Electrostatic potential of strongly nonlinear composites: Homotopy continuation approach

The homotopy continuation method is used to solve the electrostatic boundar y-value problems of strongly nonlinear composite media, which obey a curren t-field relation of J = sigma E + chi\E\E-2. With the mode expansion, the a pproximate analytical solutions of electric potential in host and inclusion regions are obtained by solving a set of nonlinear ordinary different equa tions, which are derived from the original equations with homotopy method. As an example in dimension two, we apply the method to deal with a nonlinea r cylindrical inclusion embedded in a host. Comparing the approximate analy tical solution of the potential obtained by homotopy method with that of nu merical method, we can obverse that the homotopy method is valid for solvin g boundary-value problems of weakly and strongly nonlinear media.