Two variants of parallel implementation of high-order accurate bicompact schemes for multi-dimensional inhomogeneous transport equation

Abstract

Two variants of parallel implementation of high-order accurate bicompact schemes for multi-dimensional inhomogeneous transport equation In this paper, we compare the efficiency of two parallel algorithms for solution of the equations of multidimensional high-order accurate bicompact schemes for a multidimensional inhomogeneous transport equation. The first one is a spacemarching algorithm for computing non-factorized schemes, and the second one is based on the approximate factorization of multidimensional schemes. The latter algorithm uses iterations to preserve the high (higher than second) order of accuracy of bicompact schemes in time. The convergence of these iterations is proved for a nonstationary two-dimensional and three-dimensional linear inhomogeneous transport equation with constant positive coefficients. Model computations show that the factorization scheme is preferable from the point of view of parallel implementation.