A three-grid high-order immersed finite element method for the analysis of CAD models
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00586659" target="_blank" >RIV/67985840:_____/24:00586659 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.cad.2024.103730" target="_blank" >https://doi.org/10.1016/j.cad.2024.103730</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.cad.2024.103730" target="_blank" >10.1016/j.cad.2024.103730</a>
Alternative languages
Result language
angličtina
Original language name
A three-grid high-order immersed finite element method for the analysis of CAD models
Original language description
The automated finite element analysis of complex CAD models using boundary-fitted meshes is rife with difficulties. Immersed finite element methods are intrinsically more robust but usually less accurate. In this work, we introduce an efficient, robust, high-order immersed finite element method for complex CAD models. Our approach relies on three adaptive structured grids: a geometry grid for representing the implicit geometry, a finite element grid for discretising physical fields and a quadrature grid for evaluating the finite element integrals. The geometry grid is a sparse VDB (Volumetric Dynamic B+ tree) grid that is highly refined close to physical domain boundaries. The finite element grid consists of a forest of octree grids distributed over several processors, and the quadrature grid in each finite element cell is an octree grid constructed in a bottom-up fashion. The resolution of the quadrature grid ensures that finite element integrals are evaluated with sufficient accuracy and that any sub-grid geometric features, like small holes or corners, are resolved up to a desired resolution. The conceptual simplicity and modularity of our approach make it possible to reuse open-source libraries, i.e. openVDB and p4est for implementing the geometry and finite element grids, respectively, and BDDCML for iteratively solving the discrete systems of equations in parallel using domain decomposition. We demonstrate the efficiency and robustness of the proposed approach by solving the Poisson equation on domains described by complex CAD models and discretised with tens of millions of degrees of freedom. The solution field is discretised using linear and quadratic Lagrange basis functions.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA23-06159S" target="_blank" >GA23-06159S: Vortical structures: advanced identification and efficient numerical simulation</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Computer-Aided Design
ISSN
0010-4485
e-ISSN
1879-2685
Volume of the periodical
173
Issue of the periodical within the volume
August
Country of publishing house
GB - UNITED KINGDOM
Number of pages
17
Pages from-to
103730
UT code for WoS article
001248243600002
EID of the result in the Scopus database
2-s2.0-85194555724