Data-driven electromagnetic field simulation with a material-model-free finite element solver

This work presents a data-driven finite element magnetic field solver which bypasses material law modelling by directly incorporating material measurements into the solver. The data-driven solver seeks for a field solution that conforms to Maxwell’s equations while at the same time being closest to the given measurement data. The data-driven finite element formulation is described by a two-step minimization based on Lagrange multipliers. The resulting data-driven solver is applied to a two-dimensional quadrupole magnet model. Numerical results for data sets of increasing cardinality verify that the datadriven solution converges to the classical solution on the basis of a nonlinear material curve, here obtained with the Newton algorithm.