Wave propagation in and through a 1-dimensional dielectric slab with stochastic properties is studied as a simplified example of a broader class of wave propagation in random media. This problem can be formulated in terms of a 1-dimensional domain-integral equation in the frequency domain. For a deterministic setup, the integral equation admits an efficient matrix-vector product, owing to the properties of the Green's function and the local field-material interactions. However, when the slab has stochastic permittivity, the problem becomes nonlinear with respect to the parameters that describe the stochastic nature of the problem, which makes the full characterization of the solution to the problem more intricate. Instead of resorting to a sampling approach, like Monte-Carlo methods or stochastic collocation, the possibilities of applying intrusive polynomial chaos are investigated and the implications for the corresponding numerical scheme are addressed, as well as the conditioning and efficiency of the scheme.
|Title of host publication||An integral approach to electromagnetic scattering : a workshop on recent developments in theory and applications (INT13), 12 November 2013, Amsterdam, The Netherlands|
|Publication status||Published - 2013|
|Event||conference; INT 13; 2013-11-12; 2013-11-12 - |
Duration: 12 Nov 2013 → 12 Nov 2013
|Conference||conference; INT 13; 2013-11-12; 2013-11-12|
|Period||12/11/13 → 12/11/13|