Radial point interpolation method and high-order continuation for solving nonlinear transient heat conduction problems

Spectral Chebyshev method coupled with a high order continuation for nonlinear bending and buckling analysis of functionally graded sandwich beams

“…The aim of this work is to introduce the spectral method in the HOCM. Latterly, the HOCM with meshless methods such as MLS, WLS, or RPIM has been applied successfully for the resolution of nonlinear problems written under a strong form 19,20,24,25 or a weak form. 14,15 In this investigation, we propose to couple the spectral Chebyshev method as a discretization technique with the HOCM.…”

“…In addition, the use of beam model, which takes into account the nonlinear term neglected in several works of the literature, permits us to analyze buckling and bending problems by using the classical Timoshenko model and to handle the boundary conditions that several works could not to take into account. The HOCM has been coupled with meshless methods successfully in several works such as the moving least squares (MLS), 14,15 the method of fundamental solutions (MFS), 16‐18 and the radial point interpolation method (RPIM) 19,20 . The SCDQM has been also used in several works and showed its ability and efficiency in the computation of FG porous plates reinforced by graphene platelets 21 .…”

“…The HOCM has been coupled with meshless methods successfully in several works such as the moving least squares (MLS), 14,15 the method of fundamental solutions (MFS), [16][17][18] and the radial point interpolation method (RPIM). 19,20 The SCDQM has been also used in several works and showed its ability and efficiency in the computation of FG porous plates reinforced by graphene platelets. 21 This approach, named here SCDQM-HOCM, is illustrated on examples of nonlinear bending and buckling of the functionally graded sandwich beams under several loads and boundary conditions.…”

Radial point interpolation‐Chebychev method with asymptotic numerical method for nonlinear buckling analysis of graphene oxide powder‐reinforced composite beams

“…However, if m is a non-zero value, then m Chebychev polynomials will be added to supplement the interpolation process. [20][21][22][23][24] The RBFs that can be used are: [20][21][22]…”

Efficient resolution of incompressible Navier–Stokes equations using a robust high‐order pseudo‐spectral approach

“…$$$$ \left\{\begin{array}{c}\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0\\ {}u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}=-\frac{\partial p}{\partial x}+\frac{1}{\mathit{\operatorname{Re}}}\Delta u\\ {}u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}=-\frac{\partial p}{\partial y}+\frac{1}{\mathit{\operatorname{Re}}}\Delta v\end{array}\right., $$$$ where $$$ u $$$ and $$$ v $$$ are the velocity components in the $$$ x $$$‐ and $$$ y $$$‐directions respectively, $$$ p $$$ is the pressure and $$$ \mathit{\operatorname{Re}} $$$ is the nonnegative Reynolds number. The above nonlinear equations can be easily solved using several mesh‐free approaches that existing in the literature such as References 10,18,33,37‐40. Few papers have been published basing on a strong form of vorticity‐stream function formulation where the cited approaches find difficulty in managing hermit‐type bo...…”