رسالة جامعية
Analysis of a multiscale finite element method applied to the design of photovoltaic cells : a multiscale hybrid-mixed method for the Helmholtz equation with quasi-periodic boundary conditions ; Analyse d'une méthode d'éléments finis multi-échelles appliquée à la conception de cellules photovoltaïques : une méthode hybride-mixte multi-échelle pour l’équation de Helmholtz avec des conditions aux limites quasi-périodiques
| العنوان: | Analysis of a multiscale finite element method applied to the design of photovoltaic cells : a multiscale hybrid-mixed method for the Helmholtz equation with quasi-periodic boundary conditions ; Analyse d'une méthode d'éléments finis multi-échelles appliquée à la conception de cellules photovoltaïques : une méthode hybride-mixte multi-échelle pour l’équation de Helmholtz avec des conditions aux limites quasi-périodiques |
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| المؤلفون: | Kassali, Zakaria |
| المساهمون: | Modélisation et méthodes numériques pour le calcul d'interactions onde-matière nanostructurée (ATLANTIS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA), Université Côte d'Azur (UniCA), Université Côte d'Azur, Stéphane Lanteri, Théophile Chaumont Frelet |
| المصدر: | https://theses.hal.science/tel-04056632Test ; Numerical Analysis [math.NA]. Université Côte d'Azur, 2023. English. ⟨NNT : 2023COAZ4003⟩. |
| بيانات النشر: | HAL CCSD |
| سنة النشر: | 2023 |
| المجموعة: | HAL Université Côte d'Azur |
| مصطلحات موضوعية: | Numerical analysis, Wave propagation, Helmholtz equation, Finite element methods, Multiscale methods, Periodic structure, Quasi-periodic boundary condition, Analyse numérique, Propagation des ondes, Équation de Helmholtz, Méthodes des éléments finis, Méthodes multi-échelles, Structure périodique, Condition aux limites quasi-périodique, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] |
| الوصف: | The objective of this thesis is the mathematical and numerical study of wave propagation in periodic and heterogeneous media modeled by the Helmholtz equation with quasi-periodic boundary conditions. In the current context of climate change, photovoltaic solar devices are emerging as an effective tool for a clean energy transition. This circumstance significantly pushes scientific research on the development of these devices. In turn, this background motivates the study of light propagation in these solar cells, which the Helmholtz equation can model with a quasi-periodic boundary condition. This unusual boundary condition represents a particular case of trapping geometries and gives rise to the appearance of some quasi-resonant frequencies. This work presents frequency-explicit stability results in the homogeneous case revealing the effect of these quasi-resonant frequencies on the use of perfectly matched layers (PML) and finite element discretizations. The Fourier expansion available in this case allows our study to go through the analysis of some parameterized one-dimensional Helmholtz problems satisfied by the Fourier modes. We also provide a frequency-explicit analysis for more general physical coefficients where Fourier expansion does not work. Specifically, we consider multilayer media, and our study uses the alternative ``Morawetz multiplier'' technique to obtain frequency-explicit results, which are of particular interest since they enter into the stability and convergence analysis of finite element discretizations. The second part of this work is devoted to the use of a two-level finite element method named the multiscale hybrid-mixed (MHM) method to solve our model problem. This method arises from a hybridization procedure using coarse mesh, and its multiscale basis functions are locally computed via independent cell problems. We first provide frequency-explicit error estimates, showing that the MHM method is more accurate and stable than the standard finite element method in the presence of ... |
| نوع الوثيقة: | doctoral or postdoctoral thesis |
| اللغة: | English |
| العلاقة: | NNT: 2023COAZ4003; tel-04056632; https://theses.hal.science/tel-04056632Test; https://theses.hal.science/tel-04056632/documentTest; https://theses.hal.science/tel-04056632/file/2023COAZ4003.pdfTest |
| الإتاحة: | https://theses.hal.science/tel-04056632Test https://theses.hal.science/tel-04056632/documentTest https://theses.hal.science/tel-04056632/file/2023COAZ4003.pdfTest |
| حقوق: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.29303AB1 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |