Details
| Translated title of the contribution | Adaptive Verfeinerung für unstrukturierte T-Splines mit linearer Komplexität |
|---|---|
| Original language | English |
| Article number | 102117 |
| Journal | CAD Computer Aided Design |
| Volume | 96 |
| Early online date | 3 Jun 2022 |
| Publication status | Published - Jun 2022 |
Abstract
Keywords
- Adaptive refinement, T-splines, Unstructured meshes
ASJC Scopus subject areas
- Engineering(all)
- Aerospace Engineering
- Engineering(all)
- Automotive Engineering
- Mathematics(all)
- Modelling and Simulation
- Computer Science(all)
- Computer Graphics and Computer-Aided Design
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In: CAD Computer Aided Design, Vol. 96, 102117, 06.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Adaptive Refinement for Unstructured T-Splines with Linear Complexity
AU - Maier, Roland
AU - Morgenstern, Philipp
AU - Takacs, Thomas
N1 - Funding information: Roland Maier acknowledges support by the German Research Foundation (DFG) in the Priority Program 1748 Reliable simulation techniques in solid mechanics ( PE2143/2-2 ) and by the Göran Gustafsson Foundation for Research in Natural Sciences and Medicine . The research of Thomas Takacs is partially supported by the Austrian Science Fund (FWF) together with the government of Upper Austria through the project P30926-NBL entitled “Weak and approximate -smoothness in isogeometric analysis”.
PY - 2022/6
Y1 - 2022/6
N2 - We present an adaptive refinement algorithm for T-splines on unstructured 2D meshes. While for structured 2D meshes, one can refine elements alternatingly in horizontal and vertical direction, such an approach cannot be generalized directly to unstructured meshes, where no two unique global mesh directions can be assigned. To resolve this issue, we introduce the concept of direction indices, i.e., integers associated to each edge, which are inspired by theory on higher-dimensional structured T-splines. Together with refinement levels of edges, these indices essentially drive the refinement scheme. We combine these ideas with an edge subdivision routine that allows for I-nodes, yielding a very flexible refinement scheme that nicely distributes the T-nodes, preserving global linear independence, analysis-suitability (local linear independence) except in the vicinity of extraordinary nodes, sparsity of the system matrix, and shape regularity of the mesh elements. Further, we show that the refinement procedure has linear complexity in the sense of guaranteed upper bounds on a) the distance between marked and additionally refined elements, and on b) the ratio of the numbers of generated and marked mesh elements.
AB - We present an adaptive refinement algorithm for T-splines on unstructured 2D meshes. While for structured 2D meshes, one can refine elements alternatingly in horizontal and vertical direction, such an approach cannot be generalized directly to unstructured meshes, where no two unique global mesh directions can be assigned. To resolve this issue, we introduce the concept of direction indices, i.e., integers associated to each edge, which are inspired by theory on higher-dimensional structured T-splines. Together with refinement levels of edges, these indices essentially drive the refinement scheme. We combine these ideas with an edge subdivision routine that allows for I-nodes, yielding a very flexible refinement scheme that nicely distributes the T-nodes, preserving global linear independence, analysis-suitability (local linear independence) except in the vicinity of extraordinary nodes, sparsity of the system matrix, and shape regularity of the mesh elements. Further, we show that the refinement procedure has linear complexity in the sense of guaranteed upper bounds on a) the distance between marked and additionally refined elements, and on b) the ratio of the numbers of generated and marked mesh elements.
KW - Adaptive refinement
KW - T-splines
KW - Unstructured meshes
UR - http://www.scopus.com/inward/record.url?scp=85131459469&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2109.00448
DO - 10.48550/arXiv.2109.00448
M3 - Article
VL - 96
JO - CAD Computer Aided Design
JF - CAD Computer Aided Design
SN - 0010-4485
M1 - 102117
ER -