A QR accelerated volume-to-surface boundary condition for the finite-element solution of eddy-current problems

We are concerned with the solution of time-dependent electromagnetic eddy-current problems using a finite-element formulation on three-dimensional unstructured meshes. We allow for multiple conducting regions, and our goal is to develop an efficient computational method that does not require a computational mesh of the air/vacuum regions. This requires a sophisticated global boundary condition specifying the total fields on the conductor boundaries. To meet this requirement, we propose a volume-to-surface boundary condition based on the Biot-Savart law. We found the Biot-Savart approach to be very accurate. In addition, this approach can be accelerated via a low-rank QR approximation of the discretized Biot-Savart law.