High order edge finite element approximations for the time-harmonic Maxwell's equations

Marcella Bonazzoli; Elena Gaburro; Victorita Dolean; Francesca Rapetti

doi:10.1109/CAMA.2014.7003328

High order edge finite element approximations for the time-harmonic Maxwell's equations

Marcella Bonazzoli, Elena Gaburro, Victorita Dolean, Francesca Rapetti

Mathematics And Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

5 Citations (Scopus)

Abstract

The time-harmonic Maxwell's equations model the propagation of electromagnetic waves and are therefore fundamental equations for the simulation of many modern devices in everyday life. The numerical solution of these equations is hampered by some fundamental problems especially in the high frequency regime. Fine meshes have to be used in order to accurately represent the solution and also to avoid the pollution effect, which is very well known for the Helmholtz equations. We propose in this paper to address this problem by considering high order finite element approximations and in particular Whitney edge elements.

Original language	English
Title of host publication	2014 IEEE Conference on Antenna Measurements and Applications, CAMA 2014
Place of Publication	Piscataway, NJ
Publisher	IEEE
Number of pages	4
ISBN (Electronic)	9781479936786
DOIs	https://doi.org/10.1109/CAMA.2014.7003328
Publication status	Published - 8 Jan 2015
Event	2014 IEEE Conference on Antenna Measurements and Applications, CAMA 2014 - Antibes Juan-les-Pins, France Duration: 16 Nov 2014 → 19 Nov 2014

Conference

Conference	2014 IEEE Conference on Antenna Measurements and Applications, CAMA 2014
Country/Territory	France
City	Antibes Juan-les-Pins
Period	16/11/14 → 19/11/14

Keywords

Maxwell's equations
Helmholtz equations

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10.1109/CAMA.2014.7003328

Cite this

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title = "High order edge finite element approximations for the time-harmonic Maxwell's equations",

abstract = "The time-harmonic Maxwell's equations model the propagation of electromagnetic waves and are therefore fundamental equations for the simulation of many modern devices in everyday life. The numerical solution of these equations is hampered by some fundamental problems especially in the high frequency regime. Fine meshes have to be used in order to accurately represent the solution and also to avoid the pollution effect, which is very well known for the Helmholtz equations. We propose in this paper to address this problem by considering high order finite element approximations and in particular Whitney edge elements.",

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Bonazzoli, M, Gaburro, E, Dolean, V & Rapetti, F 2015, High order edge finite element approximations for the time-harmonic Maxwell's equations. in 2014 IEEE Conference on Antenna Measurements and Applications, CAMA 2014., 7003328, IEEE, Piscataway, NJ, 2014 IEEE Conference on Antenna Measurements and Applications, CAMA 2014, Antibes Juan-les-Pins, France, 16/11/14. https://doi.org/10.1109/CAMA.2014.7003328

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AU - Bonazzoli, Marcella

AU - Gaburro, Elena

AU - Dolean, Victorita

AU - Rapetti, Francesca

PY - 2015/1/8

Y1 - 2015/1/8

N2 - The time-harmonic Maxwell's equations model the propagation of electromagnetic waves and are therefore fundamental equations for the simulation of many modern devices in everyday life. The numerical solution of these equations is hampered by some fundamental problems especially in the high frequency regime. Fine meshes have to be used in order to accurately represent the solution and also to avoid the pollution effect, which is very well known for the Helmholtz equations. We propose in this paper to address this problem by considering high order finite element approximations and in particular Whitney edge elements.

AB - The time-harmonic Maxwell's equations model the propagation of electromagnetic waves and are therefore fundamental equations for the simulation of many modern devices in everyday life. The numerical solution of these equations is hampered by some fundamental problems especially in the high frequency regime. Fine meshes have to be used in order to accurately represent the solution and also to avoid the pollution effect, which is very well known for the Helmholtz equations. We propose in this paper to address this problem by considering high order finite element approximations and in particular Whitney edge elements.

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KW - Helmholtz equations

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U2 - 10.1109/CAMA.2014.7003328

DO - 10.1109/CAMA.2014.7003328

M3 - Conference contribution book

AN - SCOPUS:84946530850

BT - 2014 IEEE Conference on Antenna Measurements and Applications, CAMA 2014

PB - IEEE

CY - Piscataway, NJ

T2 - 2014 IEEE Conference on Antenna Measurements and Applications, CAMA 2014

Y2 - 16 November 2014 through 19 November 2014

ER -

High order edge finite element approximations for the time-harmonic Maxwell's equations

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