论文标题
源稳定的线性移动导体问题的Galerkin配方具有边缘元素
The Source Stabilized Galerkin Formulation for Linear Moving Conductor Problems with Edge Elements
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
The phenomenon of linear motion of conductor in a magnetic field is commonly found in electric machineries such as, electromagnetic brakes, linear induction motor, electromagnetic flowmeter etc. The design and analysis of the same requires an accurate evaluation of induced currents and the associated reaction magnetic fields. The finite element method is a generally employed numerical technique for this purpose. However, it needs stabilization techniques to provide an accurate solution. In this work, such a stabilization technique is developed for the edge elements. The stability and hence the accuracy is brought in by a suitable representation of the source term. The stability and accuracy of the proposed scheme is first shown analytically and then demonstrated with the help of 2D and 3D simulations. The proposed scheme is parameter-free and it would require a graded regular mesh along the direction of motion.
