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Nonlinear conjugate gradient method for identifying Young’s modulus of the elasticity imaging inverse problem. (English) Zbl 07480128

Summary: Application of elasticity imaging inverse problem to identify Young’s modulus in the elasticity problems in human’s life is an interesting research area. In this study, we identify the modulus of elasticity for solving elasticity imaging inverse problem using a modified output least-squares method. Numerical convergence in the displacements of the direct problem for elasticity is investigated. To study the elasticity imaging inverse problem in an optimization framework, we utilize the sensitivity and adjoint problems to conceptualize a new model for computing the gradient of the minimizer. Discrete formulae in the model are then used to devise a scheme for an efficient computation gradient of the modified output least-squares objective function using the nonlinear conjugate gradient method. Numerical experiments demonstrate the effectiveness of the proposed technique.

MSC:

65N20 Numerical methods for ill-posed problems for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs

Software:

OpenQSEI; Matlab
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