Super-convergence of reproducing kernel approximation
Super-convergence of reproducing kernel approximation
复制标题
再现核近似的超收敛性
DOI：
10.1016/j.cma.2019.04.038
复制
发表时间：
2019
影响因子：
7.2
通讯作者：
Foster, John T.
中科院分区：
文献类型：
--
作者：
Leng, Yu;Tian, Xiaochuan;Foster, John T.
再生核质点法（RKPM）是一种产生于力学领域的无网格方法，特别适用于处理大变形和奇异性问题。当插值阶p为偶数时，我们给出了再生核（RK）逼近在Sobolev范数下的超收敛性的理论分析。超收敛现象是指收敛速度高于一般期望的阶数。我们区分了连续RK近似和离散RKP近似。当p为偶数时，连续的RK近似被证明是超收敛的，而离散的RK近似只有在粒子分布均匀、RK核函数和支撑尺寸有特殊选择的情况下才具有超收敛性。此外，超收敛不存在的离散RKP近似与一般的RK支持大小。然后引入伪超收敛的概念，解释了为什么在理论上不成立，但在实践中有时在一般情况下观察到超收敛现象。我们的分析是一般的多维RK近似。
The reproducing kernel particle methods (RKPM) are meshfree methods arising in mechanics, especially in dealing with problems involving large deformation and singularities. We provide a theoretical analysis of super-convergence in Sobolev norms for reproducing kernel (RK) approximations when the interpolation order p is even. Super-convergence phenomenon means the convergence rate is higher than the order that is generally expected. We distinguish the continuous RK approximation and the discrete RKP approximation. While the continuous RK approximations are proven to be super-convergent when p is even, its discrete counterpart has super-convergence only with uniform particle distribution and special choices of RK kernel functions and support sizes. Moreover, super-convergence does not exist for the discrete RKP approximation with general RK support sizes. The concept of pseudo-super-convergence is then introduced to explain why in practice the super-convergence phenomenon is sometimes observed for general cases although in theory it is not true. Our analysis is general for multi-dimensional RK approximations.
影响因子：
1.7
作者：
W. Han;Wing Kam Liu
通讯作者：
Wing Kam Liu
DOI：
10.1002/fld.1650200824
发表时间：
1995-04-30
影响因子：
1.8
作者：
LIU, WK;JUN, S;ZHANG, YF
通讯作者：
ZHANG, YF
影响因子：
4.1
作者：
Chen, JS;Pan, C;Wu, CT
通讯作者：
Wu, CT