Maxwell's equations in bicomplex (quaternion) form: An alternative to the Helmholtz P.D.E.

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dc.contributor.author Anastassiu, HT en
dc.contributor.author Atlamazoglou, PE en
dc.contributor.author Kaklamani, DI en
dc.date.accessioned 2014-03-01T02:41:56Z
dc.date.available 2014-03-01T02:41:56Z
dc.date.issued 2001 en
dc.identifier.uri https://dspace.lib.ntua.gr/xmlui/handle/123456789/30675
dc.subject Closed Form Solution en
dc.subject Differential Equation en
dc.subject Helmholtz Equation en
dc.subject Inhomogeneous Media en
dc.subject Magnetic Field en
dc.subject Second Order Equation en
dc.subject Vector Field en
dc.subject First Order en
dc.subject.other Digital signal processing en
dc.subject.other Maxwell equations en
dc.subject.other Permittivity en
dc.subject.other Vectors en
dc.subject.other Bicomplex numbers en
dc.subject.other Electromagnetic wave propagation en
dc.title Maxwell's equations in bicomplex (quaternion) form: An alternative to the Helmholtz P.D.E. en
heal.type conferenceItem en
heal.identifier.primary 10.1109/DIPED.2001.965025 en
heal.identifier.secondary http://dx.doi.org/10.1109/DIPED.2001.965025 en
heal.publicationDate 2001 en
heal.abstract The concept of bicomplex numbers is introduced in Electromagnetics, with direct application to the solution of Maxwell's equations. It is shown that, with the assistance of a bicomplex vector field, defined as a combination of the electric and the magnetic fields, the number of unknown quantities is practically reduced by half, whereas the Helmholtz equation may no longer be necessary in the development of the final solution. Bicomplex, first order differential equations are involved, instead of conventional, complex second order equations, and the solution procedure is greatly simplified. A direct consequence of this observation is the derivation of closed form solutions of the Maxwell's equations for a special class of inhomogeneous media, which cannot be easily extracted from the Helmholtz equation alone. en
heal.journalName Proceedings of 6th International Seminar/Workshop on: Direct and Inverse problems of Electromagnetic and Acoustic Wave Theory en
dc.identifier.doi 10.1109/DIPED.2001.965025 en
dc.identifier.spage 20 en
dc.identifier.epage 24 en

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