Robust Numerical Integration Using Wave-Digital Concepts

Fettweis, A.

doi:10.1007/s11045-005-6236-3

Cited by 38 publications

(62 citation statements)

References 29 publications

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“…Fettweis 2006;Fettweis and Nitsche 1991a;Bilbao 2004 for a partial list) indicated that almost all passive physical phenomena, when properly formulated, can be described by means of multidimensional (MD) Kirchhoff circuits that are internally MD passive. While such results are interesting in their own right, one of the main motivations has been to deduce robust numerical models for such phenomena from the multidimensional passive Kirchhoff circuits by following the wave digital principles (Fettweis 2006). The essential virtues of numerical modelling of this type, as contrasted with those commonly pursued in numerical literature without necessary attention to the physics of the system, are manifold and have been enumerated in detail in Fettweis (2006).…”

Section: Introductionmentioning

confidence: 99%

“…While such results are interesting in their own right, one of the main motivations has been to deduce robust numerical models for such phenomena from the multidimensional passive Kirchhoff circuits by following the wave digital principles (Fettweis 2006). The essential virtues of numerical modelling of this type, as contrasted with those commonly pursued in numerical literature without necessary attention to the physics of the system, are manifold and have been enumerated in detail in Fettweis (2006). Indeed, the fluid dynamic problems including the nonlinear phenomena described by the equations of the Navier-Stokes type (including heat conduction in the fluid) form important examples of this larger study.…”

Section: Introductionmentioning

confidence: 99%

“…3 we derive the (2+1)-D passive Kirchhoff circuit realization of the shallow water system. The main ingredients of this derivation are the generic tools used in the approach (i.e., the Kirchhoff paradigm), one of which is to use the nonlinear versions of dynamic elements e.g., the inductances and capacitances considered, for example, in Fettweis (2006). The other key element involves scaling the time variable by a factor called the conversion velocity v 3 (this renders the dimension of the time axis to have the unit of length), and subsequently use a transformation of the independent coordinates.…”

Section: Introductionmentioning

confidence: 99%

“…As shown later, v 3 , in general, may be a function of time, in which case we may actually talk about a "warped" time. It should be chosen in such a way that the elements in the resulting Kirchhoff circuits are passive (Fettweis 2006;Fettweis and Basu 2011). Since it is proportional to the final computational load (Fettweis 2006;Fettweis and Nitsche 1991b) it should be kept as small as possible.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A new look at 2D shallow water equations of fluid dynamics via multidimensional Kirchhoff paradigm

Basu

Fettweis

2015

Multidim Syst Sign Process

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We discuss a new method of how the (nonlinear) 2D shallow water fluid dynamic problems inspired by ocean hydraulics, meteorology etc. can be modeled by internally passive multidimensional Kirchhoff circuits which subsequently pave the way for robust numerical simulation of the system by wave digital techniques. While the specific fluid dynamic equations dealt with in this paper are important in their own right and can be used to model a number of physical phenomena, the treatment is only one of many examples of the basic tenet that it should be possible to model all properly described physical systems by multidimensional internally passive Kirchhoff circuits. We refer to this as the Kirchhoff paradigm. In the context of the present specific problem, the paper thus helps to bridge connections between physics and circuits and systems theory at a deeper level than has been exploited before.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A new look at 2D shallow water equations of fluid dynamics via multidimensional Kirchhoff paradigm

Basu

Fettweis

2015

Multidim Syst Sign Process

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“…As has been shown, wave digital filters exhibit outstanding properties such as inherent stability, robustness, low coefficient sensitivity, and absence of parasitic oscillations or limit cycles, which are all guaranteed even under finite word-length conditions [2][3][4]. This concept has also successfully been applied to numerical solutions of ordinary differential equations by digital simulation of nonlinear circuits, even with chaotic behavior [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Wave digital simulation of passive systems in linear state‐space form

Ochs

2009

Int J Numerical Modelling

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SUMMARYThis paper deals with wave digital modeling of passive state-space models. The set of differential equations must be of linear state-space form, but all parameters can be time-variant and/or nonlinear. For such statespace models, a canonical internally passive reference circuit is presented and used for deriving wave digital structures. In order to show the usability, special solutions for important basic linear time-variant models are compared with wave digital simulation results. Moreover, the wave digital modeling of a nonlinear and time-variant oscillator is discussed. Especially for a lossless oscillator an implementation is proposed, which preserves energy under finite-arithmetic conditions. This is verified by comparing simulation results with the analytical solution of a gravity pendulum.

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A network‐theoretical perspective on oscillator‐based Ising machines

Beattie

Ochs

2023

Circuit Theory & Apps

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Summary The standard van Neumann computer excels at many things. However, it can be very inefficient in solving optimization problems with a large solution space. For that reason, a novel analog approach, the oscillator‐based Ising machine, has been proposed as a better alternative for dealing with such problems. In this work, we review the concept of oscillator‐based Ising machine and address how optimization problems can be mapped onto such machines when the quadratic unconstrained binary optimization (QUBO) formulation is given. Furthermore, we provide an ideal circuit that can be used in combination with the wave digital concept for real‐time simulated annealing. The functionality of this circuit is explained on the basis of a Lyapunov stability analysis. The latter also provides an answer for the decision‐making question: When has the Ising machine solved a mapped problem? At the end, we provide emulation results demonstrating the correlation between functionality and stability. Our results are based on an eigenvalue analysis of the linearized system and demonstrate that all eigenvalues converge to the left complex half plane, once an optimization problem has been optimally solved. This implies that the system enters an attractor region and is hence forced to eventually converge to the optimal solution.

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Robust Numerical Integration Using Wave-Digital Concepts

Cited by 38 publications

References 29 publications

A new look at 2D shallow water equations of fluid dynamics via multidimensional Kirchhoff paradigm

A new look at 2D shallow water equations of fluid dynamics via multidimensional Kirchhoff paradigm

Wave digital simulation of passive systems in linear state‐space form

A network‐theoretical perspective on oscillator‐based Ising machines

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