Result: Coupling of the ultra-weak variational formulation and an integral representation using a fast multipole method in electromagnetism

Title:
Coupling of the ultra-weak variational formulation and an integral representation using a fast multipole method in electromagnetism
Authors:
DARRIGRAND, E, MONK, P
Source:
The seventh international conference on mathematical and numerical aspects of waves (WAVES'05)Journal of computational and applied mathematics. 204(2):400-407
Publisher Information:
Amsterdam: Elsevier, 2007.
Publication Year:
2007
Physical Description:
print, 10 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Fonctions spéciales, Special functions, Equations intégrales, Integral equations, Théorie des opérateurs, Operator theory, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Algorithme, Algorithm, Algoritmo, Analyse numérique, Numerical analysis, Análisis numérico, Complexité algorithme, Algorithm complexity, Complejidad algoritmo, Condition aux limites, Boundary condition, Condiciones límites, Electromagnétisme, Electromagnetism, Electromagnetismo, Equation Maxwell, Maxwell equation, Ecuación Maxwell, Indice conditionnement, Condition number, Numero de condicionamiento, Maillage, Grid pattern, Celdarada, Mathématiques appliquées, Applied mathematics, Matemáticas aplicadas, Méthode élément fini, Finite element method, Método elemento finito, Opérateur intégral, Integral operator, Operador integral, Représentation intégrale, Integral representation, Representación integral, Résolution problème, Problem solving, Resolución problema, Surface, Superficie, 33E10, 45P05, 47Gxx, ABC, Fast multipole method, Ultra-weak variational formulation
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
IRMAR.Université de Rennes I. Campus de Beaulieu, 35042 Rennes, France
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, United States
ISSN:
0377-0427
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=18782973
Rights:
Copyright 2007 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.18782973
Database:
PASCAL Archive

Further Information

Many different methods have been developed for the solution of the time-harmonic Maxwell equations in exterior domains at high frequency. Volume-based methods have the drawback of needing an artificial boundary far from the obstacle. Integral formulations enable one to avoid this difficulty by solving a problem on the surface of the obstacle. However, integral operators imply dense systems with bad condition numbers. The ultra-weak variational formulation (UWVF) is a volume-based method using plane wave basis functions that allows the use of a coarser mesh in comparison with more classical low order finite element methods. However, the UWVF still involves the problem of the artificial boundary. In this paper, we suggest the use of an integral representation of the unknown field to obtain an exact artificial boundary condition. In this way the distance between the obstacle and the artificial boundary can be reduced. The use of the fast multipole method ensures a low cost for the calculation of various integral operators used in the representation. In this paper we describe the combined algorithm, demonstrate its accuracy on a model problem and discuss the complexity of the algorithm.