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Publications in Scientific Journals:

K. Roppert, S. Schoder, M. Kaltenbacher, F. Toth:
"Non-conforming Finite Elements";
International Compumag Society Newsletter (invited), 25 (2018), 3; 4 - 18.



English abstract:
We investigate flexible discretization techniques
for the approximate solution of electromagnetic field
problems. In order to keep as much exibility as possible,
we use independently generated grids which are well
suited for approximating the solution of decoupled local
sub-problems in each subdomain, coupled on a common
interface. Therefore, we have to deal with the situation
of non-conforming grids appearing at the common interface
of two subdomains. Special care has to be taken in order
to define and implement the appropriate discrete coupling
operators. The Finite Element method is applied and used
in two approaches to handle non-conforming grids: (1)
Classical mortaring and (2) Nitsche-type mortaring. The
first approach guarantees a strong coupling of the
flux by introducing a Lagrange multiplier and a weak coupling of
the magnetic vector potential. The Nitsche-type mortaring
does not need the additional Lagrange multiplier and handles
the coupling by symmetrizing the bilinear form, as well as
adding a special interface term to penalize the jump of the
magnetic vector potential.
The first part of this contribution descibes step by step the
FE formulations of both non-conforming grid techniques and
its application to two 2D examples: solenoid and gear wheel
sensor. The second part focuses on the correct Nitsche-type
mortaring formulation for 3D electromagnetics and its
application to induction heating. Thereby, the application
of a multi-harmonic ansatz (harmonic balance finite element
method) allows to solve the nonlinear electromagnetic field
problem in the frequency domain.


Electronic version of the publication:
https://publik.tuwien.ac.at/files/publik_273654.pdf


Created from the Publication Database of the Vienna University of Technology.