A Schwarz auditive method with high order interface conditions and nonoverlapping subdomains
A second order anti-diffusive Lagrange-remap scheme for two-component flows
We build a non-dissipative second order algorithm for the approximate resolution of the one-dimensional Euler system of compressible gas dynamics with two components. The considered model was proposed in [1]. The algorithm is based on [8] which deals with a non-dissipative first order resolution in Lagrange-remap formalism. In the present paper we describe, in the same framework, an algorithm that is second order accurate in time and space, and that...
A Second Order Splitting Method for the Cahn-Hilliard Equation.
A second-order finite volume element method on quadrilateral meshes for elliptic equations
In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in -norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method.
A second-order finite volume element method on quadrilateral meshes for elliptic equations
In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in H1-norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method.
A second-order multi-fluid model for evaporating sprays
The aim of this paper is to present a method using both the ideas of sectional approach and moment methods in order to accurately simulate evaporation phenomena in gas-droplets flows. Using the underlying kinetic interpretation of the sectional method [Y. Tambour, Combust. Flame 60 (1985) 15–28] exposed in [F. Laurent and M. Massot, Combust. Theory Model. 5 (2001) 537–572], we propose an extension of this approach based on a more accurate representation of the droplet size number density in each...
A second-order multi-fluid model for evaporating sprays
The aim of this paper is to present a method using both the ideas of sectional approach and moment methods in order to accurately simulate evaporation phenomena in gas-droplets flows. Using the underlying kinetic interpretation of the sectional method [Y. Tambour, Combust. Flame60 (1985) 15–28] exposed in [F. Laurent and M. Massot, Combust. Theory Model.5 (2001) 537–572], we propose an extension of this approach based on a more accurate representation of the droplet size number density in each...
A second-order upwinding finite difference scheme for the steady Navier-Stokes equations in primitive variables in a driven cavity with a multigrid solver
A self-adaptive trust region method for the extended linear complementarity problems
By using some NCP functions, we reformulate the extended linear complementarity problem as a nonsmooth equation. Then we propose a self-adaptive trust region algorithm for solving this nonsmooth equation. The novelty of this method is that the trust region radius is controlled by the objective function value which can be adjusted automatically according to the algorithm. The global convergence is obtained under mild conditions and the local superlinear convergence rate is also established under...
A self-consistent numerical method for simulation of quantum transport in high electron mobility transistor. I: The Boltzmann-Poisson-Schrödinger solver.
A self-consistent numerical method for simulation of quantum transport in high electron mobility transistor. II: The full quantum transport.
A self-scaling memoryless BFGS based conjugate gradient method using multi-step secant condition for unconstrained minimization
Conjugate gradient methods are widely used for solving large-scale unconstrained optimization problems, because they do not need the storage of matrices. Based on the self-scaling memoryless Broyden-Fletcher-Goldfarb-Shanno (SSML-BFGS) method, new conjugate gradient algorithms CG-DESCENT and CGOPT have been proposed by W. Hager, H. Zhang (2005) and Y. Dai, C. Kou (2013), respectively. It is noted that the two conjugate gradient methods perform more efficiently than the SSML-BFGS method. Therefore,...
A semi-discrete high resolution scheme for nonlinear scalar conservation laws.
A semifeasible trust-region model algorithm for minimization with inequality constraint.
A Semi-Implicit Mid-Point Rule for Stiff Systems of Ordinary Differential Equations
A semi-smooth Newton method for solving elliptic equations with gradient constraints
Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.
A semi-smooth Newton method for solving elliptic equations with gradient constraints
Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.
A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems
Sensitivity analysis (with respect to the regularization parameter) of the solution of a class of regularized state constrained optimal control problems is performed. The theoretical results are then used to establish an extrapolation-based numerical scheme for solving the regularized problem for vanishing regularization parameter. In this context, the extrapolation technique provides excellent initializations along the sequence of reducing regularization parameters. Finally, the favorable numerical behavior...
A set oriented approach to global optimal control
We describe an algorithm for computing the value function for “all source, single destination” discrete-time nonlinear optimal control problems together with approximations of associated globally optimal control strategies. The method is based on a set oriented approach for the discretization of the problem in combination with graph-theoretic techniques. The central idea is that a discretization of phase space of the given problem leads to an (all source, single destination) shortest path problem...
A set oriented approach to global optimal control
We describe an algorithm for computing the value function for “all source, single destination” discrete-time nonlinear optimal control problems together with approximations of associated globally optimal control strategies. The method is based on a set oriented approach for the discretization of the problem in combination with graph-theoretic techniques. The central idea is that a discretization of phase space of the given problem leads to an (all source, single destination) shortest path...