On the Equivalence Between Least-Squares and Kernel Approximations in Meshless Methods

By Xiaozhong Jin, Gang Li, N. Aluru. 2001

60 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a83f2ac9b90d6a965079f55e790db83497ee42e0

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. Sergio R. Idelsohn
2. Eugenio Oñate
3. S. Shen
4. Facundo Del Pin
5. Gang Li
6. Nam Mai-Duy
7. Xiaozhong Jin
8. S. De

In Mechanics of Materials

1. Eugenio Oñate
2. Sergio R. Idelsohn
3. Xiaozhong Jin
4. S. De
5. S. Shen
6. N. Aluru
7. Gang Li
8. Facundo Del Pin

In Numerical Analysis

1. Nam Mai-Duy
2. N. Aluru
3. S. De
4. Satya N. Atluri
5. S. Shen
6. Gang Li
7. Xiaozhong Jin
8. Sergio R. Idelsohn

Citations in the corpus

• A chemo-electro-mechanical mathematical model for simulation of pH sensitive hydrogels (2004, methodology): “The finite cloud method (Aluru and Li, 2001; Jin et al., 2001) has been used for the solution of the coupled chemo-electro-mechanical equations.”
• Solving high order ordinary differential equations with radial basis function networks (2005, methodology): “In contrast to the traditional methods, the domain of analysis in the present procedures using multiquadrics is discretized into a number of distinct points (instead of a number of intervals) since there are no intervals required for both processes: integration of ODEs and interpolation of the field”
• Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS (2004, unknown): “Numerical discretization is done using FCM (see [17], [18], and [19] for details on FCM).”
• The meshless finite element method (2003, background): “More recently, the equivalence between MLSQ and RPKM for polynomial basis has been proven, so that both methods may now be considered to be based on the same shape functions [4, 5 ].”
• Meshless Local Petrov-Galerkin Collocation Method for Two-dimensional Heat Conduction Problems (2007, background): “The characteristic of MLS has been widely discussed in literatures [Alturi and Zhu (1998), Jin et al. (2001)], and will not be restated here.”
• Positivity conditions in meshless collocation methods (2004, methodology): “Least-squares and kernel based approaches are two techniques that have gained considerable attention for construction of meshless approximation functions (see [2] for a detailed discussion on leastsquares and kernel approximations).”
• The Meshless Local Petrov-Galerkin (MLPG) Method: A Simple \& Less-costly Alternative to the Finite Element and Boundary Element Methods (2002, methodology): “The equivalence between the MLS and the RKPM is also discussed in Jin, Li & Aluru (2001) .”