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We propose transmission conditions of order 1, 2 and 3
approximating the shielding behaviour of thin conducting curved
sheets for the magneto-quasistatic eddy current model in 2D. This
model reduction applies to sheets whose thicknesses are at
the order of the skin depth or essentially smaller. The sheet has
itself not to be resolved, only its midline is represented by an
interface. The computation is directly in one step with almost no
additional cost. We prove the well-posedness w.r.t. to...
We propose transmission conditions of order 1, 2 and 3
approximating the shielding behaviour of thin conducting curved
sheets for the magneto-quasistatic eddy current model in 2D. This
model reduction applies to sheets whose thicknesses are at
the order of the skin depth or essentially smaller. The sheet has
itself not to be resolved, only its midline is represented by an
interface. The computation is directly in one step with almost no
additional cost. We prove the well-posedness w.r.t. to...
In this article, we derive a complete mathematical analysis of a
coupled 1D-2D model for 2D wave propagation in media including thin
slots. Our error estimates are illustrated by numerical results.
We are concerned with a 2D time harmonic wave propagation
problem in a medium including a thin slot whose thickness
is small with respect to the wavelength. In a previous article, we derived
formally an asymptotic expansion of the solution with respect to
using the method of matched asymptotic expansions. We also proved the
existence and uniqueness of the terms of the asymptotics. In this paper,
we complete the mathematical justification of our work by deriving optimal error estimates between...
It is rather classical to model multiperforated plates by approximate impedance boundary
conditions. In this article we would like to compare an instance of such boundary
conditions obtained through a matched asymptotic expansions technique to direct numerical
computations based on a boundary element formulation in the case of linear acoustic.
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