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Compact Equivalent Inverse of the Electric Field Integral Operator on Screens

by R. Hiptmair and C. Urzua-Torres

(Report number 2018-46)

Abstract
We study explicit inverses of the variational electric field boundary integral operator on orientable topologically simple Lipschitz screens. We describe them as solution operators of variational problems set in low-regularity standard trace spaces. On flat disks these variational problems do not involve the inversion of any non-local operators and supply an inverse up to a compact perturbation. This result lays the foundation for operator preconditioning for the discretized electric field integral equation.

Keywords: Boundary integral operators; Electric field integral equation; Screens; Hodge decomposition

@Techreport{HU18_800,
  author = {R. Hiptmair and C. Urzua-Torres},
  title = {Compact Equivalent Inverse of the Electric Field Integral
Operator on Screens},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2018-46},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2018/2018-46.pdf },
  year = {2018}
}

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