NAMColloquium Multilevel representations of random fields and adaptive solvers for random partial differential equations |  |
Speaker:Prof. Dr. Markus Bachmayr, RWTH Aachen
Organizer:Institut für Numerische und Angewandte Mathematik
Details:
Uncertainties in coefficient functions of partial differential equations
can be modelled by assuming these coefficients to be random fields. By
expanding these random fields as function series with scalar random
coefficients, one obtains formulations of random PDEs as a deterministic
problems with countably many additional parameters. The adaptive methods
for solving these problems considered in this talk are designed to make
use of multilevel structure in series representations of random fields.
We first consider how such multilevel representations can be obtained in
the cases of stationary random fields on domains and of isotropic random
fields on the sphere. We then turn to how such representations can be
utilized in the context of sparse polynomial expansions of solutions of
random PDEs. Based on joint works with Albert Cohen, Ron DeVore, Ana
Djurdjevac, Dinh Dung, Giovanni Migliorati, Christoph Schwab, and Igor
Voulis.
can be modelled by assuming these coefficients to be random fields. By
expanding these random fields as function series with scalar random
coefficients, one obtains formulations of random PDEs as a deterministic
problems with countably many additional parameters. The adaptive methods
for solving these problems considered in this talk are designed to make
use of multilevel structure in series representations of random fields.
We first consider how such multilevel representations can be obtained in
the cases of stationary random fields on domains and of isotropic random
fields on the sphere. We then turn to how such representations can be
utilized in the context of sparse polynomial expansions of solutions of
random PDEs. Based on joint works with Albert Cohen, Ron DeVore, Ana
Djurdjevac, Dinh Dung, Giovanni Migliorati, Christoph Schwab, and Igor
Voulis.
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Type:Colloquium
Language:English
Category:Research
Host:Dr. Igor Voulis
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Direct link to event:https://events.goettingen-campus.de/event?eventId=10956001
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