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Annales Des Télécommunications

, Volume 40, Issue 7–8, pp 331–340 | Cite as

Quelques méthodes numériques pour résoudre des équations en électromagnétisme

  • Tapan K. Sarkar
  • Ercument Arvas
Applications des Techniques Numériques et Analytiques aux Antennes
  • 29 Downloads

Analyse

L’objet de cet article est de décrire plusieurs méthodes souvent utilisées pour résoudre des problèmes numériques en électromagnétisme. Jusqu’ à présent, la méthode matricielle a été couramment employée. Un des objectifs principaux de cette présentation est d’introduire une nouvelle classe de méthodes itératives qui, par rapport aux méthodes matricielles classiques, présentent l’avantage de pouvoir spécifier à l’avance le degré de précision avec lequel le problème sera résolu. De plus, les solutions de ces méthodes itératives (et en particulier la méthode du gradient conjugué) convergent vers la solution de l’équation en un nombre fini d’itérations, quelle que soit la valeur initiale.

Mots clés

Electromagnétisme Equation intégrodifférentielle Résolution équation Méthode numérique Méthode matricielle Itération, Problème bien posé Fonction propre Méthode moment Méthode gradient conjugué 

A survey of various numerical techniques to solve operator equations in electromagnetics

Abstract

The objective of this paper is to survey many of the popular methods utilized in solving numerical problems arising in electromagnetics. Historically, the matrix methods have been quite popular. One of the primary objectives of this paper is to introduce a new class of iterative methods, which have advantages over the classical matrix methods in the sense that a given problem may be solved to a prespecified degree of accuracy. Also, these iterative methods (particularly conjugate gradient methods) converge to the solution in a finite number of steps irrespective of the initial starting guess. Numerical examples have been presented to illustrate the principles.

Key words

Electromagnetism Integrodifferential equation Equation resolution Digital method Matrix method Iteration Well posed problem Eigenfunction Moment method Conjugate gradient method 

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Copyright information

© Institut Telecom / Springer-Verlag France 1985

Authors and Affiliations

  • Tapan K. Sarkar
    • 1
  • Ercument Arvas
    • 1
  1. 1.Department of Electrical Engineering Rochester Institute of TechnologyRochesterUSA

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