An adaptive mesh refinement scheme for hierarchical hybrid grids
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F25%3A10260666" target="_blank" >RIV/61989100:27240/25:10260666 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.21136/AM.2025.0186-25" target="_blank" >https://link.springer.com/article/10.21136/AM.2025.0186-25</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/AM.2025.0186-25" target="_blank" >10.21136/AM.2025.0186-25</a>
Alternative languages
Result language
angličtina
Original language name
An adaptive mesh refinement scheme for hierarchical hybrid grids
Original language description
This work introduces an adaptive mesh refinement technique for hierarchical hybrid grids with the goal to reach scalability and maintain excellent performance on massively parallel computer systems. On the block-structured hierarchical hybrid grids, this is accomplished by using classical, unstructured refinement only on the coarsest level of the hierarchy, while keeping the number of structured refinement levels constant over the whole domain. This leads to a compromise, where the excellent performance characteristics of hierarchical hybrid grids can be maintained at the price that the flexibility of generating locally refined meshes is constrained. Furthermore, the mesh adaptivity often relies on a posteriori error estimators or error indicators, which tend to become computationally expensive. Again, with the goal of preserving scalability and performance, a method is proposed that leverages the grid hierarchy and the full multigrid scheme. Utilizing the sequence of approximations on the nested hierarchy of grids permits the computation of a cheap error estimator that is well-suited for large-scale parallel computing. We present the theoretical foundations for both global and local error estimates, and present a rigorous analysis of their effectivity. The proposed method, including the error estimator and the adaptive coarse grid refinement, is implemented in the finite element framework HyTeG. Extensive numerical experiments are conducted to validate the effectiveness, as well as performance and scalability.
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
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Continuities
O - Projekt operacniho programu
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applications of Mathematics
ISSN
0862-7940
e-ISSN
1572-9109
Volume of the periodical
70
Issue of the periodical within the volume
6
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
31
Pages from-to
875-905
UT code for WoS article
001638940400010
EID of the result in the Scopus database
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