Biharmonic problem has been raised in many research fields, such as elasticity problem in plate geometries or the Stokes flow problem formulated by using the stream function. The fourth order partial differential equation can be solved by applying many techniques. When using finite elements C1 continuity must be assured. For this purpose Hermite interpolations constitute an appealing choice, but it imply the consideration of many degrees of freedom at each node with the consequent impact on the resulting discrete linear problem. Spectral approaches allow exponential convergence whilst a single degree of freedom is needed. However, the enforcement of boundary conditions remains a tricky task. In this paper we propose a separated representation of the stream function which transform the 2D solution in a sequence of 1D problems, each one be solved by using a spectral approximation.
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ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis
July 2–4, 2012
Nantes, France
Conference Sponsors:
- International
ISBN:
978-0-7918-4484-7
PROCEEDINGS PAPER
PGD for Solving the Biharmonic Equation
GuangTao Xu
,
GuangTao Xu
Ecole Centrale de Nantes, Nantes, France
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Francisco Chinesta
,
Francisco Chinesta
Ecole Centrale de Nantes, Nantes, France
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Adrien Leygue
,
Adrien Leygue
Ecole Centrale de Nantes, Nantes, France
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Michel Visonneau
Michel Visonneau
Ecole Centrale de Nantes, Nantes, France
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GuangTao Xu
Ecole Centrale de Nantes, Nantes, France
Francisco Chinesta
Ecole Centrale de Nantes, Nantes, France
Adrien Leygue
Ecole Centrale de Nantes, Nantes, France
Michel Visonneau
Ecole Centrale de Nantes, Nantes, France
Paper No:
ESDA2012-82484, pp. 219-223; 5 pages
Published Online:
August 12, 2013
Citation
Xu, G, Chinesta, F, Leygue, A, & Visonneau, M. "PGD for Solving the Biharmonic Equation." Proceedings of the ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. Volume 1: Advanced Computational Mechanics; Advanced Simulation-Based Engineering Sciences; Virtual and Augmented Reality; Applied Solid Mechanics and Material Processing; Dynamical Systems and Control. Nantes, France. July 2–4, 2012. pp. 219-223. ASME. https://doi.org/10.1115/ESDA2012-82484
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