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The objective of this work is to solve within a standard finite element software, the direct-retrograde coupled time hyperbolic problems that arise when dealing with the identification of material parameters in dynamic in presence of corrupted measurements by means of the adjoint state approach. This question has given rise among others to Riccati methods and shooting methods. Those methods have several drawbacks, namely their numerical complexity and the fact that their implementation in a commercial software would require to entirely re-design the implementation, which is nearly impossible. Therefore we are seeking an iterative method which could be easily implemented. The proposed method solves alternatively a direct problem and a retrograde one. In order to ensure its convergence a relaxation scheme is applied and optimized. Comparisons between the proposed approach and Riccati and shooting methods in terms of complexity, numerical cost and robustness are given in the case of an elastic bar.

Towards a non intrusive method for solving coupled direct retrograde problem in transient dynamics