论文标题
混合RBF-FD和WLS无网状强近似方法
A hybrid RBF-FD and WLS mesh-free strong-form approximation method
论文作者
论文摘要
由于无网格方法作为用于偏微分方程（PDE）系统数值分析的工具，因此已经提出了许多差分操作员近似的变体。在这项工作中，我们提出了一种无局部的无网格强方法，该方法结合了径向基函数生成的有限差异（RBF-FD）的稳定性与弥漫性近似方法（DAM）的计算有效性，形成了所谓的混合方法。为了证明混合方法的优势，我们通过在计算域中用指数强的来源解决了二维泊松问题，评估了获得的数值解决方案的计算复杂性和准确性。最后，我们采用混合方法来解决各向同性半空间上的三维Boussinesq问题，并表明实现开销可以证明是合理的。
Since the advent of mesh-free methods as a tool for the numerical analysis of systems of Partial Differential Equations (PDEs), many variants of differential operator approximation have been proposed. In this work, we propose a local mesh-free strong-form method that combines the stability of Radial Basis Function-Generated Finite Differences (RBF-FD) with the computational effectiveness of Diffuse Approximation Method (DAM), forming a so-called hybrid method. To demonstrate the advantages of a hybrid method, we evaluate its computational complexity and accuracy of the obtained numerical solution by solving a two-dimensional Poisson problem with an exponentially strong source in the computational domain. Finally, we employ the hybrid method to solve a three-dimensional Boussinesq's problem on an isotropic half-space and show that the implementation overhead can be justified.
