The electrowetting process is commonly used to handle very small amounts of liquid on a solid surface. This process can be modelled mathematically with the help of the shape optimization theory. However, solving numerically the resulting shape optimization problem is a very complex issue, even for reduced models that occur in simplified geometries. Recently, the second author obtained convincing results in the 2D axisymmetric case. In this paper, we propose and analyze a method that is suitable...
Some electromagnetic materials have, in a given frequency range, an effective dielectric permittivity and/or a magnetic permeability which are real-valued negative coefficients when dissipation is neglected. They are usually called metamaterials. We study a scalar transmission problem between a classical dielectric material and a metamaterial, set in an open, bounded subset of R, with = 23. Our aim is to characterize occurences where the problem is well-posed within the Fredholm (or coercive +...
In this paper, a weighted regularization method for the time-harmonic Maxwell equations
with perfect conducting or impedance boundary condition in composite materials is presented.
The computational domain is the union
of polygonal or polyhedral subdomains made of different materials. As a result, the electromagnetic field presents singularities
near geometric singularities, which are the interior and exterior edges and corners. The variational formulation of the
weighted regularized problem is...
Some electromagnetic materials have, in a given frequency range, an effective dielectric permittivity and/or a magnetic permeability which are real-valued negative coefficients when dissipation is neglected. They are usually called metamaterials. We study a scalar transmission problem between a classical dielectric material and a metamaterial, set in an open, bounded subset of R, with = 23. Our aim is to characterize occurences where the problem is well-posed within the Fredholm (or coercive +...
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