2. We propose some additional topological conditions that make the full coupled system of index 2. For this coupled system we prove an existence result. Our paper is organized as follows: the next section states the coupled model; Section 3 gives the index-2 decomposition and an example for our conditions developed; Section 4 contains the existence result with a sketched proof.

The existence of an LC-block then follows as a necessary condition for a PIE to exist for all values of the reactive parameters. Structural Characterization of Circuit Configurations with Undamped Oscillations 19 4 Concluding Remarks We have characterized in this communication the circuit configurations yielding purely imaginary eigenvalues for all values of capacitances and inductances in strictly passive RLC circuits. The hyperbolicity problem in general is however still open and a full structural study is in the scope of future research.

We exploit time integration to obtain estimates for the oscillation frequency and for the oscillator solution. It also provides an initialization of the probe voltage. Next we describe new techniques from bordered matrices and eigenvalue methods to improve Newton methods for Finite Difference techniques in the time domain as well as for Harmonic Balance. The method gauges the phase shift automatically. No assumption about the range of values of the Periodic Steady State solution is needed. 1 Introduction A free-running oscillator is an autonomous circuit, which has only DC bias sources connected to the circuit and, thus, no periodic excitation.

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