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You searched for subject:(extinction theorem). Showing records 1 – 2 of 2 total matches.

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University of Illinois – Urbana-Champaign

1. Yan, Su. Accuracy improvement of the second-kind Fredholm integral equations in computational electromagnetics.

Degree: MS, 1200, 2012, University of Illinois – Urbana-Champaign

In computational electromagnetics, the second-kind Fredholm integral equations (IEs) are known to have very fast iterative convergence but rather poor solution accuracy compared with the first-kind Fredholm integral equations. The loss of the numerical accuracy is mainly due to the discretization error of the identity operators involved in second-kind IEs. In the past decade, although much effort has been made to improve the numerical accuracy of the second-kind integral equations, no conclusive understandings and final resolutions are achieved. In this thesis, the widely used surface integral equations in computational electromagnetics are first presented along with the discussions of their respective mathematical and numerical properties. The integral operators involved in these integral equations are investigated in terms of their mathematical properties and numerical discretization strategies. Based on such discussions and investigations, a numerical scheme is presented to significantly suppress the discretization error of the identity operators by using the Buffa-Christiansen (BC) functions as the testing function, leading to much more accurate solutions to the second-kind integral equations for smooth objects in both perfect electric conductor (PEC) and dielectric cases, while maintaining their fast convergence properties. This technique is then generalized for generally shaped objects in both PEC and dielectric cases by using the BC functions as the testing functions, and by handling the near-singularities in the evaluation of the system matrix elements carefully. The extinction theorem is applied for accurate evaluation of the numerical errors in the calculation of scattering problems for generally shaped objects. Several examples are given to investigate and demonstrate the performance of the proposed techniques in the accuracy improvement of the second-kind surface integral equations in both PEC and dielectric cases. The reasons for the accuracy improvement are explained, and several important conclusive remarks are made. Advisors/Committee Members: Jin, Jianming (advisor).

Subjects/Keywords: Accuracy analysis; Buffa-Christiansen functions; extinction theorem; first-kind integral equations; identity operator; magnetic-field integral equation; method of weighted residuals; near-singularity extraction; N-Müller integral equations; numerical accuracy; Rayleigh-Ritz scheme; second-kind integral equations; testing scheme.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Yan, S. (2012). Accuracy improvement of the second-kind Fredholm integral equations in computational electromagnetics. (Thesis). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/34442

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Yan, Su. “Accuracy improvement of the second-kind Fredholm integral equations in computational electromagnetics.” 2012. Thesis, University of Illinois – Urbana-Champaign. Accessed February 24, 2020. http://hdl.handle.net/2142/34442.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Yan, Su. “Accuracy improvement of the second-kind Fredholm integral equations in computational electromagnetics.” 2012. Web. 24 Feb 2020.

Vancouver:

Yan S. Accuracy improvement of the second-kind Fredholm integral equations in computational electromagnetics. [Internet] [Thesis]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Feb 24]. Available from: http://hdl.handle.net/2142/34442.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Yan S. Accuracy improvement of the second-kind Fredholm integral equations in computational electromagnetics. [Thesis]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/34442

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

2. Le, Vi. Processus de branchement avec interaction : Branching processes with interaction.

Degree: Docteur es, Mathématiques, 2014, Aix Marseille Université

Cette thèse se compose de quatre chapitres:Le chapitre 1 étudie la distribution du temps de coalescence (plus récent ancêtre commun) de deux individus tirés au hasard (uniformly) dans la génération actuelle d'un processus de Bienaymé-Galton-Watson en temps continu.Dans le chapitre 2, nous obtenons une représentation de la diffusion de Feller logistique en termes des temps locaux d'un mouvement brownien réfléchi H avec une dérive qui est affine en le temps local accumulé par H à son niveau actuel.Le chapitre 3 considère la diffusion de Feller avec compétition générale. Nous donnons des conditions précises sur le terme de la concurrence, pour le but de décider si le temps d'extinction (qui est aussi la hauteur du processus) reste borné ou non lorsque la taille initiale de la population tend vers l'infini, et de même pour la masse totale du processus.Dans le chapitre 4, nous généralisons les résultats du chapitre 3 pour le cas du processus de branchement à espace d'état continu avec compétition à trajectoires discontinues.

This thesis consists of four chapters:Chapter 1 investigates the distribution of the coalescence time (most recent common ancestor) for two individuals picked at random (uniformly) in the current generation of a continuous time Bienaymé-Galton-Watson process.In chapter 2 we obtain a Ray-Knight representation of Feller's branching diffusion with logistic growth in terms of the local times of a reflected Brownian motion H with a drift that is affine in the local time accumulated by H at its current level.Chapter 3 considers the Feller's branching diffusion with general competition. We give precise conditions on the competition term, in order to decide whether the extinction time (which is also the height of the process) remains or not bounded as the initial population size tends to infinity, and similarly for the total mass of the process.In chapter 4 we generalize the results of chapter 3 to the case of continuous state branching process with competition which has discontinuous paths.

Advisors/Committee Members: Pardoux, Etienne (thesis director).

Subjects/Keywords: Processus de Bienaymé-Galton-Watson; Coalescence; Diffusion de Feller logistique; Temps local; Théorème de Ray-Knight; Processus de branchement; Compétition; Temps d'extinction; Masse totale; Bienaymé-Galton-Watson process; Coalescence; Feller diffusion with logistic growth; Local time; Ray-Knight theorem; Branching process; Competition; Extinction time; Total mass

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Le, V. (2014). Processus de branchement avec interaction : Branching processes with interaction. (Doctoral Dissertation). Aix Marseille Université. Retrieved from http://www.theses.fr/2014AIXM4743

Chicago Manual of Style (16th Edition):

Le, Vi. “Processus de branchement avec interaction : Branching processes with interaction.” 2014. Doctoral Dissertation, Aix Marseille Université. Accessed February 24, 2020. http://www.theses.fr/2014AIXM4743.

MLA Handbook (7th Edition):

Le, Vi. “Processus de branchement avec interaction : Branching processes with interaction.” 2014. Web. 24 Feb 2020.

Vancouver:

Le V. Processus de branchement avec interaction : Branching processes with interaction. [Internet] [Doctoral dissertation]. Aix Marseille Université 2014. [cited 2020 Feb 24]. Available from: http://www.theses.fr/2014AIXM4743.

Council of Science Editors:

Le V. Processus de branchement avec interaction : Branching processes with interaction. [Doctoral Dissertation]. Aix Marseille Université 2014. Available from: http://www.theses.fr/2014AIXM4743

.