A HDG Method for Elliptic Problems with Integral Boundary Condition: Theory and Applications

被引：1

作者：

Bertoluzza, Silvia ^{[1
]}

Guidoboni, Giovanna ^{[2
]}

Hild, Romain ^{[3
]}

Prada, Daniele ^{[1
]}

Prud'homme, Christophe ^{[3
]}

Sacco, Riccardo ^{[4
]}

Sala, Lorenzo ^{[5
]}

Szopos, Marcela ^{[6
]}

机构：

[1] CNR, IMATI, Pavia, Italy

[2] Univ Maine, Dept Elect & Comp Engn, Orono, ME 04469 USA

[3] Univ Strasbourg, Cemosis, IRMA UMR 7501, CNRS, 7 Rue Rene Descartes, F-67084 Strasbourg, France

[4] Politecn Milan, Dipartimento Matemat, Piazza Leonardo Vinci 32, I-20133 Milan, Italy

[5] Univ Paris Saclay, INRAE, MaIAGE, F-78350 Jouy En Josas, France

[6] Univ Paris Cite, CNRS, MAP5, F-75006 Paris, France

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2023年 / 95卷 / 01期

关键词：

Integral boundary conditions; Hybridizable Discontinuous Galerkin; 3D-0D coupling; nMOS transistor; High field magnets; Ophthalmology; DISCONTINUOUS GALERKIN; HEAT-TRANSFER; HYBRIDIZATION;

D O I：

10.1007/s10915-023-02109-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we address the study of elliptic boundary value problems in presence of a boundary condition of integral type (IBC) where the potential is an unknown constant and the flux (the integral of the flux density) over a portion of the boundary is given by a value or a coupling condition. We first motivate our work with realistic examples from nano-electronics, high field magnets and ophthalmology. We then define a general framework stemming from the Hybridizable Discontinuous Galerkin method that accounts naturally for the IBC and we provide a complete analysis at continuous and discrete levels. The implementation in the Feel++framework is then detailed and the convergence and scalability properties are verified. Finally, numerical experiments performed on the real-life motivating applications are used to illustrate our methodology.

引用

页数：33

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Riccardo Sacco
Lorenzo Sala
Marcela Szopos
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