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Power series analytical solution for 2D quasi-Laplace equation with piecewise constant conductivities

Zhi-Wei Cao 1, 2 Zhi-Feng Liu 2 Yi-Zhou Wang 2 Xiao-Hong Wang 2 Benoit Noetinger 3
1 China Nuclear Power Technology Research Institute
2 USTC - University of Science and Technology of China [Hefei]
3 IFPEN - IFP Energies nouvelles
Abstract : In this paper, the analytical solution for 2D quasi-Laplace equation with piecewise constant conductivities is provided. The analytical solution can be expressed as an infinite power series with a group of intrinsic non-integer power exponents around each singular point. Combined with the given boundary conditions, the coefficient of each term can be determined by numerical methods.
Keywords : Quasi-Laplace equation Series analytical solution Power-law behavior
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https://hal-ifp.archives-ouvertes.fr/hal-01989472
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Submitted on : Tuesday, January 22, 2019 - 2:24:15 PM
Last modification on : Thursday, February 7, 2019 - 5:14:02 PM

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Zhi-Wei Cao, Zhi-Feng Liu, Yi-Zhou Wang, Xiao-Hong Wang, Benoit Noetinger. Power series analytical solution for 2D quasi-Laplace equation with piecewise constant conductivities. Communications in Nonlinear Science and Numerical Simulation, Elsevier, 2018, 62, pp.264-281. ⟨10.1016/j.cnsns.2018.02.032⟩. ⟨hal-01989472⟩

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