Least‐square collocation and Lagrange multipliers forTaylor meshless method

2018 ◽  
Vol 35 (1) ◽  
pp. 84-113 ◽  
Author(s):  
Jie Yang ◽  
Heng Hu ◽  
Michel Potier‐Ferry
Keyword(s):  
Lagrange Multipliers ◽  
Meshless Method ◽  
Least Square ◽  
Least Square Collocation

scholarly journals Complex Variable Meshless Manifold Method for Elastic Dynamic Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Hongfen Gao ◽  
Gaofeng Wei
Keyword(s):  
Analytical Solution ◽  
Complex Variable ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Least Square ◽  
Dynamic Problems ◽  
Finite Covering ◽  
Moving Least Square ◽  
Elastic Dynamics ◽  
Good Agreement

Combining the finite covering technical and complex variable moving least square, the complex variable meshless manifold method can handle the discontinuous problem effectively. In this paper, the complex variable meshless method is applied to solve the problem of elastic dynamics, the complex variable meshless manifold method for dynamics is established, and the corresponding formula is derived. The numerical example shows that the numerical solutions are in good agreement with the analytical solution. The CVMMM for elastic dynamics and the discrete forms are correct and feasible. Compared with the traditional meshless manifold method, the CVMMM has higher accuracy in the same distribution of nodes.

scholarly journals Error Estimate and Adaptive Refinement in Mixed Discrete Least Squares Meshless Method

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
J. Amani ◽  
A. Saboor Bagherzadeh ◽  
T. Rabczuk
Keyword(s):  
Convergence Rate ◽  
Error Estimate ◽  
Least Squares ◽  
Meshless Method ◽  
Least Square ◽  
Adaptive Refinement ◽  
Error Estimator ◽  
Shape Functions ◽  
Numerical Errors ◽  
Elasticity Problems

The node moving and multistage node enrichment adaptive refinement procedures are extended in mixed discrete least squares meshless (MDLSM) method for efficient analysis of elasticity problems. In the formulation of MDLSM method, mixed formulation is accepted to avoid second-order differentiation of shape functions and to obtain displacements and stresses simultaneously. In the refinement procedures, a robust error estimator based on the value of the least square residuals functional of the governing differential equations and its boundaries at nodal points is used which is inherently available from the MDLSM formulation and can efficiently identify the zones with higher numerical errors. The results are compared with the refinement procedures in the irreducible formulation of discrete least squares meshless (DLSM) method and show the accuracy and efficiency of the proposed procedures. Also, the comparison of the error norms and convergence rate show the fidelity of the proposed adaptive refinement procedures in the MDLSM method.

Numerical Analysis of Electromagnetic Levitation Employing Meshless Method Based on Weighted Least Square Method

2015 ◽  
Vol 15 (1) ◽  
pp. 29-34 ◽  
Author(s):  
Shuhei Matsuzawa ◽  
Kenta Mitsufuji ◽  
Yurika Miyake ◽  
Katsuhiro Hirata ◽  
Fumikazu Miyasaka
Keyword(s):  
Magnetic Field ◽  
Meshless Method ◽  
Fluid Motion ◽  
Electromagnetic Levitation ◽  
Least Square Method ◽  
Least Square ◽  
Weighted Least Square ◽  
Frequency Magnetic Field ◽  
Thermo Physical Properties ◽  
The Magnetic Field

AbstractElectromagnetic levitation is a kind of magnetohydrodynamic phenomena which is useful to measure the thermo-physical properties of pure metals under high temperature. However, this phenomenon is complicated and detailed mechanisms of this phenomenon have not been clarified yet. This study proposes the meshless method based on weighted least square method for the analysis of electromagnetic levitation. In this study, the fluid motion equation and the magnetic field equation are coupled by this method. The behavior of a molten metal under high-frequency magnetic field is calculated by this method.

