  Generalized Polynomial Chaos (gPC) expansions are well established for
forward uncertainty propagation in many application areas. Although the
associated computational effort may be reduced in comparison to Monte Carlo
techniques, for instance, further convergence acceleration may be important to
tackle problems with high parametric sensitivities. In this work, we propose
the use of conformal maps to construct a transformed gPC basis, in order to
enhance the convergence order. The proposed basis still features orthogonality
properties and hence, facilitates the computation of many statistical
properties such as sensitivities and moments. The corresponding surrogate
models are computed by pseudo-spectral projection using mapped quadrature
rules, which leads to an improved cost accuracy ratio. We apply the methodology
to Maxwell's source problem with random input data. In particular, numerical
results for a parametric finite element model of an optical grating coupler are
given.
