We studied the harmonic magnetodynamic behavior (without free space wave propagation) of a resonant surface metamaterial, made of many identical and regularly arranged LC cells. The circuit model gives the exact solution, but it is not numerically efficient for simulating very large structures (e.g. 1000×1000 cells giving 10 6 unknowns with a full 10 6 ×10 6 matrix). For the first time, we highlight the modal characteristics of the spatial solutions, which makes it possible to explain their frequency and spatial related properties. From these results, we show under what assumptions it is possible to significantly lighten the system of equations, which opens the way to develop more efficient numerical methods.
In this paper, a coupling of the Finite Element Method (FEM) and the Boundary Element Method (BEM) is used to model the behaviour of magnetoelectric effects in composite structures. This coupling of numerical methods makes it possible not to have to consider a free domain, and thus to use a single mesh for the magnetic, mechanical and electrical problems. This results in a consequent reduction of the number of unknowns which is accompanied by shorter computation times compared to a classical FEM approach. A mixed magnetic vector potentialreduced magnetic scalar potential formulation is used for the magnetic problem, and classical FEM formulations are used for electrical and mechanical problems. The resulting global algebraic system is solved by a block Gauss-Seidel solver.
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