Continuous-Time Algorithms for Solving Maxwell's Equations using Analog Circuits

Udayanga, Nilan; Hariharan, S. I.; Mandal, Soumyajit; Belostotski, Leonid; Bruton, L.T.

doi:10.1109/iscas45731.2020.9181014

Cited by 4 publications

(2 citation statements)

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“…So analog computing might have advantages over digital signal processing for some computational problems (such as the detection problem discussed in this paper), which cannot be solved on digital computers. Additionally, analog computing is known to have potentially significant advantages in terms of energy consumption, computation time and bandwidth efficiency; active research in this field still exists (see, e.g., [61], [62], [63], [64], [65], [66]). Moreover, novel approaches and materials have recently stimulated new research on analog computing [67], [68].…”

Section: Discussion and Future Problemsmentioning

confidence: 99%

On non-detectability of non-computability and the degree of non-computability of solutions of circuit and wave equations on digital computers

Boche,

Pohl

2022

Preprint

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It is known that there exist mathematical problems of practical relevance which cannot be computed on a Turing machine. An important example is the calculation of the first derivative of continuously differentiable functions. This paper precisely classifies the non-computability of the first derivative, and of the maximum-norm of the first derivative in the Zheng-Weihrauch hierarchy. Based on this classification, the paper investigates whether it is possible that a Turing machine detects this non-computability of the first derivative by observing the data of the problem, and whether it is possible to detect upper bounds for the peak value of the first derivative of continuously differentiable functions. So from a practical point of view, the question is whether it is possible to implement an exit-flag functionality for observing non-computability of the first derivative. This paper even studies two different types of exit-flag functionality. A strong one, where the Turing machine always has to stop, and a weak one, where the Turing machine stops if and only if the input lies within the corresponding set of interest.It will be shown that non-computability of the first derivative is not detectable by a Turing machine for two concrete examples, namely for the problem of computing the input-output behavior of simple analog circuits and for solutions of the three-dimensional wave equation. In addition, it is shown that it is even impossible to detect an upper bound for the maximum norm of the first derivative. In particular, it is shown that all three problems are not even semidecidable. Finally, we briefly discuss implications of these results for analog and quantum computing.

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Section: Discussion and Future Problemsmentioning

confidence: 99%

On non-detectability of non-computability and the degree of non-computability of solutions of circuit and wave equations on digital computers

Boche,

Pohl

2022

Preprint

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“…We build on such prior work by developing a circuit theoretic formulation of FDTD solutions to the 1D Schrödinger equation that naturally maps to fully-parallel implementations using analog switched capacitor (SC) circuits. The work is motivated by recent progress on low-power high-speed analog computation of Maxwell's equations [10], which has resulted in fully-parallel analog computers in 180 nm CMOS that solve the wave equation 420× faster than state of the art NVIDIA GPUs while consuming only 200 mW of power [11], [12].…”

Section: Introductionmentioning

confidence: 99%

Analog Switched-Capacitor Circuits for Solving the Schrödinger Equation

Liang

Malavipathirana

Hariharan

et al. 2021

2021 IEEE International Symposium on Circuits and Systems (ISCAS)

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This paper describes a circuit theoretic formulation for simulating the Schrödinger equation using classical analog circuits. Update equations for a finite difference time domain (FDTD) Schrödinger equation solver with absorbing boundary conditions (ABCs) are used to derive signal flow graphs that naturally map to switched capacitor (SC) circuits. A prototype implementation of a fully-parallel SC FDTD solver with 128 spatial points and a clock frequency of 2 MHz is analyzed and simulated using a standard 180 nm CMOS process.

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Can artificial intelligence do the job of a theoretical physicist?

Nieto-Chaupis

2023

2023 International Conference on Electrical, Communication and Computer Engineering (ICECCE)

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Continuous-Time Algorithms for Solving Maxwell's Equations using Analog Circuits

Cited by 4 publications

References 0 publications

On non-detectability of non-computability and the degree of non-computability of solutions of circuit and wave equations on digital computers

On non-detectability of non-computability and the degree of non-computability of solutions of circuit and wave equations on digital computers

Analog Switched-Capacitor Circuits for Solving the Schrödinger Equation

Can artificial intelligence do the job of a theoretical physicist?

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