The Neural Network Approach to Automatic Construction of Adaptive Meshes on Multiply-connected Domains

O. Nechaeva
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引用次数: 1

Abstract

The neural network approach to automatic construction of adaptive meshes, which we have developed for simply-connected domains, is here extended to the case of multiply-connected domains, i.e. those with holes. This approach is based on Kohonen's self-organizing maps (SOM) and refers to a class of methods in which an adaptive mesh is a result of transformation of a fixed uniform mesh. Within the approach, a composite algorithm has been proposed in which the SOM algorithm is applied alternatively to boundary and interior mesh nodes. In the case of multiply-connected domains, this algorithm is applied to specify automatically the holes in a fixed mesh. Also, a modified composite algorithm is proposed that provides the consistency of SOM algorithms alternatively applied to both the outer and inner borders and to the interior of the domain. The mesh smoothing algorithm is proposed for multiply-connected domains. The quality of the resulting meshes is admissible according to generally accepted quality criteria.
多连通域自适应网格自动构建的神经网络方法
我们为单连通域开发的自动构建自适应网格的神经网络方法,在这里被扩展到多连通域,即那些有孔的域。该方法基于Kohonen的自组织映射(SOM),指的是一类将固定均匀网格转换为自适应网格的方法。在该方法中,提出了一种复合算法,其中SOM算法交替应用于边界和内部网格节点。在多个连通域的情况下,该算法可以自动指定固定网格中的孔。此外,还提出了一种改进的复合算法,该算法提供了SOM算法在域的内外边界和内部交替应用的一致性。提出了多连通域的网格平滑算法。根据普遍接受的质量标准,所得网格的质量是可以接受的。
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