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A quadrilateral edge element scheme with minimum dispersion

by R. Hiptmair and P. Ledger

(Report number 2003-17)

Abstract
This paper describes a novel quadrilateral edge element discretisation of Maxwell's equations in which the effects of dispersion are minimised. A modified edge finite element stencil is proposed and it is subsequently shown how this can be expressed in terms of new material coefficients thus allowing us to incorporate both Dirchlet and Neumann boundary conditions in a natural fashion. To demonstrate the success of the proposed procedure, we include a series numerical examples. First we apply the approach to plane and circular wave propagation problems. Secondly, we apply the approach to a series of electromagnetic scattering problems. For the electromagnetic scattering computations, we monitor the effect of the modified edge finite element stencil on the scattering width output. We use a hp-edge element code as a benchmark for all our electromagnetic scattering computations.

Keywords:

@Techreport{HL03_44,
  author = {R. Hiptmair and P. Ledger},
  title = {A quadrilateral edge element scheme with minimum dispersion},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2003-17},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2003/2003-17.pdf },
  year = {2003}
}

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