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.
Received: 30 January 2000
Accepted manuscript online:
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