Purpose

The purpose of this paper is to use different model order reduction techniques to cope with the computational effort of solving large systems of equations. By appropriate decomposition of the electromagnetic field problem, the number of degrees of freedom (DOF) can be efficiently reduced. In this contribution, the Proper Generalized Decomposition (PGD) and the Proper Orthogonal Decomposition (POD) are used in the frame of the T-Ω-formulation, and the feasibility is elaborated.

Design/methodology/approach

The POD and the PGD are two methods to reduce the model order. Particularly in the context of eddy current problems, conventional time-stepping algorithms can lead to many numerical simulations of the studied problem. To simulate the transient field, the T-Ω-formulation is used which couples the magnetic scalar potential and the electric vector potential. In this paper, both methods are studied on an academic example of an induction furnace in terms of accuracy and computational effort.

Findings

Using the proposed reduction techniques significantly reduces the DOF and subsequently the computational effort. Further, the feasibility of the combination of both methods with the T-Ω-formulation is given, and a fundamental step toward fast simulation of eddy current problems is shown.

Originality/value

In this paper, the PGD is combined for the first time with the T-Ω-formulation. The application of the PGD and POD and the following comparison illustrate the great potential of these techniques in combination with the T-Ω-formulation in context of eddy current problems.

中文翻译：

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模型阶数减少技术应用于磁动力T-Ω公式

目的

本文的目的是使用不同的模型降阶技术来解决求解大型方程组的计算工作。通过适当分解电磁场问题，可以有效地减少自由度（DOF）的数量。在此贡献中，在T-Ω-公式的框架中使用了适当的广义分解（PGD）和适当的正交分解（POD），并阐述了可行性。

设计/方法/方法

POD和PGD是减少模型顺序的两种方法。特别是在涡流问题的背景下，常规的时间步长算法可以导致所研究问题的许多数值模拟。为了模拟瞬态场，使用了T-Ω-公式，该公式将磁标量电势和矢量势耦合。在本文中，就准确性和计算量而言，在一个感应炉的学术实例上研究了这两种方法。

发现

使用提出的归约技术会大大降低自由度，从而减少计算量。此外，给出了将这两种方法与T-Ω-公式相结合的可行性，并显示了快速模拟涡流问题的基本步骤。

创意/价值

在本文中，PGD首次与T-Ω-公式结合使用。PGD​​和POD的应用以及以下比较说明，在涡流问题的背景下，这些技术与T-Ω-配方相结合的巨大潜力。