A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlin...A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.展开更多
To address large scale industrial processes,a novel Lagrangian scheme is proposed to decompose a refinery scheduling problem with operational transitions in mode switching into a production subproblem and a blending a...To address large scale industrial processes,a novel Lagrangian scheme is proposed to decompose a refinery scheduling problem with operational transitions in mode switching into a production subproblem and a blending and delivery subproblem.To accelerate the convergence of Lagrange multipliers,some auxiliary constraints are added in the blending and delivery subproblem.A speed-up scheme is presented to increase the efficiency for solving the production subproblem.An initialization scheme of Lagrange multipliers and a heuristic algorithm to find feasible solutions are designed.Computational results on three cases with different lengths of time horizons and different numbers of orders show that the proposed Lagrangian scheme is effective and efficient.展开更多
文摘A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.
基金Supported by the National Natural Science Foundation of China(61273039,21276137)the National Science Fund for Distinguished Young Scholars of China(61525304)
文摘To address large scale industrial processes,a novel Lagrangian scheme is proposed to decompose a refinery scheduling problem with operational transitions in mode switching into a production subproblem and a blending and delivery subproblem.To accelerate the convergence of Lagrange multipliers,some auxiliary constraints are added in the blending and delivery subproblem.A speed-up scheme is presented to increase the efficiency for solving the production subproblem.An initialization scheme of Lagrange multipliers and a heuristic algorithm to find feasible solutions are designed.Computational results on three cases with different lengths of time horizons and different numbers of orders show that the proposed Lagrangian scheme is effective and efficient.
