Convergence and Accuracy of the Method of Iterative Approximate Factorization of Operators in Multidimensional High-Accuracy Bicompact Schemes

作     者：Rogov, B.V. Chikitkin, A.V. 

作者机构：Keldysh Institute of Applied Mathematics Russian Academy of Sciences Moscow 125047 Russian Federation Moscow Institute of Physics and Technology (National Research University) Dolgoprudnyi 141700 Moscow oblast Russian Federation 

出 版 物：《Mathematical Models and Computer Simulations》 (Math. Models Comput. Simul.)

年 卷 期：2020年第12卷第5期

页      面：660-675页

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

主　　题：bicompact schemes iterative approximate factorization method multidimensional inhomogeneous advection equation parallel algorithms 

摘      要：Abstract: The convergence and accuracy of a method for solving high-order accurate bicompact schemes having the fourth order of approximation in spatial variables on a minimum stencil for a multidimensional inhomogeneous advection equation are investigated. The method is based on the approximate factorization of difference operators of multidimensional bicompact schemes. In addition, it uses iterations to preserve a high (higher than the second) order of accuracy of bicompact schemes in time. The convergence of these iterations for both two- and three-dimensional bicompact schemes as applied to the linear inhomogeneous advection equation with positive constant coefficients is proved using the spectral method. The efficiency of two parallel algorithms for solving equations of multidimensional bicompact schemes is compared. One of them is the spatial marching algorithm for calculating unfactorized schemes, and the other is based on iterative approximate factorization of difference operators of the schemes. © 2020, Pleiades Publishing, Ltd.