中国物理B ›› 2000, Vol. 9 ›› Issue (6): 464-468.doi: 10.1088/1009-1963/9/6/012

• • 上一篇    下一篇

ELECTROSTATIC POTENTIAL OF STRONGLY NONLINEAR COMPOSITES: HOMOTOPY CONTINUATION APPROACH

魏恩泊, 顾国庆   

  1. College of Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
  • 收稿日期:2000-01-30 出版日期:2000-06-15 发布日期:2005-06-12
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 19834070).

ELECTROSTATIC POTENTIAL OF STRONGLY NONLINEAR COMPOSITES: HOMOTOPY CONTINUATION APPROACH

Wei En-bo (魏恩泊), Gu Guo-qing (顾国庆)   

  1. College of Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
  • Received:2000-01-30 Online:2000-06-15 Published:2005-06-12
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 19834070).

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.

Abstract: 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=$\sigma$ E+$\chi$|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)

  • 02.60.Cb
02.60.Lj (Ordinary and partial differential equations; boundary value problems) 41.20.Cv (Electrostatics; Poisson and Laplace equations, boundary-value problems)