helmholtz equation

KKT Preconditioners for PDE-Constrained Optimization with the Helmholtz Equation

  • Drew P. Kouri
  • Denis Ridzal
  • Ray Tuminaro
    • Categories Control Applications, Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    This paper considers preconditioners for the linear systems that arise from optimal control and inverse problems involving the Helmholtz equation. Specifically, we explore an all-at-once approach. The main contribution centers on the analysis of two block preconditioners. Variations of these preconditioners have been proposed and analyzed in prior works for optimal control problems where the … Read more

    A Mixed-Integer PDE-Constrained Optimization Formulation for Electromagnetic Cloaking

  • Sven Leyffer
  • Todd S. Munson
  • Ryan Vogt
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Optimization of Systems modeled by PDEs Tags , , ,

    We formulate a mixed-integer partial-differential equation constrained optimization problem for designing an electromagnetic cloak governed by the 2D Helmholtz equation with absorbing boundary conditions. Our formulation is an alternative to the topology optimization formulation of electromagnetic cloaking design. We extend the formulation to include uncertainty with respect to the angle of the incidence wave, and … Read more