Meshless Virtual Boundary Least-Square Collocation Method for 2-D Elastic Problems

2010 ◽  
Author(s):  
Zhijia Zhang ◽  
Qiang Xu
Keyword(s):  
Collocation Method ◽  
Least Square ◽  
Virtual Boundary ◽  
Least Square Collocation

Fast Multipole Virtual Boundary Element - Least Square Method for Solving 2-D Elastic Problems

2011 ◽  
Vol 204-210 ◽  
pp. 2196-2201
Author(s):  
Yan Tao Jiang ◽  
Si Tian Chen ◽  
Cheng Hua Li
Keyword(s):  
Boundary Element ◽  
Large Scale ◽  
Fast Multipole Method ◽  
Main Idea ◽  
Least Square Method ◽  
Least Square ◽  
Fast Multipole ◽  
Large Scale Problems ◽  
Virtual Boundary ◽  
Virtual Boundary Element

In this paper, the fast multipole virtual boundary element - least square method (Fast Multipole VBE - LSM) is proposed and used to simulate 2-D elastic problems, which is based on the fast multipole method (FMM) and virtual boundary element - least square method (VBE - LSM).The main idea of the method is to change computational model by applying the FMM to conventional VBE - LSM. The memory and operations could be reduced to be of linear proportion to the degree of freedom (DOF) and large scale problems could be effectively solved on a common desktop with this method. Numerical results show that this method holds virtues of high feasibility, accuracy and efficiency. Moreover, the idea of this method can be generalized and extended in application.

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.

Least square collocation as applied to the analysis of strip transmission lines

1979 ◽  
Vol 67 (2) ◽  
pp. 314-315 ◽  
Author(s):  
T.K. Seshadri ◽  
S. Mahapatra ◽  
K. Rajaiah
Keyword(s):  
Transmission Lines ◽  
Least Square ◽  
Least Square Collocation
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