Abstract:
The problem of scattering has been extensively studied due to its broad range of application. Examples go from radar sensing to free space communications passing through medical ultrasound and acoustic tiling among others. In particular the physical formulation for the electromagnetic case derives from Maxwell's equation. Even further, assuming time-harmonic dependence of the resulting fields we can summarize Maxwell's equation into just one type of differential equation: the Helmholtz equation. Standard methods for solving Helmholtz's equation rely on substituting the differential equation by an integral equation on the constraint boundary. In cases in which the obstacle presents edges or a non regular boundary, such critical points induce singularities on the solution of the integral equation. This implies that finding a solution by numerical methods become a challenging task. We introduce here a novel solver for the integral equation derived from the transverse electric high frequency scattering problem in 2 by a screen obstacle. It involves not only state of the art numerical techniques such as the Fourier Continuation but also new ones introduced in this work. We recall that by an solver we mean that under a prescribed error tolerance the size of the involved matrices will remain constant as k increases and therefore the after all cost of computation too. This property is of very important numerical value not only because of the computing cost but also due to the memory constraints of the hardware. In chapter 1 we will deduce the Helmholtz equation from Maxwell's equations and study the corresponding solution space. Later on, in chapter 2 we obtain the fundamental solution for the equation and introduce some operators used to state the boundary integral equation. Chapter 3 presents the integral equation that we solve as well as our ansatz for the representation formula of the solution. In order to develop our solver we make use of some results of asymptotic theory regarding highly oscillatory functions. Also we will make use of recently presented close forms for integral with logarithmic singularities. Such tools are shown in chapter 4. The development of our solver involves solving highly oscillatory coupled equations. In chapter 5 we introduce a novel method for solving such equations numerically: the Pinot Method. In chapter 6 we describe the Fourier Continuation Method and introduce some new spectral quadratures developed for this work. Finally, the solver is presented in chapter 7 together with numerical results.
Citación:
---------- APA ----------
Carossi, Pedro Agustín. (2016). Métodos de alta frecuencia para el problema de dispersión electromagnética. (Tesis de Grado. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales.). Recuperado de https://hdl.handle.net/20.500.12110/seminario_nMAT000970_Carossi
---------- CHICAGO ----------
Carossi, Pedro Agustín. "Métodos de alta frecuencia para el problema de dispersión electromagnética". Tesis de Grado, Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales, 2016.https://hdl.handle.net/20.500.12110/seminario_nMAT000970_Carossi
Estadísticas:
Descargas mensuales
Total de descargas desde :
https://bibliotecadigital.exactas.uba.ar/download/seminario/seminario_nMAT000970_Carossi.pdf
Distrubución geográfica
