Fictitious Domain with Least-Squares Spectral Element Method to Explore Geometric Uncertainties by Non-Intrusive Polynomial Chaos Method

In this paper the Non-Intrusive Polynomial Chaos Method coupled to a Fictitious Domain approach has been applied to oneand twodimensional 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. Keyword: Non-Intrusive Polynomial Chaos, Fictitious Domain, Lagrange multipliers, LeastSquares Spectral Element Method.