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

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

Domains: Mathematics [math]

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, 2018, 62, pp.264-281. ⟨10.1016/j.cnsns.2018.02.032⟩. ⟨hal-01989472⟩