Automatic conformal decomposition of elements cut by NURBS

Jakob W. Steidl; Thomas Peter Fries

Automatic conformal decomposition of elements cut by NURBS

Institute of Structural Analysis (2020)

Research output: Chapter in Book/Report/Conference proceeding › Conference paper

Abstract

In fictitious domain and extended finite element methods, elements cut by boundaries or interfaces are frequently present. They pose challenges with respect to the application of boundary and interface conditions, numerical integration, and the conditioning of the system of equations. A different path is the automatic decomposition of cut elements into smaller, conforming finite elements. Herein, we propose a concept for the automatic decomposition of elements cut by (curved) NURBS which automatically generates higher-order Lagrange elements on the two sides of the interfaces. The NURBS data, defining boundaries and interfaces in two dimensions, is converted into implicit level-set data by evaluating signed distance computations at all nodes in the background mesh. Based on the findings in [1] this data is then used for the decomposition into sub-elements. First numerical results are achieved as a proof-of-concept.

Original language	English
Title of host publication	ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering
Publisher	National Technical University of Athens
Pages	2591-2600
Number of pages	10
Volume	2
ISBN (Electronic)	9786188284401
Publication status	Published - 2016
Event	7th European Congress on Computational Methods in Applied Sciences and Engineering: ECCOMAS 2016 - Crete, Greece Duration: 5 Jun 2016 → 10 Jun 2016 https://www.eccomas2016.org/

Conference

Conference	7th European Congress on Computational Methods in Applied Sciences and Engineering
Abbreviated title	ECCM 2016
Country/Territory	Greece
City	Crete
Period	5/06/16 → 10/06/16
Internet address	https://www.eccomas2016.org/

Keywords

Conformal decomposition
Fictitious domain method
Level set method
NURBS
Signed distance

ASJC Scopus subject areas

Applied Mathematics

Cite this

Automatic conformal decomposition of elements cut by NURBS. / Steidl, Jakob W.; Fries, Thomas Peter.
ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering. Vol. 2 National Technical University of Athens , 2016. p. 2591-2600.

Research output: Chapter in Book/Report/Conference proceeding › Conference paper

Steidl, JW & Fries, TP 2016, Automatic conformal decomposition of elements cut by NURBS. in ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering. vol. 2, National Technical University of Athens , pp. 2591-2600, 7th European Congress on Computational Methods in Applied Sciences and Engineering, Crete, Greece, 5/06/16.

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AB - In fictitious domain and extended finite element methods, elements cut by boundaries or interfaces are frequently present. They pose challenges with respect to the application of boundary and interface conditions, numerical integration, and the conditioning of the system of equations. A different path is the automatic decomposition of cut elements into smaller, conforming finite elements. Herein, we propose a concept for the automatic decomposition of elements cut by (curved) NURBS which automatically generates higher-order Lagrange elements on the two sides of the interfaces. The NURBS data, defining boundaries and interfaces in two dimensions, is converted into implicit level-set data by evaluating signed distance computations at all nodes in the background mesh. Based on the findings in [1] this data is then used for the decomposition into sub-elements. First numerical results are achieved as a proof-of-concept.

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Automatic conformal decomposition of elements cut by NURBS

Abstract

Conference

Keywords

ASJC Scopus subject areas

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