Three-dimensional finite-volume time-domain modeling of graphitic fault zones in the Athabasca Basin using unstructured grids

In this thesis, numerical modeling methods for geophysical time-domain electromag- netic (EM) problems and their applications in modeling graphitic faults in the Atha- basca Basin are investigated. A finite-volume time-domain numerical modeling method is developed. The method uses unstructured Delaunay-Voronoï dual meshes. Such unstructured meshes are more flexible and efficient when models containing geological units with complex geometries and topography need to be considered. A model build- ing procedure is established to construct arbitrarily complex models with topography. The procedure locally refines the mesh quality at certain areas such as loop sources and receivers in order to obtain better numerical results. For modeling time-domain EM problems, two approaches are used: the electric field approach and the potential approach. The electric field method directly solves the electric field Helmholtz equation while the potential method solves the Helmholtz equation expressed using vector and scalar potentials. The electric field method is simpler in theory and results in a smaller linear system of equations compared to potential methods. The potential method, on the other hand, is more complex intheory and a larger linear system of equations needs to be solved. However, using the potentials method enables the decomposition of the electric field into galvanic and inductive parts, which is helpful for understanding the physics behind the behaviour of the EM fields in the ground. In addition, the linear system of equations is better conditioned which potentially allows the use of iterative methods to solve it. Both methods are validated by comparing the modeling results with analytic solu- tions for homogeneous half-space models and numerical results for models presented in the literature. The modeling methods developed in this thesis are then applied to the modeling of real EM data collected in the Athabasca Basin. Thin, steeply dip- ping graphitic fault systems, which are linked to the formation of uranium deposits are present in the basin and have a large conductivity contrast with the background host. Because of the close relationship between the graphitic faults and the uranium deposits, time-domain EM surveys are important tools for uranium exploration in the basin. Geological models of the graphitic fault systems are discretized with unstruc- tured grids using the model building procedure developed in this thesis. Two real data sets that were previously collected from the Athabasca Basin are modeled and the modeling results are compared with the real data. The match between the calculated three-component responses and real data is good for models built based on geological information, drilling information, and trial-and-error. These models can help us to infer the complex geometry and conductivity features of the subsurface conductor be- yond the areas targeted by drilling. Therefore, 3D modeling of realistic, complicated real-life conductive targets such as in the uranium exploration in the Athabasca Basin or any other classic mineral exploration for a conductive target with complex shape is an important tool

A state of the art review of the Particle Finite Element Method (PFEM)

The particle finite element method (PFEM) is a powerful and robust numerical tool for the simulation of multi-physics problems in evolving domains. The PFEM exploits the Lagrangian framework to automatically identify and follow interfaces between different materials (e.g. fluid–fluid, fluid–solid or free surfaces). The method solves the governing equations with the standard finite element method and overcomes mesh distortion issues using a fast and efficient remeshing procedure. The flexibility and robustness of the method together with its capability for dealing with large topological variations of the computational domains, explain its success for solving a wide range of industrial and engineering problems. This paper provides an extended overview of the theory and applications of the method, giving the tools required to understand the PFEM from its basic ideas to the more advanced applications. Moreover, this work aims to confirm the flexibility and robustness of the PFEM for a broad range of engineering applications. Furthermore, presenting the advantages and disadvantages of the method, this overview can be the starting point for improvements of PFEM technology and for widening its application fields.Technology Innovation Program funded by the Ministry of Trade, Industry & Energy (MI, Korea), Grant/Award Number: 10053121; Universiti Teknologi PETRONAS (UTP) Internal Grant, Grant/Award Number: URIF 0153AAG24Peer ReviewedPostprint (published version

