In this work the authors simulate a contaminant transