Exponential basis functions in solution of static and time harmonic elastic problems in a meshless style

DOI10.1002/nme.2718zbMath1183.74350OpenAlexW2102277080MaRDI QIDQ3549871

B. Movahedian, B. Boroomand, Soheil Soghrati

Publication date: 29 March 2010

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nme.2718

zbMATH Keywords

fundamental solutionexponential functionsmeshless methoddiscrete transformationexponential basiselasto-staticelasto-dynamic

Mathematics Subject Classification ID

Related Items (22)

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Cites Work

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• The method of fundamental solutions for the Cauchy problem in two-dimensional linear elasticity
• Positivity conditions in meshless collocation methods
• The generalized finite element method for Helmholtz equation. II: Effect of choice of handbook functions, error due to absorbing boundary conditions and its assessment
• Boundary integral equations
• Stability and convergence of the method of fundamental solutions for Helmholtz problems on analytic domains
• The generalized finite point method
• Convergence order estimates of meshless collocation methods using radial basis functions
• The method of fundamental solutions for elliptic boundary value problems
• The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics
• Special short wave elements for flow acoustics
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Simple modifications for stabilization of the finite point method
• Generalization of robustness test procedure for error estimators. Part I: formulation for patches near kinked boundaries
• Generalization of robustness test procedure for error estimators. Part II: test results for error estimators using SPR and REP
• Dynamic solution of unbounded domains using finite element method: discrete Green's functions in frequency domain
• The method of fundamental solutions for inverse boundary value problems associated with the steady-state heat conduction in anisotropic media
• Element‐free Galerkin methods
• Method of fundamental solutions: singular value decomposition analysis
• Dispersion analysis and error estimation of Galerkin finite element methods for the Helmholtz equation
• Convergence of Unsymmetric Kernel‐Based Meshless Collocation Methods

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