Fictitious Domain with Least-Squares Spectral Element Method to explore geometric uncertainties by Chaos Collocation

In this paper Chaos Collocation method coupled to Fictitious Domain approach has been applied to one- and two-dimensional elliptic problems defined on random domains in order to demonstrate the accuracy and convergence of the methodology. Chaos Collocation method replaces a stochastic process with a set of deterministic problems, which can be separately solved, so that the big advantage of Chaos Collocation is that it is non-intrusive and existing deterministic solvers can be used. For the analysis of differential problems obtained by Chaos Collocation, Fictitious Domain method with Least-Squares Spectral Element approximation has been employed. This algorithm exploits a fictitious computational domain, where the boundary constraints, immersed in the new simple shaped domain, are enforced by means of Lagrange multipliers. For this reason its main advantage lies in the fact that only a Cartesian mesh, that represents the enclosure, needs to be generated. Excellent accuracy properties of developed method are demonstrated by numerical experiments.