SEMINAIRE D'ANALYSE NUMERIQUE
Année universitaire 2009-2010
Jeudi 11 mars 2010 :
Kersten SCHMIDT
(INRIA POEMS)
Modelling in Electromagnetics with the hp-FEM and Asymptotic Expansions
The talk is devoted to three aspects in electromagnetic modelling:
- the Eddy current model, a magneto-quasistatic approximation, to Maxwell's equations,
- the discretisation by hp-adaptive spaces with edge elements on curved meshes and meshes with hanging nodes, and
- the derivation of higher order transmission conditions for thin conducting sheets by asymptotic expansions.
Eddy current model. In the
first part I will show estimates of the modelling error of the Eddy
current model, which is the standard model for low frequency
applications.
hp-FEM. The hp-adaptive
FEM combines cell-subdivision and enlargement of polynomial
degrees. On geometrically refined meshes it is able to approximate
solutions in the presence of geometrical singularities with exponential
convergence. I will present ideas of the H(curl)-conforming
discretisation in the numerical C++ library Concepts, which included
the incorporation of curved cells and the handling of hanging nodes.
Asymptotics. Geometrically
small details like thin layered structures or thin sheets may hardly
(by extreme costs) be resolvable by FE meshes. With asymptotic
expansion techniques the solution close and far away the object are
separately investigated with the goal of approximate interface
conditions. I will show stable transmission conditions of order 2 and 3
for the case of thin conducting sheets for the 2D eddy current model.
