A QR Accelerated Volume-to-Surface Boundary Condition for the Finite-Element Solution of Eddy-Current Problems

Abstract

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. We propose a Biot-Savart law based volume-to-surface boundary condition to meet this requirement. This Biot-Savart approach is demonstrated to be very accurate. In addition, this approach can be accelerated via a low-rank QR approximation of the discretized Biot-Savart law. Index TermsMaxwell's equations, computational electromagnetics, low-rank approximation, Biot-Savart law, eddy currents, electromagnetic diffusion, parallel processing.