Discontinuous Skeletal methods approximate the solution of boundary-value problems by attaching discrete unknowns to mesh faces (hence the term skeletal) while allowing these discrete unknowns to be chosen independently on each mesh face (hence the term discontinuous). Cell-based unknowns, which can be eliminated locally by a Schur complement technique (also known as static condensation), are also used in the formulation. Salient examples of high-order Discontinuous Skeletal methods are Hybridizable Discontinuous Galerkin methods and the recently-devised Hybrid High-Order methods. Some major benefits of Discontinuous Skeletal methods are that their construction is dimension-independent and that they offer the possibility to use general meshes with polytopal cells and non-matching interfaces. In this work, we show how this mathematical flexibility can be efficiently replicated in a numerical software using generic programming. We describe a number of generic algorithms and data structures for high-order Discontinuous Skeletal methods within a “write once, run on any kind of mesh” framework. The computational efficiency of the implementation is assessed on the Poisson model problem discretized using various polytopal meshes and the Hybrid High-Order method.
Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming / Cicuttin, M.; Di Pietro, D. A.; Ern, A.. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 0377-0427. - ELETTRONICO. - 344:(2018), pp. 852-874. [10.1016/j.cam.2017.09.017]
Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming
Cicuttin M.;
2018
Abstract
Discontinuous Skeletal methods approximate the solution of boundary-value problems by attaching discrete unknowns to mesh faces (hence the term skeletal) while allowing these discrete unknowns to be chosen independently on each mesh face (hence the term discontinuous). Cell-based unknowns, which can be eliminated locally by a Schur complement technique (also known as static condensation), are also used in the formulation. Salient examples of high-order Discontinuous Skeletal methods are Hybridizable Discontinuous Galerkin methods and the recently-devised Hybrid High-Order methods. Some major benefits of Discontinuous Skeletal methods are that their construction is dimension-independent and that they offer the possibility to use general meshes with polytopal cells and non-matching interfaces. In this work, we show how this mathematical flexibility can be efficiently replicated in a numerical software using generic programming. We describe a number of generic algorithms and data structures for high-order Discontinuous Skeletal methods within a “write once, run on any kind of mesh” framework. The computational efficiency of the implementation is assessed on the Poisson model problem discretized using various polytopal meshes and the Hybrid High-Order method.File | Dimensione | Formato | |
---|---|---|---|
main.pdf
accesso riservato
Tipologia:
2a Post-print versione editoriale / Version of Record
Licenza:
Non Pubblico - Accesso privato/ristretto
Dimensione
1.31 MB
Formato
Adobe PDF
|
1.31 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11583/2978974