Title: Nonlinear stochastic Galerkin and collocation methods: application to a ferromagnetic cylinder rotating at high speed
Authors: Rosseel, Eveline
De Gersem, Herbert
Vandewalle, Stefan # ×
Issue Date: 2010
Publisher: Global Science Press
Series Title: Communications in Computational Physics vol:8 issue:5 pages:947-975
Abstract: The stochastic Galerkin and stochastic collocation method are two
state-of-the-art methods for solving partial differential equations (PDE)
containing random coefficients. While the latter method, which is based on
sampling, can straightforwardly be applied to nonlinear stochastic PDEs, this is
nontrivial for the stochastic Galerkin method and approximations are required.
In this paper, both methods are used for constructing high-order solutions of a
nonlinear stochastic PDE representing the magnetic vector potential in a
ferromagnetic rotating cylinder. This model can be used for designing
solid-rotor induction machines in various machining tools. A precise
design requires to take ferromagnetic saturation effects into account
and uncertainty on the nonlinear magnetic material properties. Implementation issues of the stochastic Galerkin method are addressed and a numerical comparison of the
computational cost and accuracy of
both methods is performed. The
stochastic Galerkin method requires in general less stochastic unknowns than the
stochastic collocation approach to reach a certain level of accuracy, however at
a higher computational cost.
ISSN: 1815-2406
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
Physics, Campus Kulak Kortrijk
× corresponding author
# (joint) last author

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