An Optimal Radius of Influence Domain in Element-Free Galerkin Method

Optimal influence cover for an element free Galerkin MFree method based on artificial neural network

“…The difference in profit at this upper limit is small, but the computational cost is more optimal compared with 20 points. This number (16) respects the size range of the influence domain which is described by Doblow and Belystchko [17] and Sheng [22].…”

“…This process is made for multiple fixed nodes in the range of 5-16 (see Section 3.2). Furthermore, for the interpretation of the obtained results, we calculate the minimum global error e σ (x g ) obtained this time from the local minimum errors of each Gauss point for the 12 scenarios (fixed number of nodes in the influence domain [5][6][7][8][9][10][11][12][13][14][15][16]. Table 2 presents an example of the results obtained for 203 nodes, the minimum global energy norm e Min σ E = 0, 00753011 enhances the result obtained with 11 nodes fixed in the cover by e σ E = 0, 00819991 which is 8.2%.…”

“…A weighting function is employed to determine the intensity of a node's effect at different points in its cover. The shape of the local supports can be arbitrary, such as circle, square, or rectangle (conventional domains) in 2D geometries [16] and circular, square, or rectangular parallelepipeds in 3D geometries.…”