Special Functions and HHL Quantum Algorithm for Solving Moving Boundary Value Problems Occurring in Electric Contact Phenomena

2021 IEEE 66th Holm Conference on Electrical Contacts (HLM) Pub Date : 2020-10-04 DOI:10.1109/HLM51431.2021.9671227

Merey M. Sarsengeldina, Z. Nashed

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引用次数: 2

Abstract

This series of studies is devoted to developing and employing mathematical methods along with quantum algorithms for solving moving boundary value problems which occur in heat and mass transfer problems. In this particular study we develop mathematical framework where we utilize special functions and Harrow-Hassidim-Lloyd (HHL) quantum algorithm for finding exact and approximate solutions of Generalized Heat Equation with moving boundaries and as examples we consider plane and spherical cases. In spherical case the Generalized Heat Equation is reduced to linear moving boundary value problem with discontinuous coefficients and solved exactly. In plane case we use collocation method for approximate solution of Inverse Two-Phase Stefan problem. Experimental verification of suggested mathematical framework has been tested for modeling arcing phenomena in composite electrical contacts with AgCdO (90%) and Ni (10%). HHL algorithm was applied and run on IBM Q with Qiskit and the code is openly available on https://github.com/users/Schrodinger-cat-kz/projects/2.

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求解电接触现象中移动边值问题的特殊函数和HHL量子算法

这一系列的研究致力于发展和运用数学方法和量子算法来解决发生在传热和传质问题中的移动边值问题。在这个特殊的研究中，我们开发了数学框架，其中我们利用特殊函数和Harrow-Hassidim-Lloyd (HHL)量子算法来寻找具有移动边界的广义热方程的精确和近似解，并作为例子，我们考虑了平面和球面情况。在球形情况下，将广义热方程简化为具有不连续系数的线性运动边值问题，并精确求解。在平面情况下，用配点法近似求解两相反斯特芬问题。实验验证了所建议的数学框架，用于模拟AgCdO(90%)和Ni(10%)的复合电触点中的电弧现象。HHL算法通过Qiskit在IBM Q上应用和运行，代码可以在https://github.com/users/Schrodinger-cat-kz/projects/2上公开获得。

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2021 IEEE 66th Holm Conference on Electrical Contacts (HLM)

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