This work entails studying unfitted finite element discretizations for convection-diffusion equations in domains that evolve in time. In particular, these partial differential equations model the evolution of the concentration of soluble surfactants in bulk-interface domains. The work in this thesis docuses on developing numerical methods which conserve the modeled physical quantities. In this work, we propose cut finite element discretizations based on the Discontinuous Galerkin framework which are both locally and globally conservative. Local conservation is achieved on so-called macro elements, and we investigate macro element partitioning of the mesh for both stationary and time-dependent domains. Additionally, we develop globally conservative methods for time-dependent problems. We analyze the proposed methods by studying the convergence of the L2-error with respect to mesh size, condition numbers of the associated linear system matrices, and the conservation error. In numerical experiments for time-dependent problems, we show that the proposed methods have optimal convergence and that the developed macro element stabilization for time-dependent problems leads to increased accuracy while retaining stable condition numbers. Moreover, the measured conservation errors verify the global conservation of the proposed methods. / Detta arbete undersöker diskretiseringar av partiella differentialekvationer i tidsberoende domäner där beräkningsnätet inte behöver anpassas till domänens rörelse. I synnerhet betraktar vi partiella differentalekvationer som modellerar koncentrationen av lösliga ytaktiva ämnen, och skurna finita elementmetoder baserade på den Diskontinuerliga Galerkinmetoden som bevarar de modellerade fysikaliska storheterna. I detta arbete föreslås diskretiseringar som är både lokalt och globalt konservativa. Lokal konservering uppnås i så kallade makroelement, och vi undersöker makroelementpartitionering för både stationära och tidsberoende domäner. Även globalt konservativa metoder utvecklas för tidsberoende problem. De föreslagna metoderna analyseras med hjälp av numeriska exempel. Vi studerar konvergensen av L2-felet med avseende på nätstorlek, konditionstalen för de linjära systemmatriserna samt konserveringsfelet. Metoderna uppvisar optimal konvergens och makroelementstabilisering som utvecklas för tidsberoende problem leder till ökad noggrannhet, samtidigt som konditionstalen förblir stabila. Dessutom veritifierar de uppmättta konserveringsfelen den globala konserveringen hos de föreslagna metoderna.

This work is concerned with the theoretical analysis of the space-time discontinuous Galerkin method applied to the numerical solution of nonstationary nonlinear convection-diffusion problem in a time- dependent domain. At first, the problem is reformulated by the use of the arbitrary Lagrangian-Eulerian (ALE) method, which replaces the classical partial time derivative by the so-called ALE derivative and an additional convection term. Then the problem is discretized with the use of the ALE space-time discontinuous Galerkin method. On the basis of a technical analysis we obtain an unconditional stability of this method. An important step in the analysis is the generalization of a discrete characteristic function associated with the approximate solutionin a time-dependentdomainand the derivationof its properties. Further we derive an a priori error estimate of the method in terms of the interpolation error, as well as in terms of h and tau. Finally, some practical applications of the ALE space-time discontinuos Galerkin method in a time-dependent domain are given. We are concerned with the numerical solution of a nonlinear elasticity benchmark problem and moreover with the interaction of compressible viscous flow with elastic structures. The main attention is paid to the modeling of flow induced vocal fold...

