Three-Dimensional Data-Driven Magnetostatic Field Computation using Real-World Measurement Data

Abstract

Purpose -The purpose of this paper is to present the applicability of data-driven solvers to computationally demanding three-dimensional problems and their practical usability when utilizing real-world measurement data. Design/methodology/approach -Instead of using a hard-coded phenomenological material model within the solver, the data-driven computing approach reformulates the boundary value problem such that the field solution is directly computed on raw measurement data. The data-driven formulation results in a double minimization problem based on Lagrange multipliers, where the sought solution must conform to Maxwell's equations while at the same time being as close as possible to the available measurement data. The data-driven solver is applied to a three-dimensional model of an inductor excited by a DC-current. Findings -Numerical results for data sets of increasing cardinality verify that the data-driven solver recovers the conventional solution. Additionally, the practical usability of the solver is shown by utilizing real-world measurement data. This work concludes that the data-driven magnetostatic finite element solver is applicable to computationally demanding three dimensional problems, as well as in cases where a prescribed material model is not available. Originality -While the mathematical derivation of the data-driven problem is well presented in the referenced papers, the application to computationally demanding real-world problems, including real measurement data and its rigorous discussion is missing. The presented work closes this gap and shows the applicability of data-driven solvers to challenging, real-world test cases.