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Electromagnetic device modeling using a new adaptive wavelet finite element method

机译:使用新型自适应小波有限元方法的电磁设备建模

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Wavelets provide sparse representations of integral and differential operators through a multiresolution approximation. This property is well-suited for adaptive implementation of numerical techniques, which is a common topic among researchers nowadays. The current state of the wavelet theory also allows flexible construction of transforms customized to certain applications, which is an important feature considering that the generalization of wavelet techniques to a large class of real-world numerical simulations is still limited. In this paper, it is proposed an adaptive wavelet finite element method for achieving operator-orthogonality between approximation spaces, a property which eliminates coupling among levels of resolution - a common shortcoming of adaptive methods. The resulting method is easily extended to any given finite element application and requires less computation power when compared to other adaptive techniques. These features are showcased by comparing the proposed technique to the popular h-refinement method using electromagnetic device simulations involving Dirichlet and Neumann boundary conditions, inhomogeneous and non-linear media, and irregular meshes.
机译:小波通过多分辨率近似提供了积分和微分算子的稀疏表示。此属性非常适合数字技术的自适应实现,这是当今研究人员的常见话题。小波理论的当前状态还允许针对特定应用定制的变换的灵活构造,这是一个重要特征,考虑到小波技术对大量实际数值模拟的推广仍然受到限制。在本文中,提出了一种自适应小波有限元方法,用于实现近似空间之间的算子正交性,该属性消除了分辨率级别之间的耦合,这是自适应方法的一个普遍缺陷。与其他自适应技术相比,所得方法很容易扩展到任何给定的有限元应用,并且需要较少的计算能力。通过将提议的技术与流行的h精炼方法进行比较来展示这些特征,该方法使用涉及Dirichlet和Neumann边界条件,非均匀和非线性介质以及不规则网格的电磁设备模拟。

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