Homotopy Continuation Approach to Electrostatic Boundary-Value Problems of Nonlinear Media |
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Authors: | GU Guoqing YU Kinwah |
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Institution: | 1. College of Systems Science and Systems Engineering, University of Shanghai Science and Technology, Shanghai 200093, China;
2. Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong |
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Abstract: | The homotopy continuation method is employed to solve electrostatic boundaryvalue problems of nonlinear media. The difficulty associated with matching the inherently nonlinear boundary conditions on the interface is overcome by the mode expansion method, by which the nonlinear partial 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 nonlinear boundary conditions. As an illustration, we study two cases:(a) nonlinear inclusion in linear host and (b) linear inclusion-in nonlinear host, both in two dimensions. The homotopy method is validated by comparing the results with the exact solution of case (a) and the results derived by perturbation method in case (b). |
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Keywords: | nonlinear media homotopy continuation method electrostatic boundaryvalue problem |
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