Wind power is a rapidly increasing resource of electrical power world-wide. With the increasing number of wind turbines installed one major concern is the noise they generate. Sometimes already built wind turbines have to be put down or down-regulated, when certain noise levels are exceeded, resulting in economical and environmental losses. Therefore, accurate sound propagation calculations would be beneficial already in a planning stage of a wind farm. A model that can account for varying wind speeds and complex terrains could therefore be of great importance when future wind farms are planned. In this report an extended version of the classical wave equation that allows for variations in wind speed and terrain is derived which can be used to solve complex terrain and wind settings. The equation are solved with the use of Fourier transforms and Chebyshev polynomials and a numerical code is developed. The numerical code is evaluated against test cases where analytical and simple solutions exist. Tests with no wind for both totally free propagation and with a ground surface is evaluated in both 2D and 3D settings. For these simple cases the developed code shows good agreement to analytical solutions if the computational domain is sufficiently large. More advanced test cases with wind and terrain is not evaluated in this report and needs further validation. If the sound pressure needs to be calculated for a large area, and if the frequency is high, the developed model has problems regarding computational time and memory. These problems could be solved by further development of the numerical code or by using other solution methods.

This thesis presents the Differential Quadrature Method (DQM) for solving Helmholtz, modified Helmholtz and Helmholtz eigenvalue-eigenvector equations. The equations are discretized by using Polynomial-based and Fourier-based differential quadrature technique wich use basically polynomial interpolation for the solution of differential equation.

Mes travaux de thèse portent sur la construction de conditions aux limites absorbantes (CLAs) pour des problèmes de propagation d'ondes posés dans des milieux limités par des surfaces régulières. Ces conditions sont nouvelles car elles prennent en compte non seulement les ondes proagatives (comme la plupart des CLAs existantes) mais aussi les ondes évanescentes et rampantes. Elles sont donc plus performantes que les conditions existantes. De plus, elles sont facilement implémentables dans un schéma d'éléments finis de type Galerkine Discontinu (DG) et ne modifie pas la condition de stabilité de Courant-Friedrichs-Lewy (CFL). Ces CLAs ont été implémentées dans un code simulant la propagation des ondes acoustiques ainsi que dans un code simulant la propagation des ondes en régime harmonique. Les comparaisons réalisées entre les nouvelles conditions et celles qui sont les plus utilisées dans la littérature montrent que prendre en compte les ondes évanescentes et les ondes rampantes permet de diminuer les réflexions issues de la frontière artificielle et donc de rapprocher la frontière artificielle du bord de l'obstacle. On limite ainsi les coûts de calcul, ce qui est un des avantages de mes travaux. De plus, compte tenu du fait que les nouvelles CLAs sont écrites pour des frontières quelconques, elles permettent de mieux adapter le domaine de calcul à la forme de l'obstacle et permettent ainsi de diminuer encore plus les coûts de calcul numérique. / In my PhD, I have worked on the construction of absorbing boundary conditions (ABCs) designed for wave propagation problems set in domains bounded by regular surfaces. These conditions are new since they take into account not only propagating waves (as most of the existing ABCs) but also evanescent and creeping waves. Therefore, they outperform the existing ABCs. Moreover, they can be easily implemented in a discontinuous Galerkin finite element scheme and they do not change the Courant-Friedrichs-Lewy stability condition. These ABCs have been implemented in two codes that respectively simulate the propagation of acoustic waves and harmonic waves. The comparisons performed between these ABCs and the ABCs mostly used in the litterature show that when we take into account evanescent and creeping waves, we reduce the reflections coming from the artificial boundary. Therefore, thanks to these new ABCs, the artificial boundary can get closer to the obstacle. Consequently, we reduce the computational costs which is one of the advantages of my work. Moreover, since these new ABCs are written for any kind of boundary, we can adapt the shape of the computational domain and thus we can reduce again the computational costs.

The existence and -if exists- the nature of the solutions of the scalar wave equation in spacetimes with closed timelike curves are investigated. The general properties of the solutions on some class of spacetimes are obtained. Global monochromatic solutions of the scalar wave equation are obtained in flat wormholes of dimensions 2+1 and 3+1. The solutions are in the form of infinite series involving cylindirical and spherical wave functions and they are elucidated by the multiple scattering method. Explicit solutions for some limiting cases are illustrated as well. The results of 2+1 dimensions are verified by using numerical methods.

Cieľom predloženej diplomovej práce je numerické riešenie šírenia elektromagnetických vĺn v tuneli. Za týmto účelom bola sformulovaná integrálna rovnica a numericky riešená pomocou metódy hraničných prvkov (BEM). Implementácia v prostredí MATLAB sľubne poukazuje na nízke výpočtové nároky oproti štandardným diferenciálnych diskretizačným metódam. Súčasťou projektu je vykreslenie rozloženia elektromagnetického poľa pre rôzne profily tunelov. Overenie výsledkov je vykonané pomocou zjednodušeného analytického modelu. V rámci práce je pozorované štúdium vplyvov zmien profilu tunela a rôznych impedančných podmienok na stenách tunela na výsledné rozloženie elektromagnetického poľa vo vnútri tunela.