Quantifying the Impact of Random Surface Perturbations on Reflective Gratings

Finite-Element Domain Approximation for Maxwell Variational Problems on Curved Domains

“…Finally, we were able to consider integer degrees of regularity only in theorems 5.9 and 5.13 (s ∈ {1 : k}). This stems from the same deficiency in lemma A.2 and further improvements are left as future work as well as extensions to more specific and varied Maxwell variational problems such as problems in periodic media, FEM/BEM couplings and applications in uncertainty quantification [6,5,36]. and, for any pair i, j ∈ {1 : 3}, it holds that…”

Fast solver for quasi-periodic 2D-Helmholtz scattering in layered media

“…Future work considers: (i) including cut-off frequencies in our analysis, (ii) extending our results to three dimensional Helmholtz equations and Maxwell's equations on periodic domains and (iii) applications in uncertainty quantification [40] and shape optimization [6]. Each of these subfigures present error convergence curves for the two scenarios of refraction indices considered and specified in Table 1.…”

“…Current highly demanding operation conditions for such devices require solving thousands of specific settings for design optimization or the quantification of shape or parameter uncertainties in the relevant quantities of interest, challenging the scientific computing community to continuously develop ever more efficient, fast and robust solvers (cf. [8,18,31,39,40] and references therein). Assuming impinging time-harmonic plane waves, scattered and transmitted fields have been solved by a myriad of mathematical formulations and associated solution schemes.…”

“…[2,4,9,11,21,33]), pure or coupled implementations of finite and boundary element methods (cf. [3,4,22,34,40] or [36,Chapter 5]) and Nyström methods [15,17,19,24,30].…”

Helmholtz scattering by random domains: first-order sparse boundary element approximation

“…Yet, direct numerical approximation of these tensor systems gives rise to the infamous curse of dimensionality. This can be, in turn, remedied by applying the general sparse tensor approximation theory originally developed by von Petersdorff and Schwab [35], and which has multiple applications ranging from diffraction by gratings [29] to neutron diffusion [14] problems. In our case, numerically, we will employ the Galerkin boundary element method (BEM) to solve the arising first kind BIEs.…”