Error analysis of the finite element method calculations depending on the operating range

Abstract

Paper presents an analysis of the FEM modeling error in the function of the simulation range. Test was conducted on the open-source Finite Element Method software, which utilizes Whitney edge elements for solving Maxwell’s equations. Simulations focused on the magnetic flux distribution around the Helmholtz coils setup. Due to the utilization of analytically solvable example, comparison of simulation results with reliable reference result was possible. Simulations were conducted on a typical Helmholtz coils setup powered by constant current. In order to simulate electromagnetic phenomenon in the air surrounding the setup, both coils were placed in sphere, which provided proper simulation space. Also, the external surface of the sphere is utilized for application of boundary conditions for the differential equations solved during the modeling. Thus, proper selection of the simulation range is crucial for obtaining reliable results. On the other hand, utilization of excessively large simulation space significantly increases computation cost. This paper focuses on the optimization of a modeling range in the function of obtaining reliable and accurate results by minimization of modeling error, as well as on minimization of computation time.