POD–Galerkin Model Order Reduction for Parametrized Time Dependent Linear Quadratic Optimal Control Problems in Saddle Point Formulation

[1]  Gianluigi Rozza,et al.  Stabilized reduced basis methods for parametrized steady Stokes and Navier-Stokes equations , 2020, Comput. Math. Appl..

[2]  Gianluigi Rozza,et al.  Reduced order methods for parametrized non-linear and time dependent optimal flow control problems, towards applications in biomedical and environmental sciences , 2019, ENUMATH.

[3]  Gianluigi Rozza,et al.  Reduced order methods for parametric optimal flow control in coronary bypass grafts, toward patient‐specific data assimilation , 2019, International journal for numerical methods in biomedical engineering.

[4]  Karen Veroy,et al.  Certified Reduced Basis Methods for Parametrized Elliptic Optimal Control Problems with Distributed Controls , 2017, Journal of Scientific Computing.

[5]  Gianluigi Rozza,et al.  Model Reduction for Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering , 2017, SIAM J. Sci. Comput..

[6]  A. Quarteroni,et al.  Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts , 2017, Biomechanics and Modeling in Mechanobiology.

[7]  Stefan Volkwein,et al.  Multiobjective PDE-constrained optimization using the reduced-basis method , 2017, Advances in Computational Mathematics.

[8]  Karen Veroy,et al.  Certified Reduced Basis Methods for Parametrized Distributed Elliptic Optimal Control Problems with Control Constraints , 2016, SIAM J. Sci. Comput..

[9]  Stefan Volkwein,et al.  Reduced-Order Multiobjective Optimal Control of Semilinear Parabolic Problems , 2016, ENUMATH.

[10]  Sören Bartels,et al.  Numerical Approximation of Partial Differential Equations , 2016 .

[11]  J. Hesthaven,et al.  Certified Reduced Basis Methods for Parametrized Partial Differential Equations , 2015 .

[12]  Gianluigi Rozza,et al.  Supremizer stabilization of POD–Galerkin approximation of parametrized steady incompressible Navier–Stokes equations , 2015 .

[13]  Gianluigi Rozza,et al.  Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations , 2015, Comput. Math. Appl..

[14]  Karsten Urban,et al.  A space-time hp-interpolation-based certified reduced basis method for Burgers' equation , 2014 .

[15]  Bülent Karasözen,et al.  Distributed optimal control of time-dependent diffusion-convection-reaction equations using space-time discretization , 2014, J. Comput. Appl. Math..

[16]  Rob Stevenson,et al.  Space-time variational saddle point formulations of Stokes and Navier-Stokes equations , 2014 .

[17]  Mark Kärcher,et al.  A certified reduced basis method for parametrized elliptic optimal control problems , 2014 .

[18]  Bülent Karasözen,et al.  An all-at-once approach for the optimal control of the unsteady Burgers equation , 2014, J. Comput. Appl. Math..

[19]  Masayuki Yano,et al.  A Space-Time Petrov-Galerkin Certified Reduced Basis Method: Application to the Boussinesq Equations , 2014, SIAM J. Sci. Comput..

[20]  Dominique Chapelle,et al.  A Galerkin strategy with Proper Orthogonal Decomposition for parameter-dependent problems – Analysis, assessments and applications to parameter estimation , 2013 .

[21]  Gianluigi Rozza,et al.  Reduced Basis Method for Parametrized Elliptic Optimal Control Problems , 2013, SIAM J. Sci. Comput..

[22]  Gianluigi Rozza,et al.  Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants , 2013, Numerische Mathematik.

[23]  A. Quarteroni,et al.  A reduced computational and geometrical framework for inverse problems in hemodynamics , 2013, International journal for numerical methods in biomedical engineering.

[24]  Gianluigi Rozza,et al.  Reduction strategies for PDE-constrained oprimization problems in Haemodynamics , 2013 .

[25]  Karen Veroy,et al.  Certified Reduced Basis Methods for Parametrized Saddle Point Problems , 2012, SIAM J. Sci. Comput..

[26]  Anders Logg,et al.  Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book , 2012 .

[27]  A. Wathen,et al.  All-at-Once Solution if Time-Dependent PDE-Constrained Optimisation Problems , 2010 .

[28]  Rob P. Stevenson,et al.  Space-time adaptive wavelet methods for parabolic evolution problems , 2009, Math. Comput..

[29]  Luca Dedè,et al.  Optimal flow control for Navier–Stokes equations: drag minimization , 2007 .

[30]  Joachim Schöberl,et al.  Symmetric Indefinite Preconditioners for Saddle Point Problems with Applications to PDE-Constrained Optimization Problems , 2007, SIAM J. Matrix Anal. Appl..

[31]  Fredi Tröltzsch,et al.  Optimal Control of the Stationary Navier--Stokes Equations with Mixed Control-State Constraints , 2007, SIAM J. Control. Optim..

[32]  Tomás Roubícek,et al.  Optimal control of Navier-Stokes equations by Oseen approximation , 2007, Comput. Math. Appl..

[33]  G. Rozza,et al.  On the stability of the reduced basis method for Stokes equations in parametrized domains , 2007 .

[34]  Max Gunzburger,et al.  POD and CVT-based reduced-order modeling of Navier-Stokes flows , 2006 .

[35]  Annalisa Quaini,et al.  Numerical Approximation of a Control Problem for Advection-Diffusion Processes , 2005, System Modelling and Optimization.

[36]  Gene H. Golub,et al.  Numerical solution of saddle point problems , 2005, Acta Numerica.

[37]  N. Nguyen,et al.  An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations , 2004 .

[38]  D. Rovas,et al.  Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods , 2002 .

[39]  O. Pironneau,et al.  Applied Shape Optimization for Fluids , 2001 .

[40]  Claes Johnson,et al.  Error estimates and automatic time step control for nonlinear parabolic problems, I , 1987 .

[41]  Karsten Urban,et al.  Two Ways to Treat Time in Reduced Basis Methods , 2017 .

[42]  Eduard Bader,et al.  A Certified Reduced Basis Approach for Parametrized Linear–Quadratic Optimal Control Problems with Control Constraints (two-sided) , 2015 .

[43]  Andreas Griewank,et al.  Trends in PDE Constrained Optimization , 2014 .

[44]  Martin Stoll,et al.  All-at-once solution of time-dependent Stokes control , 2013, J. Comput. Phys..

[45]  M. Hinze,et al.  A Hierarchical Space-Time Solver for Distributed Control of the Stokes Equation , 2008 .

[46]  Stefan Volkwein,et al.  Proper orthogonal decomposition for optimality systems , 2008 .

[47]  Stefan Wendl,et al.  Optimal Control of Partial Differential Equations , 2021, Applied Mathematical Sciences.

[48]  Annalisa Quaini,et al.  Reduced basis methods for optimal control of advection-diffusion problems ∗ , 2007 .

[49]  A. Patera,et al.  Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations , 2007 .

[50]  Raino A. E. Mäkinen,et al.  Introduction to shape optimization - theory, approximation, and computation , 2003, Advances in design and control.

[51]  F. Brezzi On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers , 1974 .

[52]  I. Babuska Error-bounds for finite element method , 1971 .