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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 21 Jul 2024 20:39:22 GMT2024-07-21T20:39:22ZComparison of two approaches to compute magnetic field in problems with random domains
http://hdl.handle.net/10985/7276
Comparison of two approaches to compute magnetic field in problems with random domains
MAC, Duy Hung; MIPO, Jean-Claude; CLENET, Stephane
Methods are now available to solve numerically electromagnetic problems with uncertain input data (behaviour law or geometry). The stochastic approach consists in modelling uncertain data using random variables. Discontinuities on the magnetic field distribution in the stochastic dimension can arise in a problem with uncertainties on the geometry. The basis functions (polynomial chaos) usually used to approximate the unknown fields in the random dimensions are no longer suited. One possibility proposed in the literature is to introduce additional functions (enrichment function) to tackle the problem of discontinuity. In this study, the authors focus on the method of random mappings and they show that in this case the discontinuity are naturally taken into account and that no enrichment function needs to be added.
This paper is a postprint of a paper submitted to and accepted for publication in Science, Measurement & Technology, IET and is subject to Institution of Engineering and Technology Copyright. The copy of record is available at IET Digital Library
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/72762012-01-01T00:00:00ZMAC, Duy HungMIPO, Jean-ClaudeCLENET, StephaneMethods are now available to solve numerically electromagnetic problems with uncertain input data (behaviour law or geometry). The stochastic approach consists in modelling uncertain data using random variables. Discontinuities on the magnetic field distribution in the stochastic dimension can arise in a problem with uncertainties on the geometry. The basis functions (polynomial chaos) usually used to approximate the unknown fields in the random dimensions are no longer suited. One possibility proposed in the literature is to introduce additional functions (enrichment function) to tackle the problem of discontinuity. In this study, the authors focus on the method of random mappings and they show that in this case the discontinuity are naturally taken into account and that no enrichment function needs to be added.Transformation Methods for Static Field Problems With Random Domains
http://hdl.handle.net/10985/7274
Transformation Methods for Static Field Problems With Random Domains
MAC, Duy Hung; MIPO, Jean-Claude; CLENET, Stephane
The numerical solution of partial differential equations onto random domains can be done by using a mapping transforming this random domain into a deterministic domain. The issue is then to determine this one to one random mapping. In this paper, we present two methods-one based on the resolution of the Laplace equations, one based on a geometric transformation-to determine the random mapping. A stochastic magnetostatic example is treated to compare these methods.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/72742011-01-01T00:00:00ZMAC, Duy HungMIPO, Jean-ClaudeCLENET, StephaneThe numerical solution of partial differential equations onto random domains can be done by using a mapping transforming this random domain into a deterministic domain. The issue is then to determine this one to one random mapping. In this paper, we present two methods-one based on the resolution of the Laplace equations, one based on a geometric transformation-to determine the random mapping. A stochastic magnetostatic example is treated to compare these methods.Solution of Static Field Problems With Random Domains
http://hdl.handle.net/10985/7275
Solution of Static Field Problems With Random Domains
MAC, Duy Hung; MIPO, Jean-Claude; MOREAU, Olivier; CLENET, Stephane
A method to solve stochastic partial differential equations on random domains consists in using a one-to-one random mapping function which transforms the random domain into a deterministic domain. With this method, the randomness is then borne by the constitutive relationship of the material. In this paper, this method is applied in electrokinetics in the case of scalar potential and vector potential formulations. An example is treated and the proposed method is compared to a nonintrusive method (NIM) based on the remeshing of the random domains.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10985/72752010-01-01T00:00:00ZMAC, Duy HungMIPO, Jean-ClaudeMOREAU, OlivierCLENET, StephaneA method to solve stochastic partial differential equations on random domains consists in using a one-to-one random mapping function which transforms the random domain into a deterministic domain. With this method, the randomness is then borne by the constitutive relationship of the material. In this paper, this method is applied in electrokinetics in the case of scalar potential and vector potential formulations. An example is treated and the proposed method is compared to a nonintrusive method (NIM) based on the remeshing of the random domains.A priori error indicator in the transformation method for problems with geometric uncertainties
http://hdl.handle.net/10985/7114
A priori error indicator in the transformation method for problems with geometric uncertainties
MAC, Duy Hung; MIPO, Jean-Claude; TSUKERMAN, Igor; CLENET, Stephane
To solve stochastic problems with geometric uncertainties, one can transform the original problem in a domain with stochastic boundaries and interfaces to a problem defined in a deterministic domain with uncertainties in the material behavior. The latter problem is then discretized. There exist infinitely many random mappings that lead to identical results in the continuous domain but not in the discretized domain. In this paper, an a priori error indicator is proposed for electromagnetic problems with scalar and vector potential formulations. This leads to criteria for selecting random mappings that reduce the numerical error. In an illustrative numerical example, the proposed a priori error indicator is compared with an a posteriori estimator for both potential formulations
Version éditeur de cette publication à l'adresse suivante : http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6514655
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/71142013-01-01T00:00:00ZMAC, Duy HungMIPO, Jean-ClaudeTSUKERMAN, IgorCLENET, StephaneTo solve stochastic problems with geometric uncertainties, one can transform the original problem in a domain with stochastic boundaries and interfaces to a problem defined in a deterministic domain with uncertainties in the material behavior. The latter problem is then discretized. There exist infinitely many random mappings that lead to identical results in the continuous domain but not in the discretized domain. In this paper, an a priori error indicator is proposed for electromagnetic problems with scalar and vector potential formulations. This leads to criteria for selecting random mappings that reduce the numerical error. In an illustrative numerical example, the proposed a priori error indicator is compared with an a posteriori estimator for both potential formulationsResidual-based a posteriori error estimation for stochastic magnetostatic problems
http://hdl.handle.net/10985/9557
Residual-based a posteriori error estimation for stochastic magnetostatic problems
MAC, Duy Hung; TANG, Z.; CREUSE, E.; CLENET, Stephane
In this paper, we propose an a posteriori error estimator for the numerical approximation of a stochastic magnetostatic problem, whose solution depends on the spatial variable but also on a stochastic one. The spatial discretization is performed with finite elements and the stochastic one with a polynomial chaos expansion. As a consequence, the numerical error results from these two levels of discretization. In this paper, we propose an error estimator that takes into account these two sources of error, and which is evaluated from the residuals.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/95572015-01-01T00:00:00ZMAC, Duy HungTANG, Z.CREUSE, E.CLENET, StephaneIn this paper, we propose an a posteriori error estimator for the numerical approximation of a stochastic magnetostatic problem, whose solution depends on the spatial variable but also on a stochastic one. The spatial discretization is performed with finite elements and the stochastic one with a polynomial chaos expansion. As a consequence, the numerical error results from these two levels of discretization. In this paper, we propose an error estimator that takes into account these two sources of error, and which is evaluated from the residuals.