Analysis of meshless weak and strong formulations for boundary value problems

DOI10.1016/j.enganabound.2017.03.010zbMath1403.65163OpenAlexW2609025418MaRDI QIDQ1655819

Wajid Khan, Siraj-ul-islam, Baseer Ullah

Publication date: 10 August 2018

Published in: Engineering Analysis with Boundary Elements (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.enganabound.2017.03.010

zbMATH Keywords

numerical integrationelement-free Galerkin methodGaussian quadratureelliptic boundary value problemsmeshless methodsHaar waveletsmoving least squares approximationlocal radial basis functions

Mathematics Subject Classification ID

Related Items (6)

RBF-FD meshless optimization using direct search (GLODS) in the analysis of composite plates ⋮ Nesterov's acceleration for level set-based topology optimization using reaction-diffusion equations ⋮ A parametrized level set based topology optimization method for analysing thermal problems ⋮ Structural optimization based on meshless element free Galerkin and level set methods ⋮ The localized radial basis functions for parameterized level set based structural optimization ⋮ Symmetric radial basis function method for simulation of elliptic partial differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Radial basis function collocation method for the numerical solution of the two-dimensional transient nonlinear coupled Burgers equations
• A method of fundamental solutions without fictitious boundary
• A least-square radial point collocation method for adaptive analysis in linear elasticity
• Simulation of macrosegregation with mesosegregates in binary metallic casts by a meshless method
• Quadrature rules for numerical integration based on Haar wavelets and hybrid functions
• Meshless methods: a review and computer implementation aspects
• A comparative study of numerical integration based on Haar wavelets and hybrid functions
• A regularized least-squares radial point collocation method (RLS-RPCM) for adaptive analysis
• Generalizing the finite element method: Diffuse approximation and diffuse elements
• A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method
• A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics
• Numerical integration of the Galerkin weak form in meshfree methods
• On boundary conditions in the element-free Galerkin method
• Nodal integration of the element-free Galerkin method
• An \(h\)-\(p\) adaptive method using clouds
• A critical assessment of the truly meshless local Petrov-Galerkin (MLPG), and local boundary integral equation (LBIE) methods
• The method of finite spheres
• Adaptive numerical integration in element-free Galerkin methods for elliptic boundary value problems
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• A new implementation of the element free Galerkin method
• Local radial basis function collocation method along with explicit time stepping for hyperbolic partial differential equations
• Exact explicit time integration of hyperbolic partial differential equations with mesh-free radial basis functions
• Local meshless method for PDEs arising from models of wound healing
• A meshfree local RBF collocation method for anti-plane transverse elastic wave propagation analysis in 2D phononic crystals
• A nodal integration technique for meshfree radial point interpolation method (NI-RPIM)
• A stabilized least-squares radial point collocation method (LS-RPCM) for adaptive analysis
• A comparison of numerical integration rules for the meshless local Petrov-Galerkin method
• Radial point interpolation collocation method (RPICM) for the solution of nonlinear Poisson problems
• Assessment of global and local meshless methods based on collocation with radial basis functions for parabolic partial differential equations in three dimensions
• Product Gauss quadrature rules vs. cubature rules in the meshless local Petrov-Galerkin method
• An accelerated, convergent, and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics
• An Overview on Meshfree Methods: For Computational Solid Mechanics
• A Comparative Study of Global and Local Meshless Methods for Diffusion-Reaction Equation
• Stabilized conforming nodal integration in the natural-element method
• Subdomain radial basis collocation method for fracture mechanics
• From Global to Local Radial Basis Function Collocation Method for Transport Phenomena
• Reproducing kernel enhanced local radial basis collocation method
• Quadrature for meshless methods
• Gradient and dilatational stabilizations for stress-point integration in the element-free Galerkin method
• Smoothed particle hydrodynamics: theory and application to non-spherical stars
• Surfaces Generated by Moving Least Squares Methods
• Meshless Galerkin methods using radial basis functions
• Element‐free Galerkin methods
• THE PARTITION OF UNITY METHOD
• Estimation of Dispersion in an Open Channel from an Elevated Source Using an Upwind Local Meshless Method
• A Local Meshless Method for Steady State Convection Dominated Flows
• The partition of unity quadrature in meshless methods
• Reproducing kernel particle methods
• All well-posed problems have uniformly stable and convergent discretizations

This page was built for publication: Analysis of meshless weak and strong formulations for boundary value problems