Co-Design of Variational Formulations of Chemo-Mechanics and the Parallel FROSch Solver Framework

  • Röver, Friederike (TU Bergakademie Freiberg)
  • Kiefer, Bjoern (TU Bergakademie Freiberg)
  • Prüger, Stefan (TU Bergakademie Freiberg)
  • Rheinbach, Oliver (TU Bergakademie Freiberg)

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Chemo-mechanics problems have gained an increasing interest over the last decades since they allow insights in, e.g., man-made and natural materials as well as other engineering fields. In this talk, we consider a fully coupled deformation-diffusion boundary value problem, as outlined in [1]. Depending on the choice of the primary variables the variational formulation possesses a minimization or saddle point structure. We focus on the co-design of the theoretical model and the parallel solver. As a parallel solver, we consider the FROSch overlapping Schwarz framework [2] of the Trilinos software library [3]. FROSch contains a parallel implementation of the GDSW two-level overlapping Schwarz domain decomposition preconditioner with an energy- minimizing coarse space. The GDSW preconditioner allows a construction which solely depends on the stiffness matrix, thus no geometric information is required. Results for the boundary value problem outlined above are presented using the deal.II software library [4] for the FE implementation incorporating FROSch as a a linear solver; see also [5]. REFERENCES [1] Böger, L. and Nateghi, A. and Miehe, C. A Minimization Principle for Deformation- Diffusion Processes in Polymeric Hydrogels and FE Implementation. Int. J. Solids Struct.,121, pp. 257–274 (2017), DOI:10.1016/j.ijolstr.2017.05.034 [2] Heinlein, A. and Klawonn, A. and Rajamanickam, S. and Rheinbach, O. FROSch: A Fast And Robust Overlapping Schwarz Domain Decomposition Preconditioner Based on Xpe- tra in Trilinos. Domain Decomposition Methods in Science and Engineering XXV, pp. 176–184(2020). DOI: 10.1007/978-3-030-56750-7 19 [3] Trilinos Public GIT Repository (2022), [4] Arndt, D. e. al The Deal.II Library, Version 9.2, J. Num. Math, 28, pp.131–146 (2020), DOI:10.1515/jnma-2020-0043 [5] Kiefer, B. and Prüger, S. and Rheinbach, O. and Röver F. Monolithic parallel overlap- ping Schwarz methods in fully-coupled nonlinear chemo-mechanics problems, Comp. Mech. (2023),