Stabilization of RBF-generated finite difference methods for convective PDEs
Stabilization of RBF-generated finite difference methods for convective PDEs
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DOI：
10.1016/j.jcp.2010.12.014
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发表时间：
2011-03-20
影响因子：
4.1
通讯作者：
Lehto, Erik
中科院分区：
文献类型：
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作者：
Fornberg, Bengt;Lehto, Erik
径向基函数 (RBF) 作为求解偏微分方程的工具而受到广泛关注，因为它们能够通过非结构化节点布局实现谱精度。这样的节点集提供了几何灵活性和局部节点细化的机会。尽管达到相同的精度需要更多的节点总数，RBF 生成的有限差分 (RBF-FD) 方法可以显着节省计算机资源（时间和内存）。这项研究提出了一种新的过滤机制，使得对于自然不具有任何稳定耗散特征的纯对流偏微分方程也能实现这种增益。 (C) 2010 Elsevier Inc. 保留所有权利。
Radial basis functions (RBFs) are receiving much attention as a tool for solving PDEs because of their ability to achieve spectral accuracy also with unstructured node layouts. Such node sets provide both geometric flexibility and opportunities for local node refinement. In spite of requiring a somewhat larger total number of nodes for the same accuracy, RBF-generated finite difference (RBF-FD) methods can offer significant savings in computer resources (time and memory). This study presents a new filter mechanism, allowing such gains to be realized also for purely convective PDEs that do not naturally feature any stabilizing dissipation. (C) 2010 Elsevier Inc. All rights reserved.