
A Lowrank Approach for Nonlinear Parameterdependent Fluidstructure Interaction Problems
Parameterdependent discretizations of linear fluidstructure interactio...
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Error analysis of an asymptotic preserving dynamical lowrank integrator for the multiscale radiative transfer equation
Dynamical lowrank algorithm are a class of numerical methods that compu...
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Solving differential Riccati equations: A nonlinear spacetime method using tensor trains
Differential algebraic Riccati equations are at the heart of many applic...
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A parameterdependent smoother for the multigrid method
The solution of parameterdependent linear systems, by classical methods...
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Extended GaussNewton and GaussNewtonADMM Algorithms for LowRank Matrix Optimization
We develop a generic GaussNewton (GN) framework for solving a class of ...
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A lowrank matrix equation method for solving PDEconstrained optimization problems
PDEconstrained optimization problems arise in a broad number of applica...
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A MultiVector Interface QuasiNewton Method with Linear Complexity for Partitioned FluidStructure Interaction
In recent years, interface quasiNewton methods have gained growing atte...
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A Lowrank Method for Parameterdependent Fluidstructure Interaction Discretizations With Hyperelasticity
In aerospace engineering and boat building, fluidstructure interaction models are considered to investigate prototypes before they are physically assembled. How a material interacts with different fluids at different Reynold numbers has to be studied before it is passed over to the manufacturing process. In addition, examining the same model not only for different fluids but also for different solids allows to optimize the choice of materials for construction even better. A possible answer on this demand is parameterdependent discretization. Furthermore, lowrank techniques can reduce the complexity needed to compute approximations to parameterdependent fluidstructure interaction discretizations. Lowrank methods have been applied to parameterdependent linear fluidstructure interaction discretizations. The linearity of the operators involved allows to translate the resulting equations to a single matrix equation. The solution is approximated by a lowrank method. In this paper, we propose a new method that extends this framework to nonlinear parameterdependent fluidstructure interaction problems by means of the Newton iteration. The parameter set is split into disjoint subsets. On each subset, the Newton approximation of the problem related to the upper median parameter is computed and serves as initial guess for one Newton step on the whole subset. This Newton step yields a matrix equation whose solution can be approximated by a lowrank method. The resulting method requires a smaller number of Newton steps if compared with a direct approach that applies the Newton iteration to the separate problems consecutively. In the experiments considered, the proposed method allowed to compute a lowrank approximation within a twentieth of the time used by the direct approach.
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