<div>In contrast to traditional steel and aluminum, short fiber reinforced polymer composites (SFRCs) provide promising alternatives in material selection for automotive and aerospace applications due to their potential to decrease weight while maintaining excellent mechanical properties. However, uncertainties about the influence of complex microstructures and defects on mechanical response have prevented widespread adoption of material models for</div><div>SFRCs. In order to build confidence in models’ predictions requires deepened insight into the heterogenous damage mechanisms. Therefore, this research takes a micro-mechanics standpoint of assessing the damage behavior of SFRCs, particularly micro-void nucleation at the fiber tips, by passing information of microstructural attributes within neighborhoods of incipient damage and non-damage sites, into a framework that establishes correlations between the microstructural information and damage. To achieve this, in-situ x-ray tomography of the gauge sections of two cylindrical injection molded dog-bone specimens, composed of E-glass fibers in a polypropylene matrix, was conducted while the specimens were monotonically loaded until failure. This was followed by (i) the development of microstructural characterization frameworks for segmenting fiber and porosity features in 3D images, (ii) the development of a digital volume correlation informed damage detection framework that confines search spaces of potential damage sites, and (iii) the use of a Gaussian process classification framework to explore the dependency of micro-void nucleation on neighboring microstructural defects by ranking each of their contributions. Specifically, the analysis considered microstructural metrics related to the closest fiber, the closest pore, and the local stiffness, and the results demonstrated that less stiff resin rich areas were more relevant for micro-void nucleation than clustered fiber tips, T-intersections of fibers, or varying porosity volumes. This analysis provides a ranking of microstructural metrics that induce microvoid nucleation, which can be helpful for modelers to validate their predictions on proclivity of damage initiation in the presence of wide distributions of microstructural features and</div><div>manufacturing defects. </div>

[pt] A presente tese tem como objetivo estudar as reações descontínuas que ocorreram nos contornos de grão (CG) sob condições de envelhecimento a altas temperaturas e identificar as fases que precipitam em função do tempo em uma liga de alto teor de Cr e Ni – Liga 33, tendo em vista o efeito destas transformações nas potenciais aplicações em indústrias de alto desempenho. Amostras na condição como recebida foram submetidas a tratamentos isotérmicos de envelhecimento a 700 graus C, 800 graus C e 900 graus C. Ênfase foi dada ao estudo do envelhecimento a 800 graus C em intervalos de tempo entre 10 minutos e 100 horas com o objetivo de promover fenômenos de precipitação nos modos convencional e descontínua. A caracterização microestrutural foi realizada por microscopia óptica (MO), microscopia eletrônica de varredura (MEV) analítica por espectroscopia por dispersão de energia de raios-X (XEDS), difração de elétrons retroespalhados (EBSD) e microscopia eletrônica de transmissão (MET) no modo convencional, utilizando contraste de difração, e no modo analítico (STEM/XEDS). Resultados obtidos por STEM/XEDS e difração de elétrons mostraram que a transformação descontínua, pela partição de solutos, gera colônias de precipitação descontínua (PD) concomitante à migração do CG e resulta na precipitação de cinco diferentes fases dentro de uma mesma colônia de PD: (1) carbeto-M(23)C(6) rico em Cr com estrutura CFC; (2) fase-eta enriquecida em Si com estrutura cúbica-diamante; (3) fase alfa rica em Cr com estrutura CCC; (4) fase intermetálica sigma com estrutura tetragonal e (5) nitreto-M(2)N rico em Cr com estrutura hexagonal. Em geral, as colônias de PD na Liga 33 evoluem no envelhecimento seguindo a sequência, a saber: nos estágios iniciais do processo ocorre precipitação intergranular (carbeto-M(23)C(6) e fase-eta) no CG original; com o aumento no tempo de envelhecimento, os contornos migraram alimentados pela difusão de soluto num processo conhecido como DIGM (diffusion-induced grain boundary migration), enquanto precipitados da fase alfa-Cr nuclearam adjacente ao CG e cresceram com morfologia lamelar acompanhando a migração do contorno, desenvolvendo, assim, as colônias de PD. Eventualmente, a fase-eta também precipita no interior da colônia e na frente de reação. Nos estágios finais do processo de crescimento das colônias de PD ocorre a formação da fase-sigma na frente de reação da PD e, posteriormente, a formação do nitreto-M(2)N na frente de reação e dentro da colônia. Foi verificado que a reação de PD é controlada, primeiramente, pela difusão de CG do Cr e, com o tempo de reação pela difusão de volume do Cr, o que resultou em um crescimento no estado não-estacionário da reação. Além da ocorrência de cinco fases precipitadas dentro da mesma colônia, outra característica marcante da reação de PD na Liga 33 refere-se à consistente evidência que a fase inicialmente precipitada nos CG (carbeto-M(23)C(6) é diferente da fase precipitado com morfologia lamelar (fase alfa-Cr) dentro da colônia. Tal observação constitui a primeira evidência para o fenômeno de PD envolvendo colônias multi-fases em materiais multicomponentes estruturais. / [en] This thesis aims at study the discontinuous reactions taking place at grain boundaries (GB) under high-temperature aging conditions