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Abstract
We consider the numerical simulation of an optimal control problem constrained by the unsteady StokesBrinkman
equation involving random data. More precisely, we treat the state, the control, the target (or the
desired state), as well as the viscosity, as analytic functions depending on uncertain parameters. This allows
for a simultaneous generalized polynomial chaos approximation of these random functions in the stochastic
Galerkin finite element method discretization of the model. The discrete problem yields a prohibitively high
dimensional saddle point system with Kronecker product structure. We develop a new alternating iterative
tensor method for an efficient reduction of this system by the lowrank Tensor Train representation. Besides,
we propose and analyze a robust Schur complementbased preconditioner for the solution of the saddlepoint
system. The performance of our approach is illustrated with extensive numerical experiments based on twoand
threedimensional examples, where the full problem size exceeds one billion degrees of freedom. The
developed Tensor Train scheme reduces the solution storage by two–three orders of magnitude, depending
on discretization parameters
Original language  English 

Pages (fromto)  2654 
Number of pages  29 
Journal  Computer Methods in Applied Mechanics and Engineering 
Volume  304 
Early online date  12 Feb 2016 
DOIs  
Publication status  Published  1 Jun 2016 
Keywords
 Stochastic Galerkin system
 PDEconstrained optimization
 Lowrank solution
 Tensor methods
 Preconditioning
 Schur complement
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Dive into the research topics of 'Lowrank solvers for unsteady StokesBrinkman optimal control problem with random data'. Together they form a unique fingerprint.Projects
 2 Finished

Tensor product numerical methods for highdimensional problems in probability and quantum calculations
1/01/16 → 31/12/18
Project: Research council

Sergey Dolgov Fellowship  Tensor Product Numerical Methods for HighDimensional Problems in Probablility and Quantum Calculations
Scheichl, R.
Engineering and Physical Sciences Research Council
1/01/16 → 31/12/18
Project: Research council