The coupling of complex variable-reproducing kernel particle method and finite element method for two-dimensional potential problems

2010 ◽  
Vol 3 (3) ◽  
pp. 277-298 ◽  
Author(s):  
Li Chen ◽  
K.M. Liew ◽  
Yumin Cheng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Complex Variable ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Two Dimensional ◽  
Reproducing Kernel Particle Method ◽  
Potential Problems ◽  
Reproducing Kernel Particle ◽  
Element Method

scholarly journals Enrichment of the Finite Element Method With the Reproducing Kernel Particle Method

1997 ◽  
Vol 64 (4) ◽  
pp. 861-870 ◽  
Author(s):  
Wing Kam Liu ◽  
R. A. Uras ◽  
Y. Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Computational Procedure ◽  
Reproducing Kernel Particle Method ◽  
The Finite Element Method ◽  
Window Functions ◽  
Reproducing Kernel Particle ◽  
Element Method

The reproducing kernel particle method (RKPM) has attractive properties in handling high gradients, concentrated forces, and large deformations where other widely implemented methodologies fail. In the present work, a multiple field computational procedure is devised to enrich the finite element method with RKPM, and RKPM with analytical functions. The formulation includes an interaction term that accounts for any overlap between the fields, and increases the accuracy of the computational solutions in a coarse mesh or particle grid. By replacing finite element method shape Junctions at selected nodes with higher-order RKPM window functions, RKPM p-enrichment is obtained. Similarly, by adding RKPM window functions into a finite element method mesh, RKPM hp-enrichment is achieved analogous to adaptive refinement. The fundamental concepts of the multiresolution analysis are used to devise an adaptivity procedure.

The meshless method for two-dimensional space-time fractional dispersion equation based on reproducing kernel particle method

2017 ◽  
Vol 06 (02) ◽  
pp. 1750015
Author(s):  
Rongjun Cheng ◽  
Fengxin Sun ◽  
Jufeng Wang
Keyword(s):  
Dispersion Equation ◽  
Reproducing Kernel ◽  
Convergence Rates ◽  
Dimensional Space ◽  
Particle Method ◽  
Equation System ◽  
Approximation Schemes ◽  
Two Dimensional ◽  
Reproducing Kernel Particle Method ◽  
Reproducing Kernel Particle

The two-dimensional space fractional dispersion equation (SFDE) is obtained from the standard dispersion equation by replacing the two second-order space derivatives by the Riemann–Liouville fractional derivatives. A numerical analysis of the two-dimensional SFDE is presented based on the reproducing kernel particle method (RKPM). The final algebraic equation system is obtained by employing Galerkin weak form and functional minimization procedure. The Riemann–Liouville operator is discretized by the shifted Grünwald formula. The fully-discrete approximation schemes for SFDE are established using center difference method and RKPM and the shifted Grünwald formula. Numerical simulations for SFDE with known exact solution were presented in the format of the tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error estimate of RKPM for SFDE has been analyzed, which shows that this method has reasonable convergence rates in spatial and temporal discretizations.

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