Weighted radial basis collocation method for boundary value problems

By Hsin‐Yun Hu, Jiun-Shyan Chen, Wei Hu. 2007

128 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/b7e62378242d7b08a642b2f08dcdb977da04f1ff

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. Jiun-Shyan Chen
2. Sheng-Wei Chi
3. Cheng‐Tang Wu
4. Lihua Wang
5. Hsin‐Yun Hu
6. C. Park
7. Wei Hu
8. Guirong Liu

In Electrical and Electronic Engineering

1. Jiun-Shyan Chen
2. Lihua Wang
3. Sheng-Wei Chi
4. Hsin‐Yun Hu
5. Cheng‐Tang Wu
6. C. Park
7. Wei Hu
8. Guirong Liu

In Mechanics of Materials

1. Jiun-Shyan Chen
2. Sheng-Wei Chi
3. Cheng‐Tang Wu
4. Lihua Wang
5. Hsin‐Yun Hu
6. C. Park
7. Wei Hu
8. Guirong Liu

Citations in the corpus

• A generalized approximation for the meshfree analysis of solids (2011, methodology): “However, they are limited to smallscale problems because of their non-locality and have been enhanced by the weighted radial basis collocation method [7] and the combined reproducing kernel (RK) and RBF approximation [8].”
• Subdomain radial basis collocation method for fracture mechanics (2010, methodology): “To achieve optimal solution accuracy, weighted collocation method [10] is introduced to balance the errors in the domain and on the boundaries.”
• Error analysis of collocation method based on reproducing kernel approximation (2011, methodology): “The work in [25, 30] introduced a concept commonly used in the radial basis function method, where the number of collocation points used to enforce zero residual of the strong form and boundary conditions is more than the number of nodal points for improved accuracy of the strong form collocation me”
• Meshfree Methods: Progress Made after 20 Years (2017, unknown): “(65) can be rewritten as where for two dimensions If N c ¼ N s , the approach is termed as the direct collocation method (Hu et al. 2007).”
• Subdomain radial basis collocation method for heterogeneous media (2009, methodology): “According to [31], the following weights are used: √ w+ g = √ w− g = √ w̄g =O(k̄ · N̄s), √ w+ h =O(s+), √ w− h =O(s−), √ w̄h =O(1) (37) where k =max( , ), k̄=max(k+,k−), N̄s =max(N+ s ,N− s ), s+ = k̄/k+, s− = k̄/k−, and are Lame’s constants in ̄ , and N s is the number of source points in ̄ .”