Domain Decomposition Methods for Time-Harmonic Electromagnetic Waves with High Order Whitney Forms

Marsic, Nicolas; Waltz, Caleb; Lee, Jin-Fa; Geuzaine, Christophe

doi:10.1109/TMAG.2015.2476510

Download

Article (Scientific journals)

Domain Decomposition Methods for Time-Harmonic Electromagnetic Waves with High Order Whitney Forms

Marsic, Nicolas; Waltz, Caleb; Lee, Jin-Fa et al.

2016 • In IEEE Transactions on Magnetics, 52 (3)

Peer Reviewed verified by ORBi

Permalink
https://hdl.handle.net/2268/194883

DOI
10.1109/TMAG.2015.2476510

Files (1)Send to Details Statistics Bibliography Similar publications

Files

Full Text

preprint_hoddm.pdf

Author preprint (337.95 kB)

Download

All documents in ORBi are protected by a user license.

Send to

RIS BibTex APA Chicago Permalink X Linkedin

Details

Keywords :

Computational electromagnetics; Domain decomposition; Finite element analysis; High performance computing

Abstract :

[en] Classically, domain decomposition methods (DDM) for time-harmonic electromagnetic wave propagation problems make use of the standard, low order, Nédélec basis functions. This paper analyzes the convergence rate of DDM when higher order finite elements are used for both volume and interface discretizations, in particular when different orders are used in the volume and on the interfaces.

Disciplines :

Electrical & electronics engineering

Author, co-author :

Marsic, Nicolas ; Université de Liège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)

Waltz, Caleb; The Ohio State University > ElectroScience Laboratory

Lee, Jin-Fa; The Ohio State University > ElectroScience Laboratory

Geuzaine, Christophe ; Université de Liège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)

Language :

English

Title :

Domain Decomposition Methods for Time-Harmonic Electromagnetic Waves with High Order Whitney Forms

Publication date :

2016

Journal title :

IEEE Transactions on Magnetics

ISSN :

0018-9464

eISSN :

1941-0069

Publisher :

IEEE, Piscataway, United States - New Jersey

Volume :

Issue :

Peer reviewed :

Peer Reviewed verified by ORBi

Tags :

CÉCI : Consortium des Équipements de Calcul Intensif
Tier-1 supercomputer

Funders :

FRIA - Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture
BELSPO - Service Public Fédéral de Programmation Politique scientifique

Available on ORBi :

since 24 March 2016

Statistics

Number of views

132 (16 by ULiège)

Number of downloads

368 (9 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

O. G. Ernst and M. J. Gander, "Why it is difficult to solve Helmholtz problems with classical iterative methods," in Numerical Analysis of Multiscale Problems (Lecture Notes in Computational Science and Engineering), vol. 83, I. G. Graham, T. Y. Hou, O. Lakkis, and R. Scheichl, Eds. Berlin, Germany: Springer-Verlag, 2012, pp. 325-363
B. Després, P. Joly, and J. E. Roberts, "A domain decomposition method for the harmonic Maxwell equations," in Iterative Methods Linear Algebra. Amsterdam, The Netherland: North-Holland. 1992, pp. 475-484
C. Geuzaine et al., "An open source domain decomposition solver for time-harmonic electromagnetic wave problems," in Proc. IEEE Conf. Antenna Meas. Appl. (CAMA), Nov. 2014, pp. 1-4
J.-C. Nédélec, "Mixed finite elements in R3," Numer. Math., vol. 35, no. 3, pp. 315-341, 1980
F. Ihlenburg and I. BabuŜka, "Finite element solution of the Helmholtz equation with high wave number part II: The h-p version of the FEM," SIAM J. Numer. Anal., vol. 34, no. 1, pp. 315-358, 1997
S. Zaglmayr, "High order finite element methods for electromagnetic field computation," Ph.D. dissertation, Dept. Inst. für Numer. Math., Johannes Kepler Univ. Linz, Linz, Austria, 2006
N. Marsic and C. Geuzaine, "Efficient finite element assembly of high order Whitney forms," IET Sci. Meas. Technol., vol. 9, no. 2, pp. 204-210, Mar. 2015
V. Rawat and J.-F. Lee, "Nonoverlapping domain decomposition with second order transmission condition for the time-harmonic Maxwell's equations," SIAM J. Sci. Comput., vol. 32, no. 6, pp. 3584-3603, 2010
M. El Bouajaji, B. Thierry, X. Antoine, and C. Geuzaine, "A quasioptimal domain decomposition algorithm for the time-harmonic Maxwell's equations," J. Comput. Phys., vol. 294, no. 1, pp. 38-57, Aug. 2015
S. Balay et al., "PETSc users manual, revision 3.5," Dept. Math. Comput. Sci., Argonne Nat. Lab., Lemont, IL, USA, Tech. Rep. ANL-95/11, 2014
P. R. Amestoy, I. S. Duff, J.-Y. L'Excellent, and J. Koster, "A fully asynchronous multifrontal solver using distributed dynamic scheduling," SIAM J. Matrix Anal. Appl., vol. 23, no. 1, pp. 15-41, 2001
L. C. Shen and J. A. Kong, Applied Electromagnetism. Pacific Grove, CA, USA: PWS, 1995
F. Ihlenburg and I. BabuŜka, "Finite element solution of the Helmholtz equation with high wave number part I: The h-version of the FEM," Comput. Math. Appl., vol. 30, no. 9, pp. 9-37, 1995
A. Nicolet, G. Demesy, F. Zolla, and B. Vial, "Quasi-modal analysis of segmented waveguides," in Proc. IEEE Conf. Antenna Meas. Appl. (CAMA), Nov. 2014, pp. 1-4
A. Vion and C. Geuzaine, "Double sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem," J. Comput. Phys., vol. 266, pp. 171-190, Jun. 2014