Approximation of p-Biharmonic Problem using WEB-Spline based Mesh-Free Method

Abstract We describe and analyze the weighted extended b-spline (WEB-Spline) mesh-free finite element method for solving the p-biharmonic problem. The WEB-Spline method uses weighted extended b-splines as basis functions on regular grids and does not require any mesh generation which eliminates a difficult, time consuming preprocessing step. Accurate approximations are possible with relatively low-dimensional subspaces. We perform some numerical experiments to demonstrate the efficiency of the WEB-Spline method.

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Simulation of Harmonic Waves Generated by the Piston-type Wave-maker in the Wave Flume via the Exponential Basis Functions Mesh-free Method and MEL Formulation

Journal of Computational Methods In Engineering ◽

10.29252/jcme.37.1.1 ◽

2018 ◽

Vol 37 (1) ◽

pp. 1-9

Author(s):

S. M. Zandi ◽

◽

A. Rafizadeh ◽

Keyword(s):

Basis Functions ◽

Harmonic Waves ◽

Wave Flume ◽

Type Wave ◽

Exponential Basis ◽

Mesh Free ◽

Mesh Free Method ◽

Wave Maker

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Solving the forward-backward heat equation in two-dimension by Radial basis functions mesh free method

Journal of Zankoy Sulaimani - Part A ◽

10.17656/jzs.10830 ◽

2020 ◽

Vol 22 (2) ◽

pp. 305-318

Author(s):

Siamak Banei ◽

◽

Kamal Shanazari ◽

Yaqub Azari ◽

◽

...

Keyword(s):

Heat Equation ◽

Radial Basis Functions ◽

Basis Functions ◽

Two Dimension ◽

Mesh Free ◽

Radial Basis ◽

Mesh Free Method

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A computational homogenization analysis of materials using the stabilized mesh-free method based on the radial basis functions

Journal of Science and Technology in Civil Engineering (STCE) - NUCE ◽

10.31814/stce.nuce2020-14(1)-06 ◽

2020 ◽

Vol 14 (1) ◽

pp. 65-76

Author(s):

Ho Le Huy Phuc ◽

Le Van Canh ◽

Phan Duc Hung

Keyword(s):

Radial Basis Functions ◽

Interpolation Method ◽

Computational Homogenization ◽

Basis Functions ◽

Computational Aspect ◽

Mesh Free ◽

Kronecker Delta ◽

Radial Basis ◽

Point Interpolation Method ◽

Mesh Free Method

This study presents a novel application of mesh-free method using the smoothed-radial basis functions for the computational homogenization analysis of materials. The displacement field corresponding to the scattered nodes within the representative volume element (RVE) is split into two parts including mean term and fluctuation term, and then the fluctuation one is approximated using the integrated radial basis function (iRBF) method. Due to the use of the stabilized conforming nodal integration (SCNI) technique, the strain rate is smoothed at discreted nodes; therefore, all constrains in resulting problems are enforced at nodes directly. Taking advantage of the shape function satisfies Kronecker-delta property, the periodic boundary conditions well-known as the most appropriate procedure for RVE are similarly imposed as in the finite element method. Several numerical examples are investigated to observe the computational aspect of iRBF procedure. The good agreement of the results in comparison with those reported in other studies demonstrates the accuracy and reliability of proposed approach. Keywords: homogenization analysis; mesh-free method; radial point interpolation method; SCNI scheme.

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A mesh-free method using exponential basis functions for laminates modeled by CLPT, FSDT and TSDT – Part I: Formulation

Composite Structures ◽

10.1016/j.compstruct.2011.06.023 ◽

2011 ◽

Vol 93 (12) ◽

pp. 3112-3119 ◽

Cited By ~ 33

Author(s):

M. Shahbazi ◽

B. Boroomand ◽

S. Soghrati

Keyword(s):

Basis Functions ◽

Exponential Basis ◽

Mesh Free ◽

Mesh Free Method

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An Efficient Method for the Numerical Solution of a Class of Nonlinear Fractional Fredholm Integro-Differential Equations

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2017-0097 ◽

2018 ◽

Vol 19 (2) ◽

pp. 165-173

Author(s):

M. H. Heydari ◽

H. Laeli Dastjerdi ◽

M. Nili Ahmadabadi

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Numerical Solution ◽

Efficient Method ◽

Numerical Experiments ◽

Computational Cost ◽

Cpu Time ◽

Mesh Free ◽

Mesh Free Method ◽

Low Computational Cost

AbstractWe introduce a mesh-free method, i.e., MLS collocation method for the numerical solution of a kind of nonlinear fractional Fredholm integro-differential equation. An error bound is provided for the proposed method which supports its convergence. Detailed numerical experiments approve its excellency in attaining the desired accuracy for a quite low computational cost. We have also compared linear basis with quadratic basis in terms of CPU time.

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A Local Meshless Method for Approximating 3D Wind Fields

Journal of Applied Meteorology and Climatology ◽

10.1175/jamc-d-15-0246.1 ◽

2016 ◽

Vol 55 (1) ◽

pp. 163-172 ◽

Cited By ~ 3

Author(s):

Darrell W. Pepper ◽

Jiajia Waters

Keyword(s):

Finite Element ◽

Finite Difference ◽

Mesh Generation ◽

Meshless Method ◽

Region Of Interest ◽

Basis Functions ◽

Wind Fields ◽

Topological Features ◽

Mesh Free ◽

Using Data

AbstractAn efficient, mesh-free numerical method has been developed for creating 3D wind fields using data from meteorological towers. Node points are placed within a region of interest, generally based upon topological features. Since meshless methods do not require connective mesh generation, storage is greatly reduced, permitting implementation of the code using MATLAB on a personal computer. Utilizing locally collocated nodes and radial basis functions, a 3D wind can be quickly created that satisfies mass consistency. The meshless method yields close approximations to results obtained with mesh-dependent finite-difference, finite-volume, and finite-element techniques.

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