A point collocation method based on reproducing kernel approximations

By N. Aluru. 2000

252 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/67007ef5fbc002612b60f00cfac67fa932251a4b

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In Civil and Structural Engineering

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Error analysis of collocation method based on reproducing kernel approximation (2011, methodology): “Since this approach requires taking higher order derivatives of the MLS approximation functions, several enhanced methods have been proposed based on RK approximation with derivative reproducing conditions [28] or diffuse derivatives [29].”
Voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids (2003, methodology): “The model di usion problem in Equation (13) is solved using a nite di erence method, or equivalently a point collocation scheme [59].”
Least squares moving particle semi-implicit method (2014, methodology): “In this analysis, MLS interpolant [50] with consistent derivative, MLSRKPM interpolant [65] with consistent derivative, standard LSMPS scheme type-A, standard LSMPS scheme type-B, and meshfree compact scheme are appropriated.”
The meshless finite element method (2003, methodology): “Liu et al. [10,11] have used the RPKM in a weak form, while Aluru [ 12 ] used it in a strong form.”
Positivity conditions in meshless collocation methods (2004, methodology): “From the consistency conditions [10], XNP i1⁄41 NiðxÞQûðxiÞ 1⁄4 XNP i1⁄41 NiðxÞ Z”
Meshfree point collocation method with intrinsic enrichment for interface problems (2007, methodology): “O ˜ nate et al. [9] and Aluru [ 10 ] suggestedacollocationmethodwithmovingleastsquare approximationswithfixedkernelfunctions.However,in their methods, because of the fixity of the kernel function, the approximation and derivatives could only be evaluated at the nodes.”
On the Equivalence Between Least-Squares and Kernel Approximations in Meshless Methods (2001, methodology): “Numerical results indicate that the improved finite cloud method exhibits superior convergence characteristics compared to our original implementation [Aluru and Li (2001)] of the finite cloud method.”
Meshfree Methods: Progress Made after 20 Years (2017, unknown): “On a different path, discrete bonded particle methods have been developed and coupled with FEM for similar applications (Beissel et al. 2006; Johnson 1994; Johnson et al. 1986, 2000, 2002, 2013) [for a review, see (Johnson 2011)].”