The LaTIn-based Mixed Domain Decomposition Method for Structural Mechanics
Résumé
The need for predictive models often leads to fine scale modeling in order to describe complex degradation mechanisms, interactions and couplings between scales and physics. Parametric or stochastic analysis is also a challenging issue in computational mechanics. Addressing such large scale nonlinear problems makes of alternative computational strategies such as parallel computing, domain decomposition methods (DDM) or reduced order modeling (ROM) appealing approaches.
In this talk, a nonoverlapping mixed domain decomposition methods based on the LaTIn (Large Time Increment) method is presented. Contrary to classical incremental solution methods, the LaTIn method gives at each iteration an approximation of the solution over the entire time/parameter-space domain which provides a suitable framework for ROM time/parameter-space representation.
Firstly, the basics of the LaTIn method are described : i) separation of equations (global but linear vs nonlinear but local), ii) a two-search directions iterative solver, and iii) a « suitable » representation of the unknowns (ROM). Model reduction by PGD (Proper Generalized Decomposition) is here used to represent the solution as a sum of products between time/parameter functions and space functions that are built on the fly throughout the computation.
Secondly, the LaTIn method is applied to domain decomposition leading to an iterative scheme that shares similar features with an augmented lagrangian formulation combined with an Uzawa-like algorithm. The resulting mixed DDM is particularly efficient and robust to deal with frictional contact interfaces. The introduction of a coarse problem (reduced interface problem) to endow the DDM with the scalability property is also discussed.