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Shear Decoupled Parallel Scalable Preconditioners for Nonlinear Thermo-Mechanical Coupled Contact Applications

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Abstract

It is necessary to solve the thermo-mechanical coupled contact problem in structural mechanical analysis, such as the dam structural analysis. Because of the complexity of coupled models, it is very difficult to solve the discretized system in structural mechanical analysis. At the same time, for real applications such as the dam structural analysis, the simulation domain has complex structures, which result in a number of mesh elements more than \(10^8\) for high resolution simulations. Therefore, the scale of the discretized system is very large. In this paper, the discretized themo-mechanical coupling contact system on hundreds million unstructured meshes is parallel solved by the Newton–Krylov method, in which the efficiency of the Krylov methods is strongly dependent on the preconditioning. An efficient preconditioning method is constructed for the themo-mechanical coupling contact problem. Three steps are used to construct the preconditioner. Firstly, for the mechanical problem, the mechanical effect is analyzed for the dam structural analysis, and a preconditioner is constructed for the elasticity problem by omitting the shearing effect. As the dominant material in a dam structural analysis is rock-soil, and rock-soil exhibits anti-shearing property, it is reasonable to omit the shearing effect for constructing the preconditioner. Furthermore, a preconditioner is constructed for the thermo-mechanical model by omitting the coupling between the thermal and mechanical effectiveness in the model. The preconditioner has a block diagonal structure, with each block being a diffusion operator. It is suitable for large scale parallel computing since each block can be solved independently. Furthermore, since each block is a diffusion operator, a multi-grid method can be employed to effectively solve each block equation. Finally, based on the preconditioning of the thermo-mechanical model, a preconditioner is constructed for the thermo-mechanical coupling contact problem by combining the dual motar method for contact problems. Numerical results show that the preconditioning method is very effective, and the convergence rate of the Krylov method can be improved dramatically when it is used to solve the themo-mechanical coupling contact problem.

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Acknowledgements

The authors gratefully acknowledge professors Rong Tian, Mozhen Zhou, and Shaoliang Hu for their help with the manuscript. Drs. Xiaoyu Duan and Biyi Wang helped to implement several numerical tests. The authors also gratefully acknowledge the referee and Chi-Wang Shu for many valuable suggestions and comments, which were very helpful for improving the original paper.

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Authors and Affiliations

  1. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, 100094, China

    Hengbin An, Zeyao Mo & Xiaowen Xu

  2. CAEP Software Center for High Performance Numerical Simulation, Beijing, 100088, China

    Hengbin An, Zeyao Mo, Jingtao Wang, Ran Xu, Longfei Wen & Xiaowen Xu

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  1. Hengbin An
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Correspondence to Zeyao Mo.

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This work was funded by National Key R&D Program of China (Nos. 2017YFA0603903, 2016YFB0201002), National Natural Science Foundation of China (No. 12171045), and Science Challenge Project (No. TZ2016002).

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An, H., Mo, Z., Wang, J. et al. Shear Decoupled Parallel Scalable Preconditioners for Nonlinear Thermo-Mechanical Coupled Contact Applications. J Sci Comput 90, 4 (2022). https://doi.org/10.1007/s10915-021-01643-4

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  • DOI: https://doi.org/10.1007/s10915-021-01643-4

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