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Weighted regularization for composite materials in electromagnetism
Published online by Cambridge University Press: 03 November 2009
Abstract
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 Ω 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 given on the subspace of
${\cal H}$(${\bf curl}$
;Ω)
whose fields $\textit{\textbf{ u}}$
satisfy $w^\alpha$
div ($\varepsilon{\textit{\textbf{u}}}$
)∈L2(Ω) and have vanishing tangential trace
or tangential trace in L2($\partial\Omega$
). The weight function $w(\bf x)$
is equivalent
to the distance of $\bf x$
to the geometric singularities and the minimal weight parameter α
is given in terms of the singular exponents of a scalar transmission problem.
A density result is proven that guarantees the approximability of the solution field by piecewise regular fields.
Numerical results for the discretization of the source problem
by means of Lagrange Finite Elements of type P1 and P2 are given on
uniform and appropriately refined two-dimensional meshes.
The performance of the method in the case of eigenvalue problems is addressed.
Keywords
- Type
- Research Article
- Information
- ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 1 , January 2010 , pp. 75 - 108
- Copyright
- © EDP Sciences, SMAI, 2009
References
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