Convergence of the natural hp-BEM for the electric field integral equation on polyhedral surfaces

A. Bespalov; N. Heuer; R. Hiptmair

doi:10.1137/090766620

Convergence of the natural hp-BEM for the electric field integral equation on polyhedral surfaces

A. Bespalov, N. Heuer, R. Hiptmair

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the variational formulation of the electric field integral equation on bounded polyhedral open or closed surfaces. We employ a conforming Galerkin discretization based on divΓ-conforming Raviart-Thomas boundary elements of locally variable polynomial degree on shape-regular surface meshes. We establish asymptotic quasi optimality of Galerkin solutions on sufficiently fine meshes or for sufficiently high polynomial degrees. © 2010 Society for Industrial and Applied Mathematics.

Original language	English
Pages (from-to)	1518-1529
Number of pages	11
Journal	SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume	48
Issue number	4
DOIs	https://doi.org/10.1137/090766620
Publication status	Published - 2010

Keywords

Boundary element method
Electric field integral equation
Electromagnetic scattering
Galerkin discretization
Hp-refinement
Noncoercive variational problems
Projection-based interpolation
Smoothed Poincaré mapping

Access to Document

10.1137/090766620

http://siamdl.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=SJNAAM000048000004001518000001&idtype=cvips

Cite this

@article{09538627c2a74b969d28d4a951fd4b58,

title = "Convergence of the natural hp-BEM for the electric field integral equation on polyhedral surfaces",

abstract = "We consider the variational formulation of the electric field integral equation on bounded polyhedral open or closed surfaces. We employ a conforming Galerkin discretization based on divΓ-conforming Raviart-Thomas boundary elements of locally variable polynomial degree on shape-regular surface meshes. We establish asymptotic quasi optimality of Galerkin solutions on sufficiently fine meshes or for sufficiently high polynomial degrees. {\textcopyright} 2010 Society for Industrial and Applied Mathematics.",

keywords = "Boundary element method, Electric field integral equation, Electromagnetic scattering, Galerkin discretization, Hp-refinement, Noncoercive variational problems, Projection-based interpolation, Smoothed Poincar{\'e} mapping",

author = "A. Bespalov and N. Heuer and R. Hiptmair",

year = "2010",

doi = "10.1137/090766620",

language = "English",

volume = "48",

pages = "1518--1529",

journal = "SIAM JOURNAL ON NUMERICAL ANALYSIS",

publisher = "Society for Industrial and Applied Mathematics",

number = "4",

}

TY - JOUR

T1 - Convergence of the natural hp-BEM for the electric field integral equation on polyhedral surfaces

AU - Bespalov, A.

AU - Heuer, N.

AU - Hiptmair, R.

PY - 2010

Y1 - 2010

N2 - We consider the variational formulation of the electric field integral equation on bounded polyhedral open or closed surfaces. We employ a conforming Galerkin discretization based on divΓ-conforming Raviart-Thomas boundary elements of locally variable polynomial degree on shape-regular surface meshes. We establish asymptotic quasi optimality of Galerkin solutions on sufficiently fine meshes or for sufficiently high polynomial degrees. © 2010 Society for Industrial and Applied Mathematics.

AB - We consider the variational formulation of the electric field integral equation on bounded polyhedral open or closed surfaces. We employ a conforming Galerkin discretization based on divΓ-conforming Raviart-Thomas boundary elements of locally variable polynomial degree on shape-regular surface meshes. We establish asymptotic quasi optimality of Galerkin solutions on sufficiently fine meshes or for sufficiently high polynomial degrees. © 2010 Society for Industrial and Applied Mathematics.

KW - Boundary element method

KW - Electric field integral equation

KW - Electromagnetic scattering

KW - Galerkin discretization

KW - Hp-refinement

KW - Noncoercive variational problems

KW - Projection-based interpolation

KW - Smoothed Poincaré mapping

U2 - 10.1137/090766620

DO - 10.1137/090766620

M3 - Article

VL - 48

SP - 1518

EP - 1529

JO - SIAM JOURNAL ON NUMERICAL ANALYSIS

JF - SIAM JOURNAL ON NUMERICAL ANALYSIS

IS - 4

ER -

Convergence of the natural hp-BEM for the electric field integral equation on polyhedral surfaces

Abstract

Keywords

Access to Document

Fingerprint

Cite this