中国物理B ›› 2000, Vol. 9 ›› Issue (6): 464-468.doi: 10.1088/1009-1963/9/6/012
魏恩泊, 顾国庆
Wei En-bo (魏恩泊), Gu Guo-qing (顾国庆)
摘要: The homotopy continuation method is used to solve the electrostatic boundary-value problems of strongly nonlinear composite media, which obey a current-field relation of J=σ E+χ|E|2E. With the mode expansion, the approximate analytical solutions of electric potential in host and inclusion regions are obtained by solving a set of nonlinear ordinary different equations, which are derived from the original equations with homotopy method. As an example in dimension two, we apply the method to deal with a nonlinear cylindrical inclusion embedded in a host. Comparing the approximate analytical solution of the potential obtained by homotopy method with that of numerical method, we can obverse that the homotopy method is valid for solving boundary-value problems of weakly and strongly nonlinear media.
中图分类号: (Numerical simulation; solution of equations)