Theory of Characteristic Modes for Nonsymmetric Surface Integral Operators
The theory of characteristic modes is formulated with nonsymmetric surface integral operators for perfect electric conductors, impedance surfaces, and homogeneous dielectric bodies. For nonsymmetric (nonself-adjoint) operators, the eigenvectors are not orthogonal with respect to the weighted inner p...
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| Vydáno v: | IEEE transactions on antennas and propagation Ročník 69; číslo 3; s. 1505 - 1512 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York
IEEE
01.03.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-926X, 1558-2221 |
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| Abstract | The theory of characteristic modes is formulated with nonsymmetric surface integral operators for perfect electric conductors, impedance surfaces, and homogeneous dielectric bodies. For nonsymmetric (nonself-adjoint) operators, the eigenvectors are not orthogonal with respect to the weighted inner product defined with the weighting operator of the generalized eigenvalue equation. Rather, this orthogonality holds between the eigenvectors of the original equation and the adjoint equation, including adjoint operators. This implies that the modal expansion, used to express any scattering or radiation solution as a linear combination of the modes, requires these two sets of eigenvectors. For matrix equations, the eigenvectors of the adjoint equation correspond to the left eigenvectors of the original equation. |
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| AbstractList | The theory of characteristic modes is formulated with nonsymmetric surface integral operators for perfect electric conductors, impedance surfaces, and homogeneous dielectric bodies. For nonsymmetric (nonself-adjoint) operators, the eigenvectors are not orthogonal with respect to the weighted inner product defined with the weighting operator of the generalized eigenvalue equation. Rather, this orthogonality holds between the eigenvectors of the original equation and the adjoint equation, including adjoint operators. This implies that the modal expansion, used to express any scattering or radiation solution as a linear combination of the modes, requires these two sets of eigenvectors. For matrix equations, the eigenvectors of the adjoint equation correspond to the left eigenvectors of the original equation. |
| Author | Wallen, Henrik Yla-Oijala, Pasi |
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| Cites_doi | 10.1109/TAP.1971.1139999 10.1007/978-3-031-01707-0 10.1093/acprof:oso/9780198508885.001.0001 10.1109/TAP.2019.2905794 10.1049/el:19820681 10.1109/LAWP.2011.2155022 10.1109/TAP.2017.2708094 10.1109/TAP.2019.2948509 10.1109/TMTT.2007.908678 10.1109/TAP.2015.2452938 10.1109/TAP.2017.2741063 10.1109/TAP.2017.2772873 10.1002/jnm.2627 10.1109/TAP.2018.2835313 10.1109/TAP.1972.1140154 10.1109/TAP.2016.2543756 |
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| SubjectTerms | Adjoint operator characteristic modes (CMs) Conductors dielectric object Dielectrics Eigenvalues Eigenvalues and eigenfunctions Eigenvectors Electric conductors Impedance impedance boundary condition (IBC) Integral equations Integrals Magnetic resonance imaging Operators (mathematics) Orthogonality perfect electric conductor (PEC) Scattering Surface impedance surface integral operator |
| Title | Theory of Characteristic Modes for Nonsymmetric Surface Integral Operators |
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