Optimization of Systems modeled by PDEs

On Theoretical and Numerical Aspects of the Shape Sensitivity Analysis for the 3D Time-dependent Maxwell’s Equations

  • Stephan Schmidt
  • Maria Schütte
  • Andrea Walther
    • Categories Optimization of Systems modeled by PDEs Tags , , , , ,

    We propose a novel approach using shape derivatives to solve inverse optimization problems governed by Maxwell’s equations, focusing on identifying hidden geometric objects in a predefined domain. The target functional is of tracking type and determines the distance between the solution of a 3D time-dependent Maxwell problem and given measured data in an $L_2$-norm. Minimization … Read more

    Thermal Optimization of the Continuous Casting Process using Distributed Parameter Identification Approach — Controlling the Curvature of Solid-Liquid Interface

  • Rouhollah Tavakoli
    • Categories Applications - Science and Engineering, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs

    Thermal optimization of vertical continuous casting process is considered in the present study. The goal is to find the optimal distribution of temperature and interfacial heat transfer coefficients corresponding to the primary and secondary cooling systems, in addition to the pulling speed, such that the solidification along the main axis of strand approaches to the … Read more

    Unconditionally energy stable time stepping scheme for Cahn-Morral equation: application to multi-component spinodal decomposition and optimal space tiling

  • Rouhollah Tavakoli
    • Categories Applications - Science and Engineering, Basic Sciences Applications, Optimization of Systems modeled by PDEs Tags , , , , , ,

    An unconditionally energy stable time stepping scheme is introduced to solve Cahn-Morral-like equations in the present study. It is constructed based on the combination of David Eyre’s time stepping scheme and Schur complement approach. Although the presented method is general and independent to the choice of homogeneous free energy density function term, logarithmic and polynomial … Read more

    A Flexible Iterative Solver for Nonconvex, Equality-Constrained Quadratic Subproblems

  • Alp Dener
  • Jason Hicken
    • Categories Constrained Nonlinear Optimization, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs Tags , , , , ,

    We present an iterative primal-dual solver for nonconvex equality-constrained quadratic optimization subproblems. The solver constructs the primal and dual trial steps from the subspace generated by the generalized Arnoldi procedure used in flexible GMRES (FGMRES). This permits the use of a wide range of preconditioners for the primal-dual system. In contrast with FGMRES, the proposed … Read more

    An Inertia-Free Filter Line-Search Algorithm for Large-Scale Nonlinear Programming

  • Naiyuan Chiang
  • Victor M. Zavala
    • Categories Nonlinear Optimization, Optimization of Systems modeled by PDEs, Stochastic Programming Tags , , , ,

    We present a filter line-search algorithm that does not require inertia information about the linear system to ensure global convergence. The proposed approach performs curvature tests along the search step to ensure descent. This feature permits more modularity in the linear algebra, enabling the use of a wider range of iterative and decomposition strategies. We … Read more

    Topology Optimization for Magnetic Circuits dedicated to Electric Propulsion

  • Carole Henaux
  • Frédéric Messine
  • Satafa Sanogo
  • Raphael Vilamot
    • Categories Applications - Science and Engineering, Optimization of Systems modeled by PDEs Tags , , , , , ,

    Abstract—In this paper, we present a method to solve inverse problems of electromagnetic circuit design which are formulated as a topology optimization problem. Indeed, by imposing the magnetic field inside a region, we search a best material distribution into variable domains. In order to perform this, we minimize the quadratic error between the prescribed magnetic … Read more

    Optimal control of leukemic cell population dynamics

  • Xavier Dupuis
    • Categories Biomedical Applications, Optimization of Systems modeled by PDEs

    We are interested in optimizing the co-administration of two drugs for some acute myeloid leukemias (AML), and we are looking for in vitro protocols as a first step. This issue can be formulated as an optimal control problem. The dynamics of leukemic cell populations in culture is given by age-structured partial differential equations, which can … Read more

    Fabrication-Adaptive Optimization, with an Application to Photonic Crystal Design

  • Robert M. Freund
  • Han Men
  • Ngoc-Cuong Nguyen
  • Jaime Peraire
  • Joel Saa-Seoane
    • Categories Basic Sciences Applications, Optimization of Systems modeled by PDEs, Robust Optimization Tags , , ,

    It is often the case that the computed optimal solution of an optimization problem cannot be implemented directly, irrespective of data accuracy, due to either (i) technological limitations (such as physical tolerances of machines or processes), (ii) the deliberate simplification of a model to keep it tractable (by ignoring certain types of constraints that pose … Read more

    Adaptive Observations And Multilevel Optimization In Data Assimilation

  • Serge Gratton
  • Monserrat Rincon-Camacho
  • Philippe L. Toint
    • Categories Nonlinear Systems and Least-Squares, Optimization of Systems modeled by PDEs Tags , ,

    We propose to use a decomposition of large-scale incremental four dimensional (4D-Var) data assimilation problems in order to make their numerical solution more efficient. This decomposition is based on exploiting an adaptive hierarchy of the observations. Starting with a low-cardinality set and the solution of its corresponding optimization problem, observations are adaptively added based on … Read more

    Conjugate-gradients versus multigrid solvers for diffusion-based correlation models in data assimilation

  • Serge Gratton
  • Philippe L. Toint
  • Jean Tshimanga Ilunga
    • Categories Nonlinear Systems and Least-Squares, Optimization of Systems modeled by PDEs

    This paper provides a theoretical and experimental comparison between conjugate-gradients and multigrid, two iterative schemes for solving linear systems, in the context of applying diffusion-based correlation models in data assimilation. In this context, a large number of such systems has to be (approximately) solved if the implicit mode is chosen for integrating the involved diffusion … Read more