The proposed method is theoretically proven to be divergence free and will not introduce the artificial charges in its numerical solutions.
The conventional meshless method using Gaussian RBF cannot preserve the divergence property of electric and magnetic fields. (2) A divergence preserved meshless method based on the vector radial basis function (RBF) is proposed to solve the Maxwell’s equations. Since the proposed method only requires to solve electrical field, computational efficiency of the proposed method is largely improved. (1) A meshless method for the wave equation is proposed to improve the efficiency based on the mathematical equivalence of the Maxwell’s equations and wave equation. Investigations on the meshless method lead to the following results. Almost 41.7% less count of floating-point operations than the original one is obtained. Theoretical proof of both the unconditional stability and the divergence property is provided. To further improve its efficiency, an efficiency improved version is proposed.
It is found that divergence preserved ADI-FDTD method maintains the unconditional stability and the same numerical dispersion as that of the traditional ADI-FDTD method, while preserving electromagnetic divergence properties. In this thesis, systematic investigations on divergence property of the divergence preserved alternatively-direction-implicit finite-difference time-domain (ADI-FDTD) method and the meshless method are carried out.
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