Contribution au développement d’une méthode temporelle pour la modélisation des structures hyperfréquences.

Abstract

Numerical simulation has become a central tool in the modeling of many microwave structures that sometimes suffer from discontinuities, which are difficult to model by conventional techniques, as required by powerful design and modeling methods. In addition, because of the increase in frequencies, it has become necessary to predict temporal responses to instantly evaluate the performance of these structures over broad frequency bands. Due to the restrictions imposed on traditional numerical methods due to its dependence on meshes, meshless methods have become an indispensable scientific tool in electromagnetic modeling because they have freed the difficulties of the classical methods discretization grid. The approximation of the Maxwell equations on the one hand and they are based essentially on the basic functions according to their mathematical formulations on the other hand, which distinguishes them from low computation costs compared with other conventional techniques. However, to obtain convergence and obtain accurate results, the meshless methods suffer from a Courant-Friedrichs-Lewy (CFL) stability problem that limits the time step must be satisfied in practical simulations. Consequently, the computation time can be prohibitive for the fine electromagnetic modeling which requires their integration with the unconditionally stable implicit schemes. In this context, on the one hand, many algorithms have been proposed to solve the Maxwell differential equations in the time domain for the simulation of some microwave structures which are: the meshless method based on the basis radial functions (RBF) and meshless radial point interpolation (RPIM) method. On the other hand, presentation of a new unconditionally stable two-dimensional radial point interpolation (RPIM) meshless method based on the Crank-Nicolson (CN) scheme. The implicit scheme of CN in the proposed algorithm is applied to only one of Maxwell's equations. This leads to solving the time-domain second-order vector wave equation. Therefore a single electromagnetic field is explicitly updated at each iteration. The CFL requirement in the proposed CN-RPIM wave equation method does not limit the time step due to its implicit formulation. To value the proposed CN-RPIM method, numerical examples are used to validate and demonstrate efficiency and accuracy. The numerical results are compared with those obtained by the explicit RPIM method and the FDTD method.