International audienceIn this paper, the interpolation functions behavior of the natural element method (NEM) and the finite element method (FEM) are compared. It is discussed how the unknown in both methods affects the stiffness matrix and contributes to NEM better accuracy. The visibility criterion and the constrained NEM are also addressed, and a pseudoalgorithm is proposed to implement the constrained Voronoï diagram, which is the base for the constrained NEM. A complex heterogeneous magnetic problem is solved by both FEM and NEM methods and their solutions are compared. It is shown that for the same discretization, the number of contributions for NEM is in general bigger than those related to the FEM and better accuracy results for NEM
In this work, new formulations for the hybrid meshless-method of moments technique are presented. The proposed approaches are applied for solving 2D electromagnetic scattering problems. The solution is obtained by dividing the problem into 2 subproblems: one internal to the scatterer and another external to it. For the internal subproblem, the meshless method is used for solving the weak form of the 2D Helmholtz equation. For the external subproblem, the Method of Moments is used for solving different combinations of electric field integral equation and magnetic field integral equation. Both subproblems are coupled by imposing the continuity of the tangential fields over the scatterer surface. The technique is applied for solving the TMz electromagnetic scattering by an infinite dielectric cylinder. Numerical and analytical results are compared to each other showing the validity and accuracy of the proposed approaches.
The problem of determining the electromagnetic scattering of arbitrary structures consisting of both dielectric and conducting materials are analyzed in this paper by the natural-element method coupled with the absorbing boundary condition (NEM-ABC). By this method, the target is first enclosed by a fictitious boundary. Maxwell's equations are then solved by NEM inside and ABC is applied on the fictitious boundary. The results are compared with analytical and finite-element method-ABC ones which show the robustness, applicability and relevance of the method.
Index Terms-Electromagnetic scattering problems, finite-element methods (FEMs), natural-element methods (NEMs).
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