2026-09-19T06:12:03Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/825072022-01-13T07:53:53Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Youssef Marzouk.
Spantini, Alessio
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics.
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
2013-11-18T21:46:45Z
2013-11-18T21:46:45Z
2013
2013
http://hdl.handle.net/1721.1/82507
862454994
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2013.
This thesis was scanned as part of an electronic thesis pilot project.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 149-155).
This thesis is about preconditioning techniques for time dependent stochastic Partial Differential Equations arising in the broader context of Uncertainty Quantification. State-of-the-art methods for an efficient integration of stochastic PDEs require the solution field to lie on a low dimensional linear manifold. In cases when there is not such an intrinsic low rank structure we must resort on expensive and time consuming simulations. We provide a preconditioning technique based on local time stretching capable to either push or keep the solution field on a low rank manifold with substantial reduction in the storage and the computational burden. As a by-product we end up addressing also classical issues related to long time integration of stochastic PDEs.
by Alessio Spantini.
S.M.
155 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Aeronautics and Astronautics.
Preconditioning techniques for stochastic partial differential equations
Thesis
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<Abstract>This thesis is about preconditioning techniques for time dependent stochastic Partial Differential Equations arising in the broader context of Uncertainty Quantification. State-of-the-art methods for an efficient integration of stochastic PDEs require the solution field to lie on a low dimensional linear manifold. In cases when there is not such an intrinsic low rank structure we must resort on expensive and time consuming simulations. We provide a preconditioning technique based on local time stretching capable to either push or keep the solution field on a low rank manifold with substantial reduction in the storage and the computational burden. As a by-product we end up addressing also classical issues related to long time integration of stochastic PDEs.</Abstract>
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