Reduced order methods for parametrized non-linear and time dependent optimal flow control problems, towards applications in biomedical and environmental sciences

Abstract

We introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, the optimal control problems require a huge computational effort in order to be solved, most of all in physical and/or geometrical parametrized settings. Reduced order methods are a reliable and suitable approach, increasingly gaining popularity, to achieve rapid and accurate optimal solutions in several fields, such as in biomedical and environmental sciences. In this work, we employ a POD-Galerkin reduction approach over a parametrized optimality system, derived from the Karush-Kuhn-Tucker conditions. The methodology presented is tested on two boundary control problems, governed respectively by (i) time dependent Stokes equations and (ii) steady non-linear Navier-Stokes equations.

References in corpus (3)

• Model Reduction For Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering
• Reduced order methods for parametric optimal flow control in coronary bypass grafts, towards patient-specific data assimilation
• POD-Galerkin Model Order Reduction for Parametrized Time Dependent Linear Quadratic Optimal Control Problems in Saddle Point Formulation

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• Reduced order methods for parametric optimal flow control in coronary bypass grafts, towards patient-specific data assimilation
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• POD-Galerkin Model Order Reduction for Parametrized Time Dependent Linear Quadratic Optimal Control Problems in Saddle Point Formulation
• Space-time POD-Galerkin approach for parametric flow control
• POD-Galerkin Model Order Reduction for Parametrized Nonlinear Time Dependent Optimal Flow Control: an Application to Shallow Water Equations
• POD-based reduced order methods for optimal control problems governed by parametric partial differential equation with varying boundary control
• A Certified Reduced Basis Method for Linear Parametrized Parabolic Optimal Control Problems in Space-Time Formulation