TY - JOUR
T1 - Nonlinear Stochastic Galerkin and Collocation Methods: Application to a Ferromagnetic Cylinder Rotating at High Speed
AU - Eveline Rosseel, Herbert De Gersem & Stefan Vandewalle
JO - Communications in Computational Physics
VL - 5
SP - 947
EP - 975
PY - 2010
DA - 2010/08
SN - 8
DO - http://doi.org/10.4208/cicp.220509.200110a
UR - https://global-sci.org/intro/article_detail/cicp/7604.html
KW - 
AB - <p style="text-align: justify;">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.</p>