Point collocation methods using the fast moving least-square reproducing kernel approximation

2003 ◽  
Vol 56 (10) ◽  
pp. 1445-1464 ◽  
Author(s):  
Do Wan Kim ◽  
Yongsik Kim
Keyword(s):  
Fast Moving ◽  
Reproducing Kernel ◽  
Least Square ◽  
Collocation Methods ◽  
Moving Least Square ◽  
Point Collocation ◽  
Kernel Approximation

A Miniaturized Electron Beam Column Simulation by the Fast Moving Least Square Reproducing Kernel Point Collocation Method

2003 ◽  
Vol 42 (Part 1, No. 6B) ◽  
pp. 3842-3848 ◽  
Author(s):  
Do Wan Kim ◽  
Yongsik Kim ◽  
Young Chul Kim ◽  
Ho Seob Kim ◽  
Seungjoon Ahn ◽  
...  
Keyword(s):  
Electron Beam ◽  
Collocation Method ◽  
Fast Moving ◽  
Reproducing Kernel ◽  
Least Square ◽  
Moving Least Square ◽  
Point Collocation

Two Implicit Meshless Finite Point Schemes for the Two-Dimensional Distributed-Order Fractional Equation

2019 ◽  
Vol 19 (4) ◽  
pp. 813-831
Author(s):  
Rezvan Salehi
Keyword(s):  
Reproducing Kernel ◽  
Point Method ◽  
Least Square ◽  
Computationally Efficient ◽  
Finite Point ◽  
Moving Least Square ◽  
Point Collocation ◽  
Finite Point Method ◽  
Distributed Order ◽  
Fractional Equation

AbstractIn this paper, the distributed-order time fractional sub-diffusion equation on the bounded domains is studied by using the finite-point-type meshless method. The finite point method is a point collocation based method which is truly meshless and computationally efficient. To construct the shape functions of the finite point method, the moving least square reproducing kernel approximation is employed. Two implicit discretisation of order{O(\tau)}and{O(\tau^{1+\frac{1}{2}\sigma})}are derived, respectively. Stability and{L^{2}}norm convergence of the obtained difference schemes are proved. Numerical examples are provided to confirm the theoretical results.

scholarly journals Coupling of Point Collocation Meshfree Method and FEM for EEG Forward Solver

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Chany Lee ◽  
Jong-Ho Choi ◽  
Ki-Young Jung ◽  
Hyun-Kyo Jung
Keyword(s):  
Reproducing Kernel ◽  
Kernel Method ◽  
Current Source ◽  
Meshfree Method ◽  
Forward Problem ◽  
Least Square ◽  
Head Model ◽  
Source Modeling ◽  
Moving Least Square ◽  
Point Collocation

For solving electroencephalographic forward problem, coupled method of finite element method (FEM) and fast moving least square reproducing kernel method (FMLSRKM) which is a kind of meshfree method is proposed. Current source modeling for FEM is complicated, so source region is analyzed using meshfree method. First order of shape function is used for FEM and second order for FMLSRKM because FMLSRKM adopts point collocation scheme. Suggested method is tested using simple equation using 1-, 2-, and 3-dimensional models, and error tendency according to node distance is studied. In addition, electroencephalographic forward problem is solved using spherical head model. Proposed hybrid method can produce well-approximated solution.

Upwinding Meshfree Point Collocation Method for Steady MHD Flow

2010 ◽  
Author(s):  
Xinghui Cai ◽  
Guanghui Su ◽  
Suizheng Qiu
Keyword(s):  
Magnetic Field ◽  
Collocation Method ◽  
Mhd Flow ◽  
Least Square ◽  
Good Convergence ◽  
Moving Least Square ◽  
Point Collocation ◽  
Coupled Equations ◽  
Meshless Collocation ◽  
Mls Approximation

In this paper, a meshfree point collocation method, with a upwinding scheme, is presented to obtain the numerical solution of the coupled equations in velocity and magnetic field for the fully developed magnetohydrodynamic (MHD) flow through a straight pipe of rectangular section with insulated walls. The moving least-square (MLS) approximation is employed to construct shape functions in conjunction with the framework of point collocation method. Computations have been carried out for different applied magnetic field orientations and different Hartmann numbers from 5 to 1,000,000. As the adaptive upwinding local support domain is introduced in the meshless collocation method, numerical results show that the method can compute MHD problems not only at low and moderate values but also at high values of the Hartmann number with high accuracy and good convergence.

scholarly journals Stress analysis of elastic bi-materials by using the localized method of fundamental solutions

2021 ◽  
Vol 7 (1) ◽  
pp. 1257-1272
Author(s):  
Juan Wang ◽  
◽  
Wenzhen Qu ◽  
Xiao Wang ◽  
Rui-Ping Xu ◽  
...  
Keyword(s):  
Stress Analysis ◽  
Large Scale ◽  
Classical Method ◽  
Fundamental Solutions ◽  
Least Square ◽  
Collocation Methods ◽  
Method Of Fundamental Solutions ◽  
Computational Domain ◽  
Desktop Computer ◽  
Moving Least Square

<abstract> <p>The localized method of fundamental solutions belongs to the family of meshless collocation methods and now has been successfully tried for many kinds of engineering problems. In the method, the whole computational domain is divided into a set of overlapping local subdomains where the classical method of fundamental solutions and the moving least square method are applied. The method produces sparse and banded stiffness matrix which makes it possible to perform large-scale simulations on a desktop computer. In this paper, we document the first attempt to apply the method for the stress analysis of two-dimensional elastic bi-materials. The multi-domain technique is employed to handle the non-homogeneity of the bi-materials. Along the interface of the bi-material, the displacement continuity and traction equilibrium conditions are applied. Several representative numerical examples are presented and discussed to illustrate the accuracy and efficiency of the present approach.</p> </abstract>

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