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A scalar potential formulation and translation theory for the time-harmonic Maxwell equations

dc.contributor.authorGumerov, Nail A.
dc.contributor.authorDuraiswami, Ramani
dc.description.abstractWe develop a computational method based on a scalar potential representation, which efficiently reduces the solution of Maxwell’s equations to the solution of two scalar Helmholtz equations. One of the key contributions of this paper is a theory for the translation of Maxwell solutions using such a representation, since the scalar potential form is not invariant with respect to translations. The translation theory is developed by introducing “conversion” operators, which enable the representation of the electric and magnetic vector fields via scalar potentials in an arbitrary reference frame. Advantages of this representation include the fact that only two Helmholtz equations need be solved, and moreover, the divergence free constraints are satisfied automatically, by construction. The availability of a translation theory for this representation can find application in methods such as the Fast Multipole Method. For illustration of the use of the representation and translation theory we implemented an algorithm for the simulation of Mie scattering off a system of spherical objects of different sizes and dielectric properties using a variant of the T-matrix method. The resulting system was solved using an iterative method based on GMRES. The results of the computations agree well with previous computational and experimental results.en
dc.format.extent1157086 bytes
dc.relation.ispartofseriesDepartment of Computer Science Technical Reportsen
dc.relation.ispartofseriesInstitute for Advanced Computer Studiesen
dc.subjectMaxwell's equationsen
dc.subjectScalar potentialen
dc.subjectFast Multipole Methodsen
dc.subjectTranslation theoryen
dc.subjectMultiple Scatteringen
dc.subjectMie Scatteringen
dc.titleA scalar potential formulation and translation theory for the time-harmonic Maxwell equationsen
dc.typeTechnical Reporten
dc.relation.isAvailableAtCollege of Computer, Methematical & Physical Sciencesen_us
dc.relation.isAvailableAtComputer Scienceen_us
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_us
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_us

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