Formulation and super-efficient solution of large-scale inverse equivalent surface-source problems with consideration of various side constraints

• Applicant: Professor Dr.-Ing. Thomas Eibert
• Subject Area: Communication Technology and Networks, High-Frequency Technology and Photonic Systems, Signal Processing and Machine Learning for Information Technology
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 429949501

Inverse equivalent source solutions determine equivalent source distributions such that they are able to reproduce radiation or scattering fields observed in a collection of sample locations. Once the sources are available, diagnostic information about the radiation or scattering object(s) can be obtained and it is also possible to compute the radiation or scattering fields in new observation locations, in particular also in the far field. In the first part of this project, a variety of super-efficient solution techniques for inverse equivalent surface source problems (IESSPs) have been investigated and realized, which are based on the concepts of hierarchical propagating plane wave representations, as known from the multilevel fast multipole method (MLFMM), and on meshless field expansions via distributed spherical harmonics expansions. In particular, it was possible to realize very directive Gaussian-beam based translation operators for the plane-wave spectra without any loss of accuracy and it was possible to generate reduced sets of spherical harmonics with directive radiation toward the solution domain, which lead to a more robust, more flexible, and more efficient solution approach. On top of these very powerful techniques, new preconditioning and start vector estimation techniques for the iterative solution process could be realized. In this continuation proposal, some of these techniques shall be further pursued, but the major focus shall be on super-efficient solution techniques for IESSP solvers with observation data above multilayered planar ground. Such scenarios are, e.g., important for automotive antenna and scattering measurements, but the super-efficient solution techniques have also great potential toward the solution of integral equations of radiation and scattering problems. The presence of multilayered planar ground imposes new challenges on the algorithms, in particular with respect to efficiency, since the successful free-space methods are not directly transferable to this scenario. In particular, it will be necessary to work with plane-wave representations which are more suitable for the multilayered ground environment, such as those based on the Weyl-identity.

• DFG Programme: Research Grants