A meshfree method for the solution of 2D and 3D second order elliptic boundary value problems in heterogeneous media

DOI10.1016/j.matcom.2023.06.004OpenAlexW4380183076MaRDI QIDQ6047611

Omid Bateniparvar, B. Boroomand, N. Noormohammadi, Danial Afifi

Publication date: 12 September 2023

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2023.06.004

zbMATH Keywords

boundary value problem2Dheterogeneousmeshfree3Dequilibrated basis functions

Mathematics Subject Classification ID

Numerical analysis (65-XX) Partial differential equations (35-XX)

Related Items

Static analysis of orthotropic nanoplates reinforced by defective graphene based on strain gradient theory using a simple boundary method

Cites Work

• Unnamed Item
• Unnamed Item
• A fictitious domain method using equilibrated basis functions for harmonic and bi-harmonic problems in physics
• An improved element-free Galerkin method for numerical modeling of the biological population problems
• An automatic 3D mesh generation method for domains with multiple materials
• Interpolating meshless local Petrov-Galerkin method for steady state heat conduction problem
• Radial basis collocation methods for elliptic boundary value problems
• Smoothed particle hydrodynamics (SPH): an overview and recent developments
• The generalized finite point method
• Analysis of 3D solids using the natural neighbour radial point interpolation method
• Generalizing the finite element method: Diffuse approximation and diffuse elements
• A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics
• Multiresolution reproducing kernel particle methods
• Numerical solution of three-dimensional Laplacian problems using the multiple scale Trefftz method
• A decomposition method for nonlinear bending of anisotropic thin plates
• Singular functions for heterogeneous composites with cracks and notches; the use of equilibrated singular basis functions
• Enrichment functions for weak singularities in 2D elastic problems with isotropic and orthotropic materials
• A Trefftz based meshfree local method for bending analysis of arbitrarily shaped laminated composite and isotropic plates
• On the solution of 3D problems in physics: from the geometry definition in CAD to the solution by a meshless method
• The method of fundamental solutions for nonlinear functionally graded materials
• Radial basis function approximations: comparison and applications
• Construction of equilibrated singular basis functions without a priori knowledge of analytical singularity order
• Weakly equilibrated basis functions for elasticity problems
• A fundamental solution method for inverse heat conduction problem
• A meshfree radial point interpolation method (RPIM) for three-dimensional solids
• A meshless method using local exponential basis functions with weak continuity up to a desired order
• Highly accurate solutions of Motz's and the cracked beam problems
• Smoothed Particle Hydrodynamics and Its Diverse Applications
• Implementation of a generalized exponential basis functions method for linear and non‐linear problems
• Simple modifications for stabilization of the finite point method
• Exponential basis functions in solution of static and time harmonic elastic problems in a meshless style
• Element‐free Galerkin methods
• A FINITE POINT METHOD IN COMPUTATIONAL MECHANICS. APPLICATIONS TO CONVECTIVE TRANSPORT AND FLUID FLOW
• Reproducing kernel particle methods for structural dynamics