Proper Generalized Decomposition Method: algorithms and applications to several stochastic PDE's
\nIn this talk, I will present various applications of the Proper Generalized Decompositon (PGD) Method for the approximate solution of Partial Differential Equations involving random (uncertain) parameters, that is SPDEs. The PGD consists in a series of functionals with separated deterministic and stochastic components. The series is sought to minimize the approximation error in a prescribed sense (often the equation resiudal). Starting from the simple case of SPES having energy functionals, e.g. elliptic equations, I will review and compare several algorithms for the approximation of the ideal decomposition. I will subsequently show that these algorithms can be successfully applied to several (moderately) non-linear problems, in particular the incompressible Navier-Stokes equations. Alternative separation formats, needed to further reduce the computational complexity of the PGD algorithms, will also be discussed. Finally, I will present recent PGD results for the uncertain wave equation which requires a multi-resolution framework to effectively deal with the complicated structure of the stochastic functionals.
Programme
\n 12:00 - 12:10 Coffee and tea
\n 12:10 - 12:15 Welcome and introduction by Assoc. Prof. Allan P. Engsig-
\n Karup, DTU Compute.
\n 12:15 - 13:00 Proper Generalized Decomposition Method: algorithms
\n and applications to several Stochastic PDEs
\n by Directeur de Recherce CNRS Olivier Le Matre,
\n Laboratoire d'Informatique pour la Mécanique et
\n les Sciences de l*Ingénieur LIMSI-CNRS, France
\n 13:00 - 13:30 Refreshments and networking
Registration
\nPlease register by sending an e-mail to Assoc. Prof. Allan P. Engsig-Karup (apek@dtu.dk) or Ph.D. Daniele Bigoni (dabi@dtu.dk), Section for Scientific Computing, Department of Applied Mathematics and Computer Science (DTU Compute), DTU.
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Proper Generalized Decomposition Method: algorithms and applications to several stochastic PDE's
\nIn this talk, I will present various applications of the Proper Generalized Decompositon (PGD) Method for the approximate solution of Partial Differential Equations involving random (uncertain) parameters, that is SPDEs. The PGD consists in a series of functionals with separated deterministic and stochastic components. The series is sought to minimize the approximation error in a prescribed sense (often the equation resiudal). Starting from the simple case of SPES having energy functionals, e.g. elliptic equations, I will review and compare several algorithms for the approximation of the ideal decomposition. I will subsequently show that these algorithms can be successfully applied to several (moderately) non-linear problems, in particular the incompressible Navier-Stokes equations. Alternative separation formats, needed to further reduce the computational complexity of the PGD algorithms, will also be discussed. Finally, I will present recent PGD results for the uncertain wave equation which requires a multi-resolution framework to effectively deal with the complicated structure of the stochastic functionals.
Programme
\n 12:00 - 12:10 Coffee and tea
\n 12:10 - 12:15 Welcome and introduction by Assoc. Prof. Allan P. Engsig-
\n Karup, DTU Compute.
\n 12:15 - 13:00 Proper Generalized Decomposition Method: algorithms
\n and applications to several Stochastic PDEs
\n by Directeur de Recherce CNRS Olivier Le Matre,
\n Laboratoire d'Informatique pour la Mécanique et
\n les Sciences de l*Ingénieur LIMSI-CNRS, France
\n 13:00 - 13:30 Refreshments and networking
Registration
\nPlease register by sending an e-mail to Assoc. Prof. Allan P. Engsig-Karup (apek@dtu.dk) or Ph.D. Daniele Bigoni (dabi@dtu.dk), Section for Scientific Computing, Department of Applied Mathematics and Computer Science (DTU Compute), DTU.
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