20180129
QuasiNewton methods are used in many fields to solve nonlinear equations without explicitly known derivatives. This is the case, e.g., in coupled multiphysics applications such as fluidstructure interactions where we combine several independent solvers in a partitioned approach coupled simulation environment. To do so, we have to solve a (in general nonlinear) interface equation that contains operator contributions from all involved singlephysics solvers. If we assume that these solvers are blackbox, quasiNewton methods are the best known method to accelerate pure interface fixed point iterations. In PDEconstrained optimization, i.e., inverse solvers that are based on gradient descent, we have to find the root of the (reduced) gradient of the objective function. Though the Hessian can usually be calculated and used in an inner Krylov method, these calculations are typically costly as they involve the solution of forward and adjoint problems. Thus, quasiNewton methods are an efficient alternative. In both cases, coupled problems and optimization, an additional advantage of quasiNewton over Newton methods is the fact that we can directly approximate the inverse Jacobian or Hessian such that no inner linear solver is required. We present a comparison of known quasiNewton methods for multiphysics such as interface quasiNewton with methods usually used in optimization, in particular the BFGS method that is, e.g., used in PETCs’s TAO package. Results for two applications – fluidstructure interaction and inverse tumor simulation – demonstrate their potential in terms of robustness, generality, and efficiency.
Category: CE SeminarTechnische Universität Darmstadt
Graduate School CE
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D64293 Darmstadt

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