Abstract
Many inverse problems arising in experimental mechanics involve solutions to partial differential equations in the forward problem, typically using finite element methods for those solutions. Given that iterative solutions to the inverse problem then involve repeated evaluations of the finite element model, it is useful to carefully consider the mesh to be used and its effect on the trade-off between accuracy and computational cost of the solution. We show that approximation theory can be applied directly to the inverse problem, not merely to the finite element model contained in the forward problem, to give bounds for the error made by using a given mesh to approximate the solution to the partial differential equation. Adaptive mesh refinement allows to focus computational effort on goals set by the quantities of interest in the inverse problem, rather than on the overall accuracy of the solution to the forward problem.
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References
Hadamard, J. Sur les probl`emes aux d´eriv´ees partielles et leur significance physique. Princeton University Bulletin 13, 49–52 (1902).
Cooreman, S., Lecompte, D., Sol, H., Vantomme, J. & Debruyne, D. Identification of mechanical material behavior through inverse modeling and DIC. Experimental Mechanics 48, 421–433 (2008).
Gr´ediac, M., Pierron, F., Avril, S. & Toussaint, E. The virtual fields method for extracting constitutive parameters from full field measurements: A review. Strain 42, 233–253 (2006).
Roux, S. & Hild, F. Digital image mechanical identification (DIMI). Experimental Mechanics 48, 495–508 (2008).
Belkassem, B., Bossuyt, S. & Sol, H. Enhanced handshaking between DIC and FE computed deformation fields in an inverse method. In SEM 2009 Annual Conference & Exposition on Experimental & Applied Mechanics (2009).
Van Hemelrijck, D., Schillemans, L., Cardon, A. H. & Wong, A. The effects of motion on thermoelastic stress analysis. Composite Structures 18, 221 – 238 (1991).
Braess, D. Finite elements: Theory, fast solvers, and applications in elasticity theory (Cambridge University Press, Cambridge, 2007).
Johnson, C. Numerical solution of partial differential equations by the finite element method (Dover Publications Inc., Mineola, NY, 2009). Reprint of the 1987 edition.
Kaipio, J. & Somersalo, E. Statistical and computational inverse problems, vol. 160 of Applied Mathematical Sciences (Springer-Verlag, New York, 2005).
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Huhtala, A.H., Bossuyt, S. (2011). Mesh Refinement for Inverse Problems with Finite Element Models. In: Proulx, T. (eds) Optical Measurements, Modeling, and Metrology, Volume 5. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0228-2_17
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DOI: https://doi.org/10.1007/978-1-4614-0228-2_17
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