This study presents a new coupled numerical approach that combines the Finite Element Method (FEM) and the Discrete Element Method (DEM) to solve contact mechanics problems [1]. This approach leverages the robustness of FEM to compute mechanical and thermal deformations, while benefiting from the recognized performance of DEM in handling contact of numerous rigid particles. Thus, DEM is employed to efficiently detect the first contact zone between domains and provide an initial estimation of contact forces. Based on these estimations, FEM is then utilized to compute the solution to the problem. The FEM solution strategy relies on a fixed-point formulation of a coupled force-displacement problem. The algorithm aims to update contact forces thanks to a penalty-like approach. This strategy enhances computational stability by avoiding poorly conditioned systems, arising in classical penalty method, while still relying on primal unknowns. The computational cost is minimized as only the right-hand side (RHS) of the system is updated during iterations, which allows us to preserve matrix factorization during the iterative process. Classical fixed-point (or Picard) iterations however diverge for this system. Hence, the convergence is ensured by using the Crossed Secant acceleration technique [2] on the contact forces, known for its robustness in oscillatory or divergent scenarios. Finally, if necessary, the contact zone is updated thanks to an active set algorithm. The efficiency and robustness of the proposed approach are demonstrated through several three-dimensional test cases, including the classical Hertzian contact benchmark and a complex industrial thermo-mechanical contact problem. Future developments will focus on evolving and testing the proposed method in a fully high-performance computing (HPC) framework, encompassing the entire workflow from contact detection to resolution (including the incorporation of friction). REFERENCES [1] P. Wriggers. Computational Contact Mechanics. Springer Berlin Heidelberg, (2006). [2] I. Ramière and T. Helfer. Iterative residual-based vector methods to accelerate fixed point iterations. Computers and Mathematics with Applications, 70(9):2210 – 2226, (2015).