A numerical assessment of partitioned implicit methods for thermomechanical problems

Abstract

Implicit partitioned methods for solving thermomechanical problems possess various advantages over monolithic schemes, such as flexibility and simplicity of implementation, at the cost of performance and robustness. This contribution’s primary purpose is to explore suitable partitioned implicit techniques for solving the thermomechanical problem with different sources of coupling. The spatial and time-discrete problem is reformulated as an equivalent root-finding problem using single-field solvers. This work considers the fixed-point method, Aitken relaxation, multisecant quasi-Newton methods, Newton–Krylov method, and polynomial vector extrapolation techniques in cycling mode, which are selected from the relevant literature. These techniques are employed to solve three different problems, including thermoelastic and thermoplastic constitutive behaviors, as well as thermomechanical contact. The methods are compared based on the CPU runtime and the number of residual evaluations, considering as well the memory requirements and the implementation effort. Overall, Broyden’s method can be regarded as the best performing and most advantageous method, with the Aitken relaxation also providing a very efficient and simple alternative. This work brings new insights into the application of partitioned implicit methods to thermomechanical problems and can motivate the selection of these techniques, which are not currently widespread in the community.