HOMOTOPY CONTINUATION APPROACH TO ELECTROSTATIC BOUNDARY-VALUE-PROBLEMS OF NONLINEAR MEDIA

The homotopy continuation method is employed to solve electrostatic bo undary-value problems of nonlinear media. The difficulty associated wi th matching the inherently nonlinear boundary conditions on the interf ace is overcome by the mode expansion method, by which the nonlinear p artial differential equations of the original problem are transformed into an infinite set of nonlinear ordinary differential equations. In this regard, the homotopy method has to be modified to handle the nonl inear boundary conditions. As an illustration, we study two cases: (a) nonlinear inclusion in linear host and (b) linear inclusion in nonlin ear host, both in two dimensions. The homotopy method is validated by comparing the results with the exact solution of case (a) and the resu lts derived by perturbation method in case (b).