An Enriched Radial Point Interpolation Method Based on Weak-Form and Strong-Form

The transient thermo-elastic problems are solved by a cell-based smoothed radial point interpolation method (CS-RPIM). For this method, the problem domain is first discretized using triangular cells, and each cell is further divided into smoothing cells. The field functions are approximated using RPIM shape functions which have Kronecker delta function property. The system equations are derived using the generalized smoothed Galerkin (GS-Galerkin) weak form. At first, the temperature field is acquired by solving the transient heat transfer problem and it is then employed as an input for the mechanical problem to calculate the displacement and stress fields. Several numerical examples with different kinds of boundary conditions are investigated to verify the accuracy, convergence rate and stability of the present method.

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A LINEARLY CONFORMING RADIAL POINT INTERPOLATION METHOD FOR SOLID MECHANICS PROBLEMS

International Journal of Computational Methods ◽

10.1142/s0219876206001132 ◽

2006 ◽

Vol 03 (04) ◽

pp. 401-428 ◽

Cited By ~ 106

Author(s):

G. R. LIU ◽

Y. LI ◽

K. Y. DAI ◽

M. T. LUAN ◽

W. XUE

Keyword(s):

Solid Mechanics ◽

Interpolation Method ◽

Weak Form ◽

Delta Function ◽

Field Function ◽

Radial Point Interpolation Method ◽

Radial Point Interpolation ◽

Integration Techniques ◽

Point Interpolation Method ◽

Point Interpolation

A linearly conforming radial point interpolation method (LC-RPIM) is presented for stress analysis of two-dimensional solids. In the LC-RPIM method, each field node is enclosed by a Voronoi polygon, and the displacement field function is approximated using RPIM shape functions of Kronecker delta function property created by simple interpolation using local nodes and radial basis functions augmented with linear polynomials to guarantee linear consistency. The system equations are then derived using the Galerkin weak form and nodal integration techniques, and the essential boundary conditions are imposed directly as in the finite element method. The LC-RPIM method is verified via various numerical examples and an extensive comparison study is conducted with the conventional RPIM, analytical approach and FEM. It is found that the presented LC-RPIM is more stable, more accurate in stress and more efficient than the conventional RPIM.

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A Local Radial Point Interpolation Method for Two-Dimensional Schrödinger Equation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.268-270.1888 ◽

2012 ◽

Vol 268-270 ◽

pp. 1888-1893

Author(s):

Wei Gang Zhai ◽

Xing Hui Cai ◽

Jiang Ren Lu ◽

Xin Li Sun

Keyword(s):

Schrödinger Equation ◽

Analytical Solutions ◽

Schrodinger Equation ◽

Interpolation Method ◽

Weak Form ◽

Time Dependent ◽

Radial Point Interpolation Method ◽

Radial Point Interpolation ◽

Point Interpolation Method ◽

Point Interpolation

A local radial point interpolation method is employed to the simulation of the time dependent Schrödinger equation with arbitrary potential function. Local weak form of the time dependent Schrödinger equation is obtained and radial point interpolation shape functions are applied in the space discretization. Computations are carried out for an example of time dependent Schrödinger equation having analytical solutions. Numerical results agreed with analytical solutions very well.

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