A Newton multigrid framework for optimal control of fluid–structure interactions
L. Failer, T. Richter
Abstract
Abstract In this paper we consider optimal control of nonlinear time-dependent fluid structure interactions. To determine a time-dependent control variable a BFGS algorithm is used, whereby gradient information is computed via a dual problem. To solve the resulting ill conditioned linear problems occurring in every time step of state and dual equation, we develop a highly efficient monolithic solver that is based on an approximated Newton scheme for the primal equation and a preconditioned Richardson iteration for the dual problem. The performance of the presented algorithms is tested for one 2d and one 3d example numerically.
Topics & Concepts
SolverOptimal controlBroyden–Fletcher–Goldfarb–Shanno algorithmDual (grammatical number)Mathematical optimizationNonlinear systemQuasi-Newton methodNewton's methodMathematicsMultigrid methodApplied mathematicsComputer scienceScheme (mathematics)Iterative methodVariable (mathematics)Linear systemGradient methodState (computer science)Numerical analysisState variableHessian matrixControl variableAlgorithmSingular controlControl theory (sociology)Advanced Numerical Methods in Computational MathematicsComputational Fluid Dynamics and AerodynamicsModel Reduction and Neural Networks