High-order 2D mesh curving methods with a piecewise linear target and application to Helmholtz problems
High-order 2D mesh curving methods with a piecewise linear target and application to Helmholtz problems
High-order simulation techniques typically require high-quality curvilinear meshes. In most cases, mesh curving methods assume that the exact geometry is known. However, in some situations only a fine linear FEM mesh is available and the connection to the CAD geometry is lost. In other applications, the geometry may be represented as a set of scanned points. In this paper, two curving methods are described that take a piecewise fine linear mesh as input: a least squares approach and a continuous optimization in the H1-seminorm. Hierarchic, modal shape functions are used as basis for the geometric approximation. This approach allows to create very high-order curvilinear meshes efficiently (q>4) without having to optimize the location of non-vertex nodes. The methods are compared on two test geometries and then used to solve a Helmholtz problem at various input frequencies. Finally, the main steps for the extension to 3D are outlined.
Curvilinear meshes, Geometry error, Helmholtz problems, High-order methods, Integrated Legendre polynomials, Linear target mesh
26-41
Ziel, V.S.
f09c1da6-370e-43ac-b9bb-5283633ebadb
Bériot, H.
d73aea9a-8247-493f-9603-e76dc60e99ba
Atak, O.
3a68e4ba-8e41-4e51-8146-651bcda11ded
Gabard, G.
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
1 December 2018
Ziel, V.S.
f09c1da6-370e-43ac-b9bb-5283633ebadb
Bériot, H.
d73aea9a-8247-493f-9603-e76dc60e99ba
Atak, O.
3a68e4ba-8e41-4e51-8146-651bcda11ded
Gabard, G.
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Ziel, V.S., Bériot, H., Atak, O. and Gabard, G.
(2018)
High-order 2D mesh curving methods with a piecewise linear target and application to Helmholtz problems.
CAD Computer Aided Design, 105, .
(doi:10.1016/j.cad.2018.07.004).
Abstract
High-order simulation techniques typically require high-quality curvilinear meshes. In most cases, mesh curving methods assume that the exact geometry is known. However, in some situations only a fine linear FEM mesh is available and the connection to the CAD geometry is lost. In other applications, the geometry may be represented as a set of scanned points. In this paper, two curving methods are described that take a piecewise fine linear mesh as input: a least squares approach and a continuous optimization in the H1-seminorm. Hierarchic, modal shape functions are used as basis for the geometric approximation. This approach allows to create very high-order curvilinear meshes efficiently (q>4) without having to optimize the location of non-vertex nodes. The methods are compared on two test geometries and then used to solve a Helmholtz problem at various input frequencies. Finally, the main steps for the extension to 3D are outlined.
Text
cad imr ziel
- Accepted Manuscript
More information
Accepted/In Press date: 11 July 2018
e-pub ahead of print date: 17 July 2018
Published date: 1 December 2018
Keywords:
Curvilinear meshes, Geometry error, Helmholtz problems, High-order methods, Integrated Legendre polynomials, Linear target mesh
Identifiers
Local EPrints ID: 424795
URI: http://eprints.soton.ac.uk/id/eprint/424795
ISSN: 0010-4485
PURE UUID: 8c1d7ca4-28f3-49f7-be93-17adc37cecb8
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Date deposited: 05 Oct 2018 11:46
Last modified: 18 Mar 2024 05:19
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Contributors
Author:
V.S. Ziel
Author:
H. Bériot
Author:
O. Atak
Author:
G. Gabard
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