Radial basis function based finite element method: formulation and applications

Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical radial basis function approximation (65D12)

Cites Work

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A smoothed Hermite radial point interpolation method for thin plate analysis
Local RBF-based differential quadrature collocation method for the boundary layer problems
A strong formulation finite element method (SFEM) based on RBF and GDQ techniques for the static and dynamic analyses of laminated plates of arbitrary shape
Theory and applications of the multiquadric-biharmonic method. 20 years of discovery 1968-1988
Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
A numerical study of some radial basis function based solution methods for elliptic PDEs
Stable computations with flat radial basis functions using vector-valued rational approximations
On using radial basis functions in a ``finite difference mode with applications to elasticity problems
A smoothed finite element method for plate analysis
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Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
Buckling analysis of Reissner-Mindlin plates subjected to in-plane edge loads using a shear-locking-free and meshfree method
Node-based smoothed radial point interpolation method for electromagnetic-thermal coupled analysis
A stable method for the evaluation of Gaussian radial basis function solutions of interpolation and collocation problems
An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications
A novel twice-interpolation finite element method for solid mechanics problems
Computation of natural frequencies of shear deformable beams and plates by an RBF-pseudospectral method
A meshfree radial point interpolation method (RPIM) for three-dimensional solids
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Stable Computation of Differentiation Matrices and Scattered Node Stencils Based on Gaussian Radial Basis Functions
XFEM with Smoothing Technique for Static Fracture Mechanics in Three-Dimension
A thin plate formulation without rotation DOFs based on the radial point interpolation method and triangular cells
Stable Computations with Gaussian Radial Basis Functions
A meshfree Hermite-type radial point interpolation method for Kirchhoff plate problems
A Hermite reproducing kernel approximation for thin-plate analysis with sub-domain stabilized conforming integration
A numerical method for heat transfer problems using collocation and radial basis functions

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