论文标题
能量稳定的全球径向基函数方法逐个求和表格
Energy-stable global radial basis function methods on summation-by-parts form
论文作者
论文摘要
径向基函数方法是数值分析中强大的工具，并且在许多不同的模拟中都证明了良好的特性。但是，对于时间依赖的部分偏微分方程，仅知道少数稳定性结果。特别是，如果包括边界条件，则经常发生稳定性问题。我们在本文中解决的问题是如何获得RBF方法的可证明的稳定性。我们使用经常在有限差和有限元社区中经常使用的逐个式操作员的一般框架来开发和构建能量稳定的径向基函数方法。
Radial basis function methods are powerful tools in numerical analysis and have demonstrated good properties in many different simulations. However, for time-dependent partial differential equations, only a few stability results are known. In particular, if boundary conditions are included, stability issues frequently occur. The question we address in this paper is how provable stability for RBF methods can be obtained. We develop and construct energy-stable radial basis function methods using the general framework of summation-by-parts operators often used in the Finite Difference and Finite Element communities.
