2023
DOI: 10.1007/s00466-022-02254-y
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Monolithic parallel overlapping Schwarz methods in fully-coupled nonlinear chemo-mechanics problems

Abstract: We consider the swelling of hydrogels as an example of a chemo-mechanical problem with strong coupling between the mechanical balance relations and the mass diffusion. The problem is cast into a minimization formulation using a time-explicit approach for the dependency of the dissipation potential on the deformation and the swelling volume fraction to obtain symmetric matrices, which are typically better suited for iterative solvers. The MPI-parallel implementation uses the software libraries deal.II, p4est an… Show more

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Cited by 3 publications
(7 citation statements)
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“…In this paper, we use the implementation and setup from [17]. For the the finite element implementation of our model problem, we employed the deal.II software library [4] version 9.2.0.…”
Section: Methodsmentioning
confidence: 99%
See 4 more Smart Citations
“…In this paper, we use the implementation and setup from [17]. For the the finite element implementation of our model problem, we employed the deal.II software library [4] version 9.2.0.…”
Section: Methodsmentioning
confidence: 99%
“…Note that the employed variational principle ensures that the linearization of the necessary optimality condition yields a symmetric system of equations. For more details, the interested reader is referred to [17,5].…”
Section: Coupled Mechanics-diffusion Problemsmentioning
confidence: 99%
See 3 more Smart Citations