and to identify the precipitated phases as a function of the time in a Cr-Fe-Ni alloy - Alloy 33, in view of the deleterious effect of these transformations on potential applications of this alloy in high-performance industries. Samples in the as-received condition were submitted to isothermal aging treatments at 700 C degrees, 800 C degrees and 900 C degrees. Emphasis was given to the study of aging at 800 C degrees in time intervals between 10 minutes and 100 hours in order to promote precipitation phenomena in the conventional and discontinuous modes. The microstructural characterization was carried out by light optical microscopy (LOM), analytical scanning electron microscopy (SEM) by X-ray energy dispersive spectroscopy (XEDS), electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM) under conventional mode using diffraction contrast and analytical mode (STEM/XEDS). Results obtained by STEM/XEDS and electron diffraction revealed that the discontinuous transformation, by solutes partitioning, generates discontinuous precipitation (DP) colonies concomitant with GB migration and results in the precipitation of five different phases within a single DP colony: (1) Cr-rich M(23)C(6)-carbide with FCC structure, (2) Si-enriched eta-phase with diamond-cubic structure, (3) Cr-rich alpha-phase with BCC structure, (4) intermetallic sigma-phase with tetragonal structure, and (5) Cr-rich M(2)N-nitride with hexagonal structure. In summary, DP colonies in Alloy 33 upon aging at 800 C degrees evolve according the following the sequence: in the initial stages of the process intergranular precipitation (M(23)C(6)-carbide and n-phase) occurs at original GB; with the increase in aging time, the boundaries migrated fed by solute atoms in a process known as diffusion-induced grain boundary migration (DIGM), whereas alpha-Cr phase precipitates have nucleated adjacent to the GB and grew with lamellar morphology accompanying the migration of the boundary thereby developing the DP colonies. Eventually, the n-phase also precipitates both within the colony and at the DP reaction-front. Over the final stages of the DP colonies growth process occurs the nucleation and growth of the sigma-phase at the GB reaction-front and, later, M(2)N-nitride precipitates also at the reaction-front and within the DP colony. It was verified that the DP reaction growth is controlled, initially by GB diffusion of Cr and, with the progress of reaction time by the volume diffusion of the Cr, which resulted in a non-steady state growth process. In addition to the occurrence of five precipitated phases within the same colony, another striking feature of the DP reaction in Alloy 33 refers to the consistent evidence that the phase initially precipitated at original GB position (M(23)C(6)-carbide) is different from the precipitated phase with lamellar morphology (alpha-Cr phase) within the colony. This observation constitutes the first evidence for the DP phenomenon resulting in multi-phase DP colonies in multicomponent structural materials.

No description available.

Diese Arbeit befasst sich mit der theoretischen Beschreibung nichtlinearer optischer Phänomene in Hinblick auf das (numerische) unstetige Galerkin-Zeitraumverfahren. Insbesondere werden zwei Materialmodelle behandelt: das hydrodynamische Modell für Metalle und das Modell für Raman-aktive Materialien. Im ersten Teil der Arbeit wird das hydordynamische Modell für Metalle unter Verwendung eines störungstheoretischen Ansatzes behandelt. Insbesondere wird dieser Ansatz genutzt, um die nichtlinearen optischen Effekte, Erzeugung zweiter Harmonischer und Summenfrequenzerzeugung, mit Hilfe des unstetigen Galerkin-Verfahrens zu studieren. In diesem Zusammenhang wird demonstriert, wie das optische Signal zweiter Ordnung von Nanoantennen optimiert werden kann. Hierzu wird ein hier erarbeitetes Schema für die Abstimmung des eingestrahten Lichtes angewandt. Zudem führt eine intelligente Wahl des Antennendesigns zu einem optimierten Signal. Im zweiten Teil dieser Arbeit wird das Modell für Raman-aktive Dielektrika behandelt. Genauer wird die nichtlineare Antwort dritter Ordnung für stimulierte Raman-Streuung hergeleitet. Diese wird dazu genutzt, um ein System aus Hilfsdifferentialgleichungen für das unstetige Galerkin-Verfahren zu konstruieren. Die Ergebnisse des erweiterten numerischen Verfahrens werden im Anschluss gezeigt und diskutiert. / This thesis is concerned with the theoretical description of nonlinear optical phenomena with regards to the (numerical) discontinuous Galerkin time-domain (DGTD) method. It deals with two different material models: the hydrodynamic model for metals and the model for Raman-active dielectrics. In the first part, we review the hydrodynamic model for metals, where we apply a perturbative approach to the model. We use this approach to calculate the second-order nonlinear optical effects of second-harmonic generation and sum-frequency generation using the DGTD method. In this context, we will see how to optimize the second-order response of plasmonic nanoantennas by applying a deliberate tuning scheme for the optical excitations as well as by choosing an intelligent nanoantenna design. In the second part, we examine the material model for Raman-active dielectrics. In particular, we see how to derive the third-order nonlinear response by which one can describe the process of stimulated Raman scattering. We show how to incorporate this third-order response into the DGTD scheme yielding a novel set of auxiliary differential equations. Finally, we demonstrate the workings of the modified numerical scheme.

