This article develops a data-driven magnetostatic finite-element (FE) solver that directly exploits the measured material data instead of a material curve constructed from it. The distances between the field solution and the measurement points are minimized while enforcing Maxwell’s equations. The minimization problem is solved by employing the Lagrange multiplier approach. The procedure wraps the FE method within an outer data-driven iteration. The method is capable of considering anisotropic materials and is adapted to deal with models featuring a combination of exact material knowledge and measured material data. Thereto, three approaches with an increasing level of intrusivity according to the FE formulation are proposed. The numerical results for a quadrupole-magnet model show that data-driven field simulation is feasible and affordable and overcomes the need of modeling the material law.

中文翻译：

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使用数据驱动的材料建模进行磁场仿真

本文开发了一种数据驱动的静磁有限元 (FE) 求解器，该求解器直接利用测量的材料数据，而不是从中构建的材料曲线。在执行麦克斯韦方程组的同时，场解和测量点之间的距离被最小化。最小化问题通过采用拉格朗日乘数方法来解决。该过程将 FE 方法包装在外部数据驱动的迭代中。该方法能够考虑各向异性材料，适用于处理具有精确材料知识和实测材料数据相结合的模型。此外，根据有限元公式，提出了三种侵入性增加的方法。