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Unified computational frameworks bridging low to high frequency simulations : fast and high fidelity modelling from brain to radio-frequency scenarios

Adrien Merlini 1, 2
2 Lab-STICC_IMTA_MOM_PIM
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
Abstract : In computational electromagnetics, boundary integral equations are the scheme of choice for solving extremely large forward electromagnetic problems due to their high efficiency. However, two of the most used of these formulations, the electric and combined field integral equations (EFIE and CFIE), suffer from stability issues at low frequency and dense discretization, limiting their applicability at both ends of the spectrum. This thesis focusses on remedying these issues to obtain full-wave solvers stable from low to high frequencies, capable of handling scenarios ranging from electromagnetic compatibility to radar applications. The solutions presented include (i) extending the quasi-Helmholtz (qH) projectors to higher order modeling thus combining stability with high order convergence rates; (ii) leveraging on the qH projectors to numerically stabilize the magnetic field integral equation and obtain a highly accurate and provably resonance-free Calderón-augmented CFIE immune to both of the aforementioned problems; and(iii) introducing a new low frequency and dense discretization stable wire EFIE based on projectors and linear B-splines. In addition, a research axis focused on enhancing Brain Computer Interface (BCIs) with high resolution electromagnetic modeling of the brain has been opened ; a particular attention is dedicated to the inverse problem of electromagnetics and the associated integral equation-based forward problem. The first results of this new line of investigations include the development of one of the first peer-reviewed, freely available framework for end-to-end simulation of BCI experiments.
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Adrien Merlini. Unified computational frameworks bridging low to high frequency simulations : fast and high fidelity modelling from brain to radio-frequency scenarios. Electromagnetism. Ecole nationale supérieure Mines-Télécom Atlantique, 2019. English. ⟨NNT : 2019IMTA0130⟩. ⟨tel-02466106⟩

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