Discrete Empirical Interpolation and unfitted mesh FEMs: application in PDE-constrained optimization

Abstract

In this work, we investigate the performance CutFEM as a high fidelity solver as well as we construct a competent and economical reduced order solver for PDE-constrained optimization problems in parametrized domains that live in a fixed background geometry and mesh. Its effectiveness and reliability will be assessed through its application for the numerical solution of quadratic optimization problems with elliptic equations as constraints, examining an archetypal case. The reduction strategy will be via Proper Orthogonal Decomposition of suitable FE snapshots, using an aggregated state and adjoint test space, while the efficiency of the offline-online decoupling will be ensured by means of Discrete Empirical Interpolation of the optimality system matrix and right-hand side, enabling thus a rapid resolution of the reduced order model for each new spatial configuration.

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References in corpus (1)

• A Reduced Order Cut Finite Element method for geometrically parameterized steady and unsteady Navier-Stokes problems

Cited by in corpus (4)

• A localized reduced basis approach for unfitted domain methods on parameterized geometries
• Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method
• Reduced Basis, Embedded Methods and Parametrized Levelset Geometry
• Boundary and distributed optimal control for a population dynamics PDE model with discontinuous in time Galerkin FEM schemes