Magnetic and Combined Field Integral Equations Based on the Quasi-Helmholtz Projectors

Boundary integral equation methods for analyzing electromagnetic scattering phenomena typically suffer from several of the following shortcomings: 1) ill-conditioning when the frequency is low; 2) ill-conditioning when the discretization density is high; 3) ill-conditioning when the structure contai...

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Bibliographic Details
Published in:IEEE transactions on antennas and propagation 2020-05, Vol.68 (5), p.3834-3846
Main Authors: Merlini, Adrien, Beghein, Yves, Cools, Kristof, Michielssen, Eric, Andriulli, Francesco P.
Format: Article
Language:English
Subjects:
Boundary integral method
Calderon strategies
combined field integral equations
Computational Physics
electric
Electric breakdown
Electric fields
Electromagnetic scattering
Frequency-domain analysis
Geometry
Ill-conditioned problems (mathematics)
Integral equations
magnetic
Magnetic resonance
Physics
preconditioning
Projectors
Scattering
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Summary:Boundary integral equation methods for analyzing electromagnetic scattering phenomena typically suffer from several of the following shortcomings: 1) ill-conditioning when the frequency is low; 2) ill-conditioning when the discretization density is high; 3) ill-conditioning when the structure contains global loops (which are computationally expensive to detect); 4) incorrect solution at low frequencies due to a loss of significant digits; and 5) the presence of spurious resonances. In this article, quasi-Helmholtz projectors are leveraged to obtain magnetic field integral equation (MFIE) that is immune to drawbacks 1)-4). Moreover, when this new MFIE is combined with a regularized electric field integral equation (EFIE), a new quasi-Helmholtz projector-combined field integral equation (CFIE) is obtained that also is immune to 5). The numerical results corroborate the theory and show the practical impact of the newly proposed formulations.
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2020.2964941