REPRODUCING KERNEL PARTICLE METHODS
REPRODUCING KERNEL PARTICLE METHODS
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DOI：
10.1002/fld.1650200824
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发表时间：
1995-04-30
影响因子：
1.8
通讯作者：
ZHANG, YF
中科院分区：
文献类型：
--
作者：
LIU, WK;JUN, S;ZHANG, YF
开发了一个新的连续再现内核插值功能，该功能探讨了窗口函数的灵活时频和空间波数定位的吸引力。该方法是由小波理论激励的，并且还具有最近提出的平滑粒子流体动力学（SPH）方法的理想属性，移动最小二乘方法（MLSM），弥漫元素方法（DEM）和无元素的galerkin方法（EFGM） 。所提出的方法维持了免费的拉格朗日或SPH方法的优势；但是，由于添加了校正函数，它给出了更准确的结果。因此，它称为再现核粒子方法（RKPM）。在计算机实施中，rkpm比DEM和EFGM更有效。此外，如果窗口函数是c-内度，则解决方案及其衍生物在整个域中也是C-内度。一维扩散方程的理论分析和数值实验揭示了扩张参数对所提出方法异常高的收敛速率的影响。对流扩散方程和可压缩欧拉方程的二维示例也与2D多尺度分解一起呈现。
A new continuous reproducing kernel interpolation function which explores the attractive features of the flexible time-frequency and space-wave number localization of a window function is developed. This method is motivated by the theory of wavelets and also has the desirable attributes of the recently proposed smooth particle hydrodynamics (SPH) methods, moving least squares methods (MLSM), diffuse element methods (DEM) and element-free Galerkin methods (EFGM). The proposed method maintains the advantages of the free Lagrange or SPH methods; however, because of the addition of a correction function, it gives much more accurate results. Therefore it is called the reproducing kernel particle method (RKPM). In computer implementation RKPM is shown to be more efficient than DEM and EFGM. Moreover, if the window function is C-infinity, the solution and its derivatives are also C-infinity in the entire domain. Theoretical analysis and numerical experiments on the 1D diffusion equation reveal the stability conditions and the effect of the dilation parameter on the unusually high convergence rates of the proposed method. Two-dimensional examples of advection-diffusion equations and compressible Euler equations are also presented together with 2D multiple-scale decompositions.