Domain Uncertainty Quantification in Computational Electromagnetics

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…”

“…(4.1) to satisfy the following conditions: Re −e ıθ (x) ≥ α > 0 for some θ ∈ [0, 2π) and α > 0 is enough to ensure the conditions in Assumption 4.3 ( cf. [5,21]).…”

“…As in[5,25], we note that if E ∈ H 0 (curl; D) is the unique solution of Problem 2.1, then ΨE ∈ H 0 (curl; D) is the unique solution of a modified Maxwell problem on D arising from transferring the sesquilinear and antilinear forms Φ(•, •) and F(•) from D to D by a change of variables (cf. in[5, Sec. 2.5.2]).…”

Conformally mapped polynomial chaos expansions for Maxwell's source problem with random input data

“…18 Holomorphy of the solution of Maxwell's source problem with respect to general shape parametrizations was established in Ref. 19 As discussed in the following, in this work we propose a method for surrogate modeling, where the basis functions are mapped polynomials based on gPC 7 combined with a mapping, which is conformal in each coordinate. To compute the corresponding coefficients we rely on pseudo-spectral projection based on mapped quadrature rules.…”

“…Note that this assumption can often be justified for boundary value problems with random influences, see, for example, Ref 18 . Holomorphy of the solution of Maxwell's source problem with respect to general shape parametrizations was established in Ref 19 …”