In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element‐free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced‐order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced‐order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two‐dimensional cases.

中文翻译：

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不可压缩磁流体动力学流的适当正交分解变分多尺度无网格无插值Galerkin方法

在最近的十年中，由于无网格方法的简便性，已经解决了用于解决大多数PDE的无网格方法。无网格方法是一种流行的无网格方法（EFG），该方法最初是为解决固体力学中的某些问题而提出的。EFG的测试和试用功能基于特殊基础。近来，已经开发了一些修改以改进EFG方法。这些改进之一是变分多尺度EFG程序。在当前的文章中，插值移动最小二乘近似的形状函数已应用于变分多尺度EFG技术，以解决不可压缩的磁流体动力学流。为了减少仿真所花费的CPU时间，我们基于适当的正交分解技术采用了降阶模型。当前的组合可以称为降阶变分多尺度EFG技术。为了说明所使用的CPU时间的减少以及所提方法的效率，我们将其应用于二维情况。