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H-$\Phi$ Field Formulation with Lumped Sources and Unbounded Domains

by D. Casati and J. Smajic and R. Hiptmair

(Report number 2019-33)

Abstract
We consider a $\mathbf{H}$-$\Phi$ field formulation to solve 3D frequency-domain eddy-current problems. This formulation uses vector and scalar tetrahedral finite elements within, respectively, the conductive and nonconductive domain. It can handle multiply-connected regions and eliminates the need to compute the source current density and source magnetic field before the actual simulation. We propose three ways to couple finite elements with the Multiple Multipole Program (MMP) and solve this $\mathbf{H}$-$\Phi$ variational form on an unbounded domain. MMP is a method that uses exact solutions of the homogeneous equations as basis functions (the so-called ''multipoles''). The desired behavior at infinity is given by the chosen multipoles: this eliminates the need of artificially truncating the computational domain. Interface conditions between the FEM and MMP domains allow to express the coupled FEM–MMP problem.

Keywords: Maxwell equations, Electromagnetic analysis, Finite element analysis, Numerical simulation

@Techreport{CSH19_837,
  author = {D. Casati and J. Smajic and R. Hiptmair},
  title = {H-$\Phi$ Field Formulation with Lumped Sources and Unbounded Domains},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2019-33},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2019/2019-33.pdf },
  year = {2019}
}

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