论文标题
与永久磁铁同步电动机应用的准椭圆形PDE的基础方法还原
Reduced basis methods for quasilinear elliptic PDEs with applications to permanent magnet synchronous motors
论文作者
论文摘要
在本文中，我们提出了用于准线性椭圆问题的经认证的还原方法（RB）方法，以及其在非线性磁静态方程中的应用，其中后来的模型永久性磁铁同步电动机（PMSM）。参数化通过域的几何形状进入，因此与非线性相结合，驱动了我们的还原问题。我们提供了一个基于残余的A-tosterii误差，该误差与贪婪的方法一起允许构建小尺寸的减小空间。我们使用经验插值方法（EIM）来保证有效的离线在线计算程序。然后，用牛顿方法的替代物获得减少的基础溶液。数值结果表明，与有限元方法相比，提出的减少基本方法提供了显着的计算增益。
In this paper, we propose a certified reduced basis (RB) method for quasilinear elliptic problems together with its application to nonlinear magnetostatics equations, where the later model permanent magnet synchronous motors (PMSM). The parametrization enters through the geometry of the domain and thus, combined with the nonlinearity, drives our reduction problem. We provide a residual-based a-posteriori error bound which, together with the Greedy approach, allows to construct reduced-basis spaces of small dimensions. We use the empirical interpolation method (EIM) to guarantee the efficient offline-online computational procedure. The reduced-basis solution is then obtained with the surrogate of the Newton's method. The numerical results indicate that the proposed reduced-basis method provides a significant computational gain, compared to a finite element method.
