The Steklov-Poincaré technique for data completion: preconditioning and filtering

Renaud Ferrier (1) , Mohamed Larbi Kadri (2) , Pierre Gosselet (1)

1 LMT - Laboratoire de Mécanique et Technologie
2 LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]

This article presents a study of primal and dual Steklov-Poincaré approaches for the identification of unknown boundary conditions of elliptic problems. After giving elementary properties of the discretized operators, we investigate the numerical solution with Krylov solvers. Different preconditioning and acceleration strategies are evaluated. We show that costless filtering of the solution is possible by post-processing Ritz elements. Assessments are provided on a 3D mechanical problem.

Mots clés: boundary data completion; inverse problem; KMF and Steklov-Poincaré algorithms

Domaines: Mécanique des structures [physics.class-ph]

Renaud Ferrier, Mohamed Larbi Kadri, Pierre Gosselet. The Steklov-Poincaré technique for data completion: preconditioning and filtering. International Journal for Numerical Methods in Engineering, 2018, 116 (4), pp.270-286. ⟨10.1002/nme.5924⟩. ⟨hal-01632526⟩