Domain Derivatives in Electromagnetic Scattering

Electromagnetic wave scattering by random surfaces: uncertainty quantification via sparse tensor boundary elements

“…Domain and shape differentiability for electromagnetic and acoustic scattering have been well investigated in the context of shape optimization and inverse problems. We only refer to Kirsch (1993), Potthast (1996) and Chandler-Wilde & Potthast (2002) and the references there. Usually, in these works explicit expressions for the first-and in certain cases second-domain derivatives for a number of boundary problems have been obtained.…”

An elementary formula for computing shape derivatives of EFIE system matrix

“…In the adjoint variable method, equation ( 11) is solved for γ, and equation ( 13) is used to compute the gradient of the objective. Notice that the adjoint problem (11) does not depend on the design, and therefore γ is the same for all design variables. In case of some particular objective functions (see e.g.…”

Integral equation methods in inverse obstacle scattering

“…The boundary condition (3.2) can be formally obtained by differentiating the boundary condition (1.2) with respect to r and, of course, is related to Hadamard's classical variational formula in fluid dynamics from 1912. The analysis on the differentiability with respect to the boundary has also been extended to other boundary conditions with appropriate changes in the resulting boundary condition for the derivative (see [29,32]). These properties of the derivative are of relevance for the application of regularization techniques to the linearized version of (3.1).…”