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

TL;DR

This paper introduces a data-driven magnetostatic finite element solver that directly uses real-world measurement data to solve 3D problems, bypassing traditional material models, and demonstrates its effectiveness on an inductor model.

Contribution

It develops a novel data-driven approach for 3D magnetostatic problems that directly incorporates measurement data into the finite element solver, enhancing practical applicability.

Findings

The data-driven solver recovers conventional solutions with increasing data cardinality.

It is applicable to complex 3D problems with real measurement data.

The approach is computationally feasible for demanding 3D simulations.

Abstract

This paper presents a practical case study of a data-driven magnetostatic finite element solver applied to a real-world three-dimensional problem. 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 the measurement data. The data-driven formulation results in a minimization problem with a Lagrange multiplier, where the sought solution must conform to Maxwell's equations while at the same time being closest to the available measurement data. The data-driven solver is applied to a three-dimensional model of an inductor excited by a DC-current. Numerical results for data sets of increasing cardinality verify that the data-driven solver recovers the conventional solution. Furthermore, this work concludes that the data-driven magnetostatic finite element solver is applicable to computationally demanding three-dimensional problems. Simulations with real world measurement data further show the practical usability of the solver.