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Generalized Polynomial Chaos (gPC) expansions are well established forforward uncertainty propagation in many application areas. Although theassociated computational effort may be reduced in comparison to Monte Carlotechniques, for instance, further convergence acceleration may be important totackle problems with high parametric sensitivities. In this work, we proposethe use of conformal maps to construct a transformed gPC basis, in order toenhance the convergence order. The proposed basis still features orthogonalityproperties and hence, facilitates the computation of many statisticalproperties such as sensitivities and moments. The corresponding surrogatemodels are computed by pseudo-spectral projection using mapped quadraturerules, which leads to an improved cost accuracy ratio. We apply the methodologyto Maxwell's source problem with random input data. In particular, numericalresults for a parametric finite element model of an optical grating coupler aregiven.

Conformally Mapped Polynomial Chaos Expansions for Maxwell's Source Problem with Random Input Data