Approximation of constrained problems using the PGD method with application to pure Neumann problems

Kenan Kergrene (1) , Serge Prudhomme (1) , Ludovic Chamoin (2) , Laforest Marc (1)

1 Département de mathématiques et de génie industriel
2 LMT - Laboratoire de Mécanique et Technologie

In this paper we introduce, analyze, and compare several approaches designed to incorporate a linear (or affine) constraint within the Proper Generalized Decomposition framework. We apply the considered methods and numerical strategies to two classes of problems: the pure Neumann case where the role of the constraint is to recover unicity of the solution; and the Robin case, where the constraint forces the solution to move away from the already existing unique global minimizer of the energy functional.

Mots clés: Model reduction; Low-rank approximation; Tensor product approximation; Proper Generalized Decomposition; Constrained problem; Mixed formulation

Domaines: Sciences de l'ingénieur [physics]

Kenan Kergrene, Serge Prudhomme, Ludovic Chamoin, Laforest Marc. Approximation of constrained problems using the PGD method with application to pure Neumann problems. Computer Methods in Applied Mechanics and Engineering, 2017, 317, pp.507-525. ⟨10.1016/j.cma.2016.12.023⟩. ⟨hal-01579975⟩