[pt] A modelagem numérica precisa de reservatórios de petróleo ainda é um desafio, devido às heterogeneidades do meio poroso e à existência de estruturas geológicas com geometrias complexas, tais como: fraturas, estratificações e heterogeneidades, que influenciam decisivamente o escoamento dos fluidos através dessas formações. O presente trabalho analisa a implementação de duas formulações numéricas aplicadas ao fluxo bifásico em meios porosos em que se procura contornar as dificuldades mencionadas acima. Inicialmente, avalia-se uma formulação numérica que emprega um processo em três passos: o método dos elementos finitos, EF, para a solução da equação da pressão, intermediariamente, utiliza-se o método de Raviart-Thomas de mais baixa ordem, RT 0, para melhor aproximação da velocidade, e a resolução da equação da saturação pelo método dos elementos finitos descontínuos, MEFD. Também é avaliada uma formulação na qual se utiliza o método dos elementos finitos mistos e híbridos, EFH, para aproximar a equação da pressão, e o método MEFD para aproximar somente a equação de saturação. O estudo dessas formulações busca avaliar a conservação de massa e analisar o esforço computacional despendido. São apresentados exemplos que avaliam cada uma das formulações em comparação com resultados da literatura. / [en] Accurate numerical modeling of oil reservoirs is still a challenge due to heterogeneity of the porous medium and the existence of geological structures with complex geometries, such as fractures, stratifications and heterogeneities that decisively influence the flow of fluids through these formations. This paper analyzes two numerical formulations of two-phase flow that seek to circumvent the difficulties mentioned. Initially, it evaluates a numerical formulation that employs a three step process: the finite element method, for solving the pressure equation, intermediately, it uses the lowest-order Raviart-Thomas, RT 0,to the best approximation of the flow velocities, and finally the solution of the saturation equation by discontinuous finite element method (MEFD). Additionally, a formulation which utilizes the mixed and hybrid finite element method (EFH), to approximate the pressure equation, and uses MEFD to approximate the saturation equation. Both implemented formulations aim to assess the mass conservation and to analyze the necessary computational effort. Examples are presented which evaluate each of the formulations as compared with results existing in literature.

Les travaux de cette thèse portent sur des méthodes de volumes finis sur maillages quelconque pour la discrétisation de problèmes d'évolution non linéaires modélisant le transport de contaminants en milieu poreux et les écoulements diphasiques.Au Chapitre 1, nous étudions une famille de schémas numériques pour la discrétisation d'une équation parabolique dégénérée de convection-reaction-diffusion modélisant le transport de contaminants dans un milieu poreux qui peut être hétérogène et anisotrope. La discrétisation du terme de diffusion est basée sur une famille de méthodes qui regroupe les schémas de volumes finis hybrides, de différences finies mimétiques et de volumes finis mixtes. Le terme de convection est traité à l'aide d'une famille de méthodes qui s'appuient sur les inconnues hybrides associées aux interfaces du maillage. Cette famille contient à la fois les schémas centré et amont. Les schémas que nous étudions permettent une discrétisation localement conservative des termes d'ordre un et d'ordre deux sur des maillages arbitraires en dimensions d'espace deux et trois. Nous démontrons qu'il existe une solution unique du problème discret qui converge vers la solution du problème continu et nous présentons des résultats numériques en dimensions d'espace deux et trois, en nous appuyant sur des maillages adaptatifs.Au Chapitre 2, nous proposons un schéma de volumes finis hybrides pour la discrétisation d'un problème d'écoulement diphasique incompressible et immiscible en milieu poreux. On suppose que ce problème a la forme d'une équation parabolique dégénérée de convection-diffusion en saturation couplée à une équation uniformément elliptique en pression. On considère un schéma implicite en temps, où les flux diffusifs sont discrétisés par la méthode des volumes finis hybride, ce qui permet de pouvoir traiter le cas d'un tenseur de perméabilité anisotrope et hétérogène sur un maillage très général, et l'on s'appuie sur un schéma de Godunov pour la discrétisation des flux convectifs, qui peuvent être non monotones et discontinus par rapport aux variables spatiales. On démontre l'existence d'une solution discrète, dont une sous-suite converge vers une solution faible du problème continu. On présente finalement des cas test bidimensionnels.Le Chapitre 3 porte sur un problème d'écoulement diphasique, dans lequel la courbe de pression capillaire admet des discontinuité spatiales. Plus précisément on suppose que l'écoulement prend place dans deux régions du sol aux propriétés très différentes, et l'on suppose que la loi de pression capillaire est discontinue en espace à la frontière entre les deux régions, si bien que la saturation de l'huile et la pression globale sont discontinues à travers cette frontière avec des conditions de raccord non linéaires à l'interface. On discrétise le problème à l'aide d'un schéma, qui coïncide