2016, Schmidt, Gunther

The paper is devoted to the electromagnetic scattering of arbitrary time-harmonic fields by periodic structures. The Floquet-Fourier transform converts the full space Maxwell problem to a twoparameter family of diffraction problems with quasiperiodic incidence waves, for which conventional grating methods become applicable. The inverse transform is given by integrating with respect to the parameters over a infinite strip in R2. For the computation of the scattered fields we propose an algorithm, which extends known adaptive methods for the approximate calculation of multiple integrals. The novel adaptive approach provides autonomously the expansion of the incident field into quasiperiodic waves in order to approximate the scattered fields within a prescribed error tolerance. Some application examples are numerically examined.

2015, Eigel, Martin, Müller, Rüdiger

We consider a system of two coupled elliptic equations, one defined on a bulk domain and the other one on the boundary surface. Problems of this kind of problem are relevant for applications in engineering, chemistry and in biology like e.g. biological signal transduction. For the a posteriori error control of the coupled system, a residual error estimator is derived which takes into account the approximation errors due to the finite element discretisation in space as well as the polyhedral approximation of the surface. An adaptive refinement algorithm controls the overall error. Numerical experiments illustrate the performance of the a posteriori error estimator and the proposed adaptive algorithm with several benchmark examples.