张量积形式的三维延拓 Kantorovich 法

THREE-DIMENSIONAL EXTENDED KANTOROVICH METHOD OF TENSOR PRODUCT FORM

摘要: 该文采用张量积的试函数逼近形式,即u(x,y,z)=X(x)^TZ(z)Y(y),成功地建立了三维延拓Kantorovich 法的算法方程式,克服了简单试函数逼近形式的迭代不收敛的数值困难。三维Poisson 方程的数值算例显示了该算法的迭代收敛性以及高精度和高效率。

Abstract: Using the function approximation of tensor product, the extended Kantorovich method was successfully applied to three-dimensional problems in the paper and the non-convergence of the iteration procedure using simple function approximation was overcame. Furthermore, the iteration convergence was displayed and high accuracy and efficiency were demonstrated by numerical examples of the three-dimensional Poisson equation.