The Study of Meshless Method Simulation of Plate Bending Problem

2012 ◽  
Vol 446-449 ◽  
pp. 3633-3638
Author(s):  
Yu Ling Jiao ◽  
Guang Wei Meng ◽  
Xu Xi Qin
Keyword(s):  
Weight Function ◽  
Elastic Plate ◽  
Basis Function ◽  
Meshless Method ◽  
Least Square ◽  
Mindlin Plate ◽  
Plate Bending ◽  
Field Function ◽  
Moving Least Square ◽  
Plate Bending Problem

moving least square meshless method is a numerical approximation based on points that do not generate the grid of cells, as long as the node information. Basis function and weight function meshless method for the calculation of accuracy have a significant impact. In order to compare the order of the base functions and powers of the radius of influence domain function meshless method for computational accuracy and efficiency , this paper selected first, second and third basis function and spline-type weight function in a different influence domain radius, respectively construct the field function. Mindlin plate element is derived based on the format of the plate bending problem meshless discrete equations. Programming examples are calculated with elastic plate bending problems non-grid solutions, and analysis and comparison of their accuracy and efficiency, results show that the meshless method using elastic plate bending problem is feasible and effective.

Validation of Meshless Method Based on Weighted Least Square Method for Simulating Electromagnetic Levitation

2016 ◽  
Vol 52 (3) ◽  
pp. 1-4 ◽  
Author(s):  
Shuhei Matsuzawa ◽  
Kenta Mitsufuji ◽  
Yurika Miyake ◽  
Katsuhiro Hirata ◽  
Fumikazu Miyasaka
Keyword(s):  
Meshless Method ◽  
Electromagnetic Levitation ◽  
Least Square Method ◽  
Least Square ◽  
Weighted Least Square

Meshless Local Petrov-Galerkin (MLPG) Method for Incompressible Viscous Fluid Flows

2006 ◽  
Author(s):  
Mohammad Haji Mohammadi
Keyword(s):  
Stream Function ◽  
Meshless Method ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Least Square ◽  
Test Problems ◽  
Gauss Point ◽  
Driven Cavity ◽  
Moving Least Square ◽  
Mlpg Method

In this paper, the truly Meshless Local Petrov-Galerkin (MLPG) method is extended for computation of unsteady incompressible flows, governed by the Navier–Stokes equations (NSE), in vorticity-stream function formulation. The present method is a truly meshless method based only on a number of randomly located nodes. The formulation is based on two equations including stream function Poisson equation and vorticity advection-dispersion-reaction eq. (ADRE). The meshless method is based on a local weighted residual method with the Heaviside step function and quartic spline as the test functions respectively over a local subdomain. Moving Least Square approximation (MLS) is employed in shape function construction for approximation of a gauss point. Due to dissatisfaction of kronecker delta property in MLS approximation, the penalty method is employed to enforce the essential boundary conditions. In order to overcome instability and numerical errors encountering in convection dominant flows, a new upwinding scheme is used to stabilize the convection operator in the streamline direction (as is done in SUPG). In this upwinding technic, instead of moving subdomains the weight function is shifted in the direction of flow. The efficiency, accuracy and robustness are demonstrated by some test problems, including the standard driven cavity together with the driven cavity flow in an L shaped cavity and flow in a Z shaped channel. The comparison of computational results shows that the developed method is capable of accurate resolution of flow fields in complex geometries.

Large Eddy Simulation of Flow Past Circular Cylinder Based on the Least Square Meshless Method

2013 ◽  
Vol 394 ◽  
pp. 128-133
Author(s):  
Yuan Ding Wang ◽  
Jun Jie Tan ◽  
Xiao Wei Cai ◽  
Deng Feng Ren
Keyword(s):  
Circular Cylinder ◽  
Large Eddy Simulation ◽  
Meshless Method ◽  
Stokes Equations ◽  
Least Square ◽  
Scale Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Eddy Simulation ◽  
Large Eddy

Large Eddy Simulation (LES) based on the least square meshless method was proposed in the present paper to simulate the classical turbulent flow around a stationary 2D circular cylinder. The subgrid scale model of Smagorinsky-Lily was employed to close the Navier-Stokes equations filtered by Favre filter. The Reynolds number is 3900 which means that the flow is subcritical and the wake is fully turbulent but the cylinder boundary is still laminar. Results obtained in this paper were evaluated by comparison with published experimental results and other numerical results. The results obtained in the present work show better agreement with the experimental values than other two-dimensional LES results .

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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