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: Jul-2009
Publisher: Department of Computer Science, K.U.Leuven
Series Title: TW Reports vol:TW541
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. 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.
Publication status: published
KU Leuven publication type: IR
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
Physics, Campus Kulak Kortrijk

Files in This Item:
File Description Status SizeFormat
TW541.pdfDocument Published 549KbAdobe PDFView/Open


All items in Lirias are protected by copyright, with all rights reserved.