||CMES: Computer Modeling in Engineering & Sciences, Vol. 22, No. 1, pp. 41-64, 2007
||Full length paper in PDF format. Size = 1,071,789 bytes
||Non-Intrusive Polynomial Chaos, Fictitious Domain, Lagrange multipliers, Least-Squares Spectral Element Method.
||In this paper the Non-Intrusive Polynomial Chaos Method coupled to a Fictitious Domain approach has been applied to one- and two-dimensional elliptic problems with geometric uncertainties, in order to demonstrate the accuracy and convergence of the methodology. The main advantage of non-intrusive formulation is that existing deterministic solvers can be used. A new Least-Squares Spectral Element method has been employed for the analysis of deterministic differential problems obtained by Non-Intrusive Polynomial Chaos. This algorithm employs a Fictitious Domain approach and for this reason its main advantage lies in the fact that only a Cartesian mesh needs to be generated. Excellent accuracy properties of method are demonstrated by numerical experiments.