A 3D Unstructured Mesh FDTD Scheme for EM Modelling

The Yee finite difference time domain (FDTD) algorithm is widely used in computational electromagnetics because of its simplicity, low computational costs and divergence free nature. The standard method uses a pair of staggered orthogonal cartesian meshes. However, accuracy losses result when it is used for modelling electromagnetic interactions with objects of arbitrary shape, because of the staircased representation of curved interfaces. For the solution of such problems, we generalise the approach and adopt an unstructured mesh FDTD method. This co-volume method is based upon the use of a Delaunay primal mesh and its high quality Voronoi dual. Computational efficiency is improved by employing a hybrid primal mesh, consisting of tetrahedral elements in the vicinity of curved interfaces and hexahedral elements elsewhere. Difficulties associated with ensuring the necessary quality of the generated meshes will be discussed. The power of the proposed solution approach is demonstrated by considering a range of scattering and/or transmission problems involving perfect electric conductors and isotropic lossy, anisotropic lossy and isotropic frequency dependent chiral materials

Drift-diffusion models for innovative semiconductor devices and their numerical solution

We present charge transport models for novel semiconductor devices which may include ionic species as well as their thermodynamically consistent finite volume discretization

Méthode des éléments naturels appliquée aux problèmes électromagnétiques : développement d’un outil de modélisation et de conception des dispositifs électriques

In order to overcome the limitations related to the finite element method’s (FEM) narrow dependency of the solution on the mesh, meshless or meshfree methods were developed over the last 20 years. These techniques present the advantage of yielding very smooth approximations, being able to respond more adequately to the increasing demands of applications. However, some intrinsic features of most of these approaches make the implementation difficult, often requiring additional specific techniques for the imposition of the boundary conditions and the treatment of physical discontinuities. Recently, the natural element method (NEM) was developed. This approach, based on the Voronoi diagram and the “natural neighbors” concepts, combines the advantages of very smooth approximations and a FEM-like implementation. This thesis focuses on the study and development of the NEM, dedicated to electrical engineering applications. The main purpose of this exploratory work is the study of the limitations, benefits and the potential of the NEM and its underlying concepts. Several analyses of NEM’s performance are presented. As far as the numerical integration, higher order approximations and the vector interpolation are concerned, original developments are proposed.Afin de surmonter les difficultés de la méthode des éléments finis (MEF) liées à la forte dépendance de la solution au maillage, des méthodes sans maillage ont été développées durant les 20 dernières années. Ces techniques ont l’avantage de procurer des approximations très régulières, capables de répondre de manière plus satisfaisante aux exigences croissantes des applications. Cependant, certaines caractéristiques intrinsèques à la plupart de ces approches rendent leur mise en œuvre difficile : souvent des techniques supplémentaires spécifiques doivent être mises en place pour imposer les conditions aux limites et traiter les discontinuités physiques. Récemment, la méthode des éléments naturels (MEN) est apparue, se basant sur les concepts de diagramme de Voronoï et de voisins naturels. C’est une approche capable d’associer les avantages d’une approximation très régulière propre aux méthodes sans maillage et une mise en œuvre quasiment identique à la MEF. Cette thèse porte sur l’étude et le développement de la MEN dédiée aux applications du génie électrique. Le but principal de ce travail exploratoire est l’étude des limitations ainsi que des avantages et du potentiel de la MEN et ses concepts sous-jacents. Les analyses de performances de la méthode sont présentées. Sur les points ouverts tels que l’intégration numérique, la montée en ordre et l’interpolation vectorielle, des développements originaux sont proposés

Contributions dans le domaine de l'analyse multirésolution de maillages surfaciques semi-réguliers. Application à la compression géométrique

The goal of this work is to find solutions for the compression and the visualization of surface meshes at different levels of details. the first part is focused on static meshes, the second part is focused on dynamic meshes, used to represent 3D animations.L’objectif de cette thèse de doctorat est de proposer des solutions aux problèmes de compression et d’affichage de maillages surfaciques à plusieurs niveaux de détails. La première partie est réservée à l’étude des maillages statiques. La deuxième partie, elle concerne l’étude des maillagesdynamiques, où nous détaillons les solutions proposées pour les objets 3D animés