Abstract
AbstractIn this work we focus on the development of a numerical algorithm for the inverse elastography problem. The goal is to perform an efficient material parameter identification knowing the elastic displacement field induced by a mechanical load. We propose to define the inverse problem through a quadratic optimization program which uses the direct problem formulation to define the objective function. In this way, we end up with a convex minimization problem which attains its minimum at the solution of a linear system. The effectiveness of our method is illustrated through numeral examples.
Funder
Centro de Matemática, Universidade de Coimbra
FCT
Publisher
Springer Science and Business Media LLC
Reference15 articles.
1. Ainsworth M, Parker C. Unlocking the secrets of locking: Finite element analysis in planar linear elasticity. Comput Methods Appl Mech Eng. 2022;395.
2. Proceedings of the 22nd ECMI conference on industrial and applied mathematics;S Barbeiro,2023
3. Proceedings of the 9th conference on Trefftz methods and 5th conference on method of fundamental solutions;S Barbeiro,2020
4. Batista A, Serranho P, Santos M, Correia C, Domingues JP, Loureiro C, Cardoso J, Barbeiro S, Morgado M, Bernardes R. Phase-resolved optical coherence elastography: an insight into tissue displacement estimation. Sensors. 2023;23(8):3974.
5. Brenner SC, Scott LR. The mathematical theory of finite element methods. Berlin: Springer; 1997.