A local meshless method for the numerical solution of space‐dependent inverse heat problems

Abstract

In this paper, a local radial basis function collocation method is proposed for the numerical solution of inverse space‐wise dependent heat source problems. Multiquadric radial basis function is used for spatial discretization. The method accuracy is tested in terms of absolute root mean square and relative root mean square error norms. Numerical tests on a noisy data are performed on both regular domain and irregular domain. To test the efficiency and accuracy of the proposed method, numerical experiments for one‐, two‐, and three‐dimensional cases are performed. Both regular and irregular geometries with uniform and nonuniform points are taken into consideration, and the numerical results are also compared with the existing methods reported in literature.

Formation of Intermetallic Phases in Ion Implantation

“…e implicit-difference scheme has been suggested for the solution of diffusion kinetic problem describing ion implantation by intermetallic phase formation. For further interesting models and methods, we refer the readers to [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. We actually suggest a model of the surface modification of nickel-aluminum ions with the relaxation of mass flows.…”

Numerical simulation of 3-D fractional-order convection-diffusion PDE by a local meshless method

“…Recently, a great effort has been expended to develop the exact and approximate behavior of fractional PDE. In this effort several enthusiastic methods have been applied for the solution of fractional PDE such as homotopy analysis method [9,10], expansion methods [11, --------------12], homotopy analysis transform method [13], fractional difference method [14], operational method [15], variational iteration method [5,[16][17][18], homotophy perturbation method [19], direct approach [20,21], Lie symmetry analysis [22], differential transform method [23], reproducing kernel method [24], extended differential transform [25], local fractional Riccati differential equation method [26], meshless methods [27,28] and Chebychev spectral method [29].…”

A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions

“…Many meshless methods have been proposed based on different construction methods of the shape function or discretization approach of the problem to be solved. The smoothed particle hydrodynamics (SPH) method [9], moving least squares (MLS) approximation [10], point interpolation method (PIM) [11], and radial basis function [12][13][14][15] are the widely used method to construct the meshless approximation. The major drawbacks of the SPH method include tensile instability and lack of approximation consistency.…”