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While waveform relaxation (also known as dynamic iteration or co-simulation) methods are known to converge for coupled systems of ordinary differential equations (ODEs), they may suffer from instabilities for coupled differential-algebraic equations (DAEs). Several convergence criteria have been developed for index-1 DAEs. We present here a convergence criterion for a coupled system of an index-2 DAE with an ODE. The analysis is motivated by the wish to combine electromagnetic field simulation with circuit simulation in a stable manner. The spatially discretized Maxwell equations in vector potential formulation with Lorenz gauging represent an ODE system. A lumped circuit model via the established modified nodal analysis is known to be a DAE system of index ≤ 2. Finally, we present sufficient network topological criteria to the coupling that are easy to check and that guarantee convergence. [ABSTRACT FROM AUTHOR]

We are interested in a convergent numerical discretization scheme for nonlinear differential algebraic equations (DAEs) coupled with elliptic constraints. The dynamics of flow networks (for example circuits) can often be described by a DAE. However, this is only the case if all network element models are lumped models. If spatial effects cannot be neglected, distributed element models have to be included. In this paper, we address the case of elliptic models for distributed network elements. Under some monotonicity and Lipschitz assumptions for the system functions, we present an error analysis for discretizations of DAEs coupled with elliptic constraints based on a Galerkin approach for the distributed model part combined with the BDF method as time discretization of the full system. [ABSTRACT FROM AUTHOR]

SUMMARY The hyperbolicity problem in circuit theory concerns the existence of purely imaginary eigenvalues in the linearization of the time-domain description of the circuit dynamics. In this paper, we characterize the circuit configurations that, in a strictly passive setting, yield purely imaginary eigenvalues for all values of the capacitances and inductances. Our framework is based on branch-oriented, semistate (differential-algebraic) circuit models that capture explicitly the circuit topology, and use several notions and results from digraph theory. So-called P-structures arising in the analysis turn out to be the key element supporting our results. The analysis is shown to hold not only for classical (RLC) circuits but also for nonlinear circuits including memristors and other mem-devices. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: We are interested in circuit simulation including distributed semiconductor models. The circuit itself is modeled by the modified nodal analysis. The stationary drift diffusion equations are used to describe the semiconductors. The complete system is then a partial differential-algebraic system. We discretize it first in space with finite elements and the Scharfetter–Gummel discretization. The resulting semi-discrete system can be analyzed as a differential-algebraic equation with properly stated leading term. We present topological index one criteria. They coincide with previous results for the non-discretized partial differential-algebraic equation. For the time discretization we use standard BDF methods (implicit Gear formulas). Finally we derive a convergence estimate for the whole partial differential-algebraic system close to equilibrium. [ABSTRACT FROM AUTHOR]

The dynamical behaviour of nonlinear electrical circuits is usually modelled in the time domain by differential-algebraic equations (DAEs). The differential-algebraic formalism drives qualitative analyses based on linearization to a matrix pencil setting. In this context, the present paper performs a spectral analysis of matrix pencils and DAEs arising in nonlinear circuit theory. Specifically, the non-singularity, hyperbolicity and asymptotic stability of equilibria are addressed in terms of circuit topology. The differential-algebraic framework puts the results beyond those already known for state-space models, unfeasible in many actual problems. The topological conditions arising in this qualitative study are proved independent of those supporting the index, and therefore they apply to both index-1 and index-2 configurations. The approach illustrates how graph theory, matrix analysis and DAE theory interact in the dynamical study of nonlinear circuits. [ABSTRACT FROM AUTHOR]

A coupled system modelling an electric circuit containing semiconductors is presented. The modified nodal analysis leads to a differential algebraic equation (DAE) describing the electric network. The nonlinear behaviour of the semiconductors is modelled by the drift diffusion equations. Coupling relations are defined and a generalization of the tractability index to systems of infinite dimensions is presented and applied to the resulting partial differential algebraic equation (PDAE). The PDAE turns out to have the same index as the electrical network equations. [ABSTRACT FROM AUTHOR]

Abstract: In this work we are interested in the numerical solution of a coupled model of differential algebraic equations (DAEs) and partial differential equations (PDEs). The DAEs describe the behavior of an electrical circuit that contains semiconductor devices and the partial differential equations constitute drift-diffusion equations modelling the semiconductor devices in the circuit. After space discretization using a finite element method, the coupled system results in a differential-algebraic system with a properly stated leading term. We investigate the structure and the properties of this DAE system. In particular, we develop structural criteria for the DAE index. This is of basic interest since DAE properties like stability, existence and uniqueness of solutions depend strongly on its index. [Copyright &y& Elsevier]

