Analysis of meshless weak and strong formulations for boundary value problems

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

“…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%.…”

“…The EFG method developed by Belystchko [11] is the standard numerical method for solving several types of partial differential equations (PDEs). It has been used for multiple practical engineering problems in heat transfer [1], crack propagation [12], elastoplastic contact problems [13], boundary problems [14], fluid mechanics, and applied mechanics. The EFG method uses local weak forms over a local sub-domain and the shape functions are constructed via the moving least-squares (MLS) approximation [15].…”

A parametrized level set based topology optimization method for analysing thermal problems

“…The LRBFs based LSM (LRBFs-LSM) for structural shape and topology optimization was introduced in [38]. Application areas of the LRBFs in a variety of real world problems include: heterogeneous media [39], turbulent flows [40], computational geosciences [41], structural mechanics [42], option pricing [43], metal casting [44], and many more [45].…”

Symmetric Radial Basis Function Method for Simulation of Elliptic Partial Differential Equations

“…Owing to this fact, several proficient and precise methods have been developed for the numerical solution of EPDEs. Contemporary contributions in this regard comprise spline collocation methods [1,2], the finite element method [3], finite difference methods [4,5], the wavelet collocation method [6], meshless methods [7][8][9], etc.…”

“…A broad variety of meshless methods underway is based on radial basis functions (RBF) [9][10][11][12]. The simplest among them is unsymmetric RBF collocation or the Kansa method [13].…”