In this paper, to obtain an efficient parallel algorithm to solve sparse block-tridiagonal linear systems, stair matrices are used to construct some parallel polynomial approximate inverse preconditioners. These preconditioners are suitable when the desired goal is to maximize parallelism....

A high-order finite element method, total variational diminishing (TVD) Runge–Kutta discontinuous Galerkin method is investigated to solve free-surface problems in hydraulic dynamics. Some cases of circular dam and rapidly varying two-dimensional flows are presented to show the efficiency and...

Proper orthogonal decomposition (POD) method has been successfully used in the reduced-order modeling of complex systems. In this paper, we extend the applications of POD method, i.e., combine the classical finite volume element (FVE) method with the POD method to obtain a reduced-order FVE...

In this paper, the weak form of the mathematical model of the traffic flow is adopted. Theoretical analyses of the discontinuous solutions of the red-and-green light models are discussed. The discontinuous Galerkin finite element method is used to numerically simulate the problems. The numerical...