Abstract
Parameter-dependent discretizations of linear fluid-structure interaction problems can be approached with low-rank methods. When discretizing with respect to a set of parameters, the resulting equations can be translated to a matrix equation since all operators involved are linear. If nonlinear fluid-structure interaction problems are considered, a direct translation to a matrix equation is not possible. We present a method that splits the parameter set into disjoint subsets and, on each subset, computes an approximation of the problem related to the upper median parameter by means of the Newton iteration. This approximation is then used as initial guess for one Newton step on a subset of problems.
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Acknowledgements
This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—314838170, GRK 2297 MathCoRe.
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Benner, P., Richter, T., Weinhandl, R. (2021). A Low-Rank Approach for Nonlinear Parameter-Dependent Fluid-Structure Interaction Problems. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_115
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DOI: https://doi.org/10.1007/978-3-030-55874-1_115
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