A reproducing kernel method with nodal interpolation property

By Jiun-Shyan Chen, Weimin Han, Y. You, Xueping Meng. 2003

98 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/43ca57d36e1c8f021a2c86adc872051123bed7fb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Wing Kam Liu
2. Gang Li
3. Dong-dong Wang
4. Hongsheng Lu
5. Shaofan Li
6. Xiaozhong Jin
7. N. Aluru
8. Zhenting Lin

In Electrical and Electronic Engineering

1. Zhenting Lin
2. Weimin Han
3. Wing Kam Liu
4. Shaofan Li
5. Jian Cao
6. Hongsheng Lu
7. Dong-dong Wang
8. C. Bucher

In Mechanics of Materials

1. Dong-dong Wang
2. Xiaozhong Jin
3. Zhenting Lin
4. N. Aluru
5. Gang Li
6. Wing Kam Liu
7. Hongsheng Lu
8. Shaofan Li

Citations in the corpus

• Positivity conditions in meshless collocation methods (2004, background): “In meshless approximations, there are various ways to satisfy the first positivity condition [23–26].”
• Reproducing kernel element method. Part I: Theoretical formulation (2004, methodology): “, Lagrangian multiplier technique [2], transformation technique [6], hierarchical enrichment technique [13,29], reproducing kernel interpolation technique [5], singular kernel function technique [6,17], collocation technique [30], window or correction function [10], and use of D Alembert s principle”
• Imposing essential boundary conditions in mesh-free methods (2004, unknown): “This approach has been generalized in [18] to get a nodal interpolation property.”
• Reproducing kernel element method Part III: Generalized enrichment and applications (2004, background): “The extra degrees of freedom associated with high order derivative can be considered as enrichment terms [4,6,11,31,36] to improve the accuracy of numerical solution through increasing the consistency order or enriching the specified enrichment functions.”
• Meshfree Methods: Progress Made after 20 Years (2017, unknown): “MLS and RK methods that have interpolation property can also be constructed (Chen et al. 2003).”
• Dispersion and transient analyses of Hermite reproducing kernel Galerkin meshfree method with sub-domain stabilized conforming integration for thin beam and plate structures (2011, methodology): “The meshfree methods [1–7] based on unstructured particle discretrization of problem domain allows a straightforward construction of arbitrary high order global conforming approximation, i.”
• New concepts for moving least squares: An interpolating non-singular weighting function and weighted nodal least squares (2008, methodology): “In [13] and [14] special procedures for reproducing kernel methods are presented, where a mixed interpolation based on a normalized kernel function to impose Kronecker delta property and an enrichment function which constitutes reproducing conditions are combined.”
• Extended isogeometric analysis for simulation of stationary and propagating cracks (2012, methodology): “Several methods have been developed to impose essential boundary conditions effectively, such as the Lagrange multiplier method [1], the penalty method [16] the Nitsche’s method [17] and the reproducing kernel nodal interpolation method [18].”