Combined asymptotic and domain decomposition methods to solve Maxwell’s equations in the high frequency regime

SCHEME: Industrial Fellowships

CALL: 2017

DOMAIN: MT - Mathematics


LAST NAME: Gasperini


INDUSTRY / PPP PARTNER: Montefiore Institute, University of Liege


KEYWORDS: Maxwell Equations, Simulation, Domain Decomposition, High Frequency, Asymptotic Solution

START: 2017-10-01

END: 2020-09-30


Submitted Abstract

New active remote sensing technologies for surround detection and monitoring applications will help facilitating industrial applications dealing with complex environmental recognition processes required for autonomously acting robots, e.g. in case of autonomously driving cars. For that purpose new electromagnetic sensor technologies are indispensable, working at comparatively high frequencies in the range of 80 GHz. Designing and incorporating such new devices into future technical applications leads to solving challenging industrial problems with complex constraints related to the interaction of EM waves with multi-materials at small wavelengths. To develop and understand the behaviour of such EM sensors in complex environments, engineering design intensively uses numerical simulation methods to solve Maxwell’s equations. Due to the fact that high frequencies are involved, commercial codes are limited to handle correctly these extreme situations, most particularly for multi-materials problems. The aim of this Ph.D. thesis is to design new numerical modelling tools for such applications, based on high frequency hybrid techniques, domain decomposition methods and surface integral equations, including multi-materials structures. During the Ph.D. thesis, a first step will be to understand how to mathematically couple various approximation techniques to build a novel scalable solver, in view of applications for multi-materials situations. The applied numerical techniques will be based on approximate asymptotic methods for large frequencies that will then be incorporated into mathematically exact formulations. The latter ones will be developed on the basis of new coupling methods between surface integral representation, possibly accelerated by fast algorithms for high frequencies (OSRC preconditioning/Adaptive Cross Approximation/FMM), and domain decomposition methods adapted to high-frequency (by integrating new asymptotic OSRC-based operators) for handling multi-materials. A second step will consider the implementation of the appropriate mathematical formulation into codes developed by the main scientific advisors. Finally, dedicated test configurations will be simulated in collaboration with IEE and compared with physical measurements.

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