Abstract: One challenge for the simulation and optimization of real gas pipe networks is the treatment of compressors. Their behavior is usually described by characteristic diagrams reflecting the connection of the volumetric flow and the enthalpy change or shaft torque. Such models are commonly used for an optimal control of compressors and compressor stations [4,7] using stationary models for the gas flow through the pipes. For transient simulations of gas networks, simplified compressor models have been studied in [1–3]. Here, we present a transient simulation of gas pipe networks with characteristic diagram models of compressors using a stable network formulation as (partial) differential‐algebraic system. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Differential-algebraic equations with higher-index give rise to essentially ill-posed problems. The overdetermined least-squares collocation for differential-algebraic equations which has been proposed recently is not much more computationally expensive than standard collocation methods for ordinary differential equations. This approach has displayed impressive convergence properties in numerical experiments, however, theoretically, till now convergence could be established merely for regular linear differential-algebraic equations with constant coefficients. We present now an estimate of the instability threshold which serves as the basic key for proving convergence for general regular linear differential-algebraic equations. [ABSTRACT FROM AUTHOR]

Differential–algebraic equations with higher index give rise to essentially ill-posed problems. Therefore, their numerical approximation requires special care. In the present paper, we state the notion of ill-posedness for linear differential–algebraic equations more precisely. Based on this property, we construct a regularization procedure using a least-squares collocation approach by discretizing the pre-image space. Numerical experiments show that the resulting method has excellent convergence properties and is not much more computationally expensive than standard collocation methods used in the numerical solution of ordinary differential equations or index-1 differential–algebraic equations. Convergence is shown for a limited class of linear higher-index differential–algebraic equations. [ABSTRACT FROM AUTHOR]

Known solvability results for nonlinear index-1 differential-algebraic equations (DAEs) are in general local and rely on the Implicit Function Theorem. In this paper, we derive a global result which guarantees unique solvability on a given time interval for a certain class of index-1 DAEs with certain monotonicity conditions. Based on this result, we show that memristive circuit DAEs arising from the modified nodal analysis are uniquely solvable if they fulfill certain passivity and network topological conditions. Furthermore we present an error estimation for the solution with respect to perturbations on the right-hand side and in the initial value. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Modern modeling approaches for circuit simulation such as themodified nodal analysis (MNA) lead to differential-algebraic equations (DAEs).The index of a DAE is a measure of the degree of numerical difficulty. Ingeneral, the higher the index is, the more difficult it is to solve the DAE.In this paper, we consider a broader class of analysis methods called thehybrid analysis. For nonlinear time-varying circuits with general dependentsources, we give a structural characterization of the tractability index of DAEsarising from the hybrid analysis. This enables us to determine the tractabilityindex efficiently, which helps to avoid solving higher index DAEs in circuitsimulation. [ABSTRACT FROM AUTHOR]

Modern modeling approaches for circuit simulation such as the modified nodal analysis (MNA) lead to differential-algebraic equations (DAEs). The index of a DAE is a measure of the degree of numerical difficulty. In general, the higher the index is, the more difficult it is to solve the DAE. In this paper, we consider a broader class of analysis methods called the hybrid analysis. For nonlinear time-varying circuits with general dependent sources, we give a structural characterization of the tractability index of DAEs arising from the hybrid analysis. This enables us to determine the tractability index efficiently, which helps to avoid solving higher index DAEs in circuit simulation. [ABSTRACT FROM AUTHOR]

In this paper we combine video compression and modern image processing methods. Iterative filter methods for prediction signals based on classic inpainting methods are introduced and extensive parameter tests are described. In order to construct an alternative prediction filter for video coding, techniques originally employed for inpainting are applied. Thereby, the structures of the underlying prediction were incorporated into the filter construction making it signal adaptive. The resulting optimization problem is solved using the so-called Alternating Direction Method of Multipliers (ADMM). The undertaken novel parameter tests are described and it is shown that they improve the coding efficiency of the tool. The suggested filter is embedded into a software based on HEVC with additional QTBT (Quadtree plus Binary Tree) and MTT (Multi-Type-Tree) block structure. Overall, the proposed filter method obtains average bitrate savings of 1.35% at an average encoder runtime increase of 28% and decoder runtime increase of 38%. UHD test sequences achieve bitrate savings of up to 3.66% for Random Access. [ABSTRACT FROM AUTHOR]

We consider partial differential algebraic systems (PDAEs) describing water transportation networks. Similar to the approach in [6], we follow the method of lines for the discretization. However, we do not consider free surface flow models but pressure flow models covering hydraulic shocks. Moreover, we include switching models reflecting the on/off state of pumpes and valves. Aiming at a stable numerical simulation of the PDAEs we present a topology based spatial discretization that results in a differential algebraic system (DAE) of index 1. Furthermore we show that the DAE index can be higher than 1 if the spatial discretization is not adapted to the position of reservoirs and demand nodes within the network. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The FP7 project nanoCOPS derives new methods for simulation during development of designs of integrated products. It covers advanced simulation techniques for electromagnetics with feedback couplings to electronic circuits, heat and stress. It is inspired by interest from semiconductor industry and by a simulation tool vendor in electronic design automation. The project is on-going and the paper presents the outcomes achieved after the first half of the project duration. [ABSTRACT FROM AUTHOR]