Iterative approximate factorization for difference operators of high-order bicompact schemes for multidimensional nonhomogeneous hyperbolic systems
- Authors: Bragin M.D.1, Rogov B.V.1,2
-
Affiliations:
- Moscow Institute of Physics and Technology (State University)
- Keldysh Institute of Applied Mathematics
- Issue: Vol 95, No 2 (2017)
- Pages: 140-143
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/224903
- DOI: https://doi.org/10.1134/S1064562417020107
- ID: 224903
Cite item
Abstract
An iterative method for solving equations of multidimensional bicompact schemes based on an approximate factorization of their difference operators is proposed for the first time. Its algorithm is described as applied to a system of two-dimensional nonhomogeneous quasilinear hyperbolic equations. The convergence of the iterative method is proved in the case of the two-dimensional homogeneous linear advection equation. The performance of the method is demonstrated on two numerical examples. It is shown that the method preserves a high (greater than the second) order of accuracy in time and performs 3–4 times faster than Newton’s method. Moreover, the method can be efficiently parallelized.
About the authors
M. D. Bragin
Moscow Institute of Physics and Technology (State University)
Author for correspondence.
Email: michael@bragin.cc
Russian Federation, Dolgoprudnyi, Moscow oblast, 141700
B. V. Rogov
Moscow Institute of Physics and Technology (State University); Keldysh Institute of Applied Mathematics
Email: michael@bragin.cc
Russian Federation, Dolgoprudnyi, Moscow oblast, 141700; Moscow, 125047