ترکیبی کارا از روش-های بدون شبکه پتروف-گالرکین موضعی و جداکننده گام زمانی برای حل عددی معادله گینزبورگ-لاندو در حالت های دوبعدی و سه بعدی

In this paper, an efficient combination of the time-splitting and meshless local Petrov-Galerkin method for the numerical solution of Ginzburg–Landau equation in‎ ‎two and three dimensions is presented. ‎The main idea of splitting scheme is separating the original equation in time into two parts, linear and nonlinear‎. ‎Since, solving the nonlinear part based on the weak form is complicated and contains error, the split-step in time will be used. we solve the nonlinear part analytically and linear part numerically by the meshless local Petrov-Galerkin method in space variables and the Crank-Nicolson method in time‎. Hence, the moving Kriging interpolation is used instated of moving least squares. Therefore, the shape functions of the meshless local Petrov-Galerkin method have the Kronecker's delta property and the boundary conditions can be implemented directly and easily‎. ‎ ‎Several examples for two and three dimensions are presented and the results are compared with their analytical solutions to demonstrate the validity and capability of this method‎.

کلیدواژه ها:

معادله گینزبورگ-لاندو ، روش بدون شبکه پتروف-گالرکین موضعی ، روش جداسازی زمان ، درونیابی متحرک کریجینگ