วิธีการแปรผันพลังงานของปัญหาค่าขอบทางไฟฟ้าสถิตในตัวกลางแบบไม่เชิงเส้น / พัฒนชัย จันทร = Variational energy methods of electrostatic boundary-value problems in nonlinear media / Patanachai Janthon
The objective of this research is to study and to solve the electrostatic boundary-value problems in nonlinear media using variational energy methods. The properties of the dielectric composite materials can be calculated using solutions to the electrostatic boundary-value problems, but the problem's complexity precludes finding the exact solution. There are many ways to evaluate the solutions, and the method chosen here is the variational energy methods. This research demonstrates that using this method with linear composite media provides results that are as precise as other methods. Furthermore, fairly good results are obtained by applying this method to strongly nonlinear composite medium, and more precise solutions can be found by having additional parameters in the trial potential function. In addition, more complex problems can be solved using this method, such as in a system in which a nonlinear dielectric sphere is surrounded by another dielectric medium where all of them are in a uniform electric field. The results were comparable with first order perturbation methods. The results of both methods are very close when considered with the nonlinearity parameter (lambda) at low values, but when larger values of lambda are considered the results of the potential function and normal component of electric displacement at the surface of dieletric sphere under the variational energy methods show slightly more continuity than the perturbation method.
