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Comparison of 2D curving methods with modal shape functions and a piecewise linear target mesh

Ziel, Verena, Hadrien Bériot, Onur Atak, Gwénaël Gabard

Proceedings, 26th International Meshing Roundtable, Elsevier, Science Direct, September 18-21 2017

INTERNATIONAL
MESHING
ROUNTABLE

26th International Meshing Roundtable
Barcelona, Spain
September 18-21, 2017

Verena Ziel, Institute of Sound and Vibration Research, University of Southampton, GB, vss1g14@soton.ac.uk
Hadrien Bériot, Siemens Industry Software NV, Simulation and Test Solutions, BE, hadrien.beriot@siemens.com
Onur Atak, Siemens Industry Software NV, Simulation and Test Solutions, BE, onur.atak@siemens.com
Gwénaël Gabard, Laboratoire d'Acoustique de l'Universit\'{e} du Maine, CNRS, FR, gwenael.gabard@univ-lemans.fr

Abstract
It is well known that high-order simulation techniques demand an accurate geometric representation and a coarse mesh. To fulfill both requirements, curved meshes are generated. In most cases, curving methods assume that the exact geometry is known. But it can be useful to develop curving methods with only a limited knowledge of the target geometry. In this paper, three curving methods are described that take a piecewise fine linear mesh as input: a least squares approach, a direct optimisation in the H^1-seminorm, and a H^1-seminorm optimisation in a reference space. Hierarchic, modal shape functions are used as basis for the geometric approximation. The methods are compared on two test geometries, a unit circle and a distorted ellipse. Considering both test cases, the direct optimisation approach shows the most promising results.

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