Projects per year
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 low-rank Tensor Train representation. Besides,
we propose and analyze a robust Schur complement-based preconditioner for the solution of the saddle-point
system. The performance of our approach is illustrated with extensive numerical experiments based on twoand
three-dimensional 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 |
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Pages (from-to) | 26-54 |
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
- PDE-constrained optimization
- Low-rank solution
- Tensor methods
- Preconditioning
- Schur complement
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Dive into the research topics of 'Low-rank solvers for unsteady Stokes-Brinkman optimal control problem with random data'. Together they form a unique fingerprint.Projects
- 2 Finished
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Tensor product numerical methods for high-dimensional problems in probability and quantum calculations
Dolgov, S. (PI)
1/01/16 → 31/12/18
Project: Research council
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Sergey Dolgov Fellowship - Tensor Product Numerical Methods for High-Dimensional Problems in Probablility and Quantum Calculations
Scheichl, R. (PI)
Engineering and Physical Sciences Research Council
1/01/16 → 31/12/18
Project: Research council