avec un schéma de volumes finis standard dans chacune des deux régions, et on démontre la convergence d'une solution approchée vers une solution faible du problème continu. Les test numériques présentés à la fin du chapitre montrent que le schéma permet de reproduire le phénomène de piégeage de la phase huile. / In Chapter 1 we study a family of finite volume schemes for the numerical solution of degenerate parabolic convection-reaction-diffusion equations modeling contaminant transport in porous media. The discretization of possibly anisotropic and heterogeneous diffusion terms is based upon a family of numerical schemes, which include the hybrid finite volume scheme, the mimetic finite difference scheme and the mixed finite volume scheme. One discretizes the convection term by means of a family of schemes which makes use of the discrete unknowns associated to the mesh interfaces, and contains as special cases an upwind scheme and a centered scheme. The numerical schemes which we study are locally conservative and allow computations on general multi-dimensional meshes. We prove that the unique discrete solution converges to the unique weak solution of the continuous problem. We also investigate the solvability of the linearized problem obtained during Newton iterations. Finally we present a number of numerical results in space dimensions two and three using nonconforming adaptive meshes and show experimental orders of convergence for upwind and centered discretizations of the convection term.In Chapter 2 we propose a finite volume method on general meshes for the numerical simulation of an incompressible and immiscible two-phase flow in porous media. We consider the case that it can be written as a coupled system involving a degenerate parabolic convection-diffusion equation for the saturation together with a uniformly elliptic equation for the global pressure. The numerical scheme, which is implicit in time, allows computations in the case of a heterogeneous and anisotropic permeability tensor. The convective fluxes, which are non monotone with respect to the unknown saturation and discontinuous with respect to the space variables, are discretized by means of a special Godunov scheme. We prove the existence of a discrete solution which converges, along a subsequence, to a solution of the continuous problem. We present a number of numerical results in space dimension two, which confirm the efficiency of the numerical method.Chapter 3 is devoted to the study of a two-phase flow problem in the case that the capillary pressure curve is discontinuous with respect to the space variable. More precisely we assume that the porous medium is composed of two different rocks, so that the capillary pressure is discontinuous across the interface between the rocks. As a consequence the oil saturation and the global pressure are discontinuous across the interface with nonlinear transmission conditions. We discretize the problem by means of a numerical scheme which reduces to a standard finite volume scheme in each sub-domain and prove the convergence of a sequence of approximate solutions towards a weak solution of the continuous problem. The numerical tests show that the scheme can reproduce the oil trapping phenomenon.

Nous présentons dans cette thèse les évolutions apportées au solveur Galerkin Discontinu Teta-CLAC, issu de la collaboration IRMA-AxesSim, au cours du projet HOROCH (2015-2018). Ce solveur permet de résoudre les équations de Maxwell en 3D, en parallèle sur un grand nombre d'accélérateurs OpenCL. L'objectif du projet HOROCH était d'effectuer des simulations de grande envergure sur un modèle numérique complet de corps humain. Ce modèle comporte 24 millions de mailles hexaédriques pour des calculs dans la bande de fréquences des objets connectés allant de 1 à 3 GHz (Bluetooth). Les applications sont nombreuses : téléphonie et accessoires, sport (maillots connectés), médecine (sondes : gélules, patchs), etc. Les évolutions ainsi apportées comprennent, entre autres : l'optimisation des kernels OpenCL à destination des CPU dans le but d'utiliser au mieux les architectures hybrides ; l'expérimentation du runtime StarPU ; le design d'un schéma d'intégration à pas de temps local ; et bon nombre d'optimisations permettant au solveur de traiter des simulations de plusieurs millions de mailles. / In this thesis, we present the evolutions made to the Discontinuous Galerkin solver Teta-CLAC – resulting from the IRMA-AxesSim collaboration – during the HOROCH project (2015-2018). This solver allows to solve the Maxwell equations in 3D and in parallel on a large amount of OpenCL accelerators. The goal of the HOROCH project was to perform large-scale simulations on a complete digital human body model. This model is composed of 24 million hexahedral cells in order to perform calculations in the frequency band of connected objects going from 1 to 3 GHz (Bluetooth). The applications are numerous: telephony and accessories, sport (connected shirts), medicine (probes: capsules, patches), etc. The changes thus made include, among others: optimization of OpenCL kernels for CPUs in order to make the best use of hybrid architectures; StarPU runtime experimentation; the design of an integration scheme using local time steps; and many optimizations allowing the solver to process simulations of several millions of cells.

