Robust and scalable h-adaptive aggregated unfitted finite elements for interface elliptic problems
This work introduces a novel, fully robust and highly-scalable, -adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method is based on a recent distributed-memory implementation of the aggregated finite element method atop a highly-scalable Cartes...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/450197 |
| Acceso en línea: | https://hdl.handle.net/2117/450197 https://dx.doi.org/10.1016/j.cma.2021.113769 |
| Access Level: | acceso abierto |
| Palabra clave: | Unfitted finite elements Interface linear elasticity Interface poisson Adaptive mesh refinement High performance scientific computing Àrees temàtiques de la UPC::Enginyeria mecànica::Mecànica de fluids |
| Sumario: | This work introduces a novel, fully robust and highly-scalable, -adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method is based on a recent distributed-memory implementation of the aggregated finite element method atop a highly-scalable Cartesian forest-of-trees mesh engine. It follows the classical approach of weakly coupling nonmatching discretisations at the interface to model internal discontinuities at the interface. We propose a natural extension of a single-domain parallel cell aggregation scheme to problems with a finite number of interfaces; it straightforwardly leads to aggregated finite element spaces that have the structure of a Cartesian product. We demonstrate, through standard numerical analysis and exhaustive numerical experimentation on several complex Poisson and linear elasticity benchmarks, that the new technique enjoys the following properties: well-posedness, robustness with respect to cut location and material contrast, optimal (h-adaptive) approximation properties, high scalability and easy implementation in large-scale finite element codes. As a result, the method offers great potential as a useful finite element solver for large-scale interface problems modelled by partial differential equations. |
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