A scalar boundary integrodifferential equation for eddy current problems using an impedance boundary condition

Abstract

At low frequencies the time harmonic electromagnetic fields exterior to a lossy, highly conducting and possibly magnetic body can be described by the eddy current approximation of Maxwell’s equations with impedance or Leontovich [18] boundary conditions if the so called penetration depth is small. We show how to reduce this problem to a scalar, hypersingular boundary integral equation (BIE) on the surface Γ of the conductor. Strong ellipticity of the associated nonsymmetric, hypersingular operator is established. Convergence of O(〈 ∇/∈ ) of the Ohmic losses for piecewise linear, continuous boundary elements is established theoretically and numerically.