Elektrische und magnetische Emitter können zur Erforschung unterschiedlicher plasmonischer Nanostrukturen genutzt werden. Indem wir die Änderung der Abstrahldynamik und in der Lebensdauer bestimmen, detektieren wir die photonische lokale Zustandsdichte. Diese Zustandsdichte, die eine Eigenschaft der Umgebung ist, ermöglicht uns nicht nur Rückschlüsse auf die elektronischen und andere physikalische Eigenschaften dieser zu treffen sondern auch die allgemeinen Eigenschaften der plasmonischen Nanostruktur im Bezug auf Licht-Materie Kopplung zu bestimmen. Eine starke Licht-Materie-Kopplung ist für die zukünftige Anwendung im Bereich der Quantentechnologien wichtig. Wenn Emitter hierbei mit plasmonischen Nanostrukturen koppeln, fokussieren letztere nicht nur das emittierte Lichts an der Oberfläche im Subwellenlängenbereich sondern ermöglichen durch die Feldüberhöhung an der Oberfläche auch eine starke Licht-Materie-Kopplung. In der Arbeit konzentrieren wir uns auf zwei grundlegend unterschiedliche plasmonische Systeme: zunächst untersuchen wir analytisch den Einfluss von Graphen auf elektrische und magnetische Emitter und diskutieren dann die Lebensdaueränderungen und Strahlungsdynamiken in der Nähe von Silber- und Goldnanostrukturen. Im ersten Teil der Arbeit analysieren wir den Einfluss von Graphen mit einer Bandlücke auf den Emitter und zeigen Möglichkeiten zur experimentellen Bestimmung der Bandlücke auf. Im zweiten Teil modellieren wir die Propagation elektromagnetischer Felder im dreidimensionalen Raum mit Hilfe der Diskontinuierlichen Galerkin Zeitraum Methode mit erweiterten Funktionalitäten. Diese verwenden wir sowohl zur theoretischen Modellierung des ersten dreidimensionalen Fluoreszenlebensdauerabbildungsmikroskopie mit einem einzelnen Quantenemitter als auch zur selbstkonsistent Beschreibung von Emittern in der Nähe eines Goldpentamers. Die Kombination der Studien betont die Stärke von Emittern elektrische, optische und magnetische Eigenschaften zu detektieren. / Electric and magnetic emitters can be used to probe different plasmonic nanostructures. By determining the modification of the radiation dynamics and the lifetimes, we can measure the photonic local density of states. This, being a property of the enviroment, does not only allow us to draw conclusions regarding the electronic and other physical properties of the latter but also regarding the general light-matter coupling properties of the plasmonic nanostructure. A strong light-matter coupling is important for future applications in quantum technology. If emitters couple specifically to plasmonic nanostructure, the latter do not only focus the emitted light at the sub-wavelength scale at the surface of the structure but also allow for such a strong light-matter coupling due to the field enhancement at the surface. In this work, we focus on two different basic plasmonic systems: first, we study analytically the influence of graphene on electric and magnetic emitters, and second we discuss lifetime modifications and radiation dynamics close to silver and gold nanostructures. In the first part of this work, we specifically focus on the influence of graphene exhibiting a finite band gap on the emitter. In the second part, we model the propagation of electromagnetic fields in three-dimensional space making use of the discontinuous Galerkin time-domain method with extended functionalities. This framework we apply to model the first three-dimensional scanning-probe fluorescence-lifetime imaging microscopy by use of a single quantum-emitter as well as for a self-consistent description of emitters in the proximity of a gold pentamer. The combination of these studies stress that the strength of emitters lies in the detection of electronic, optical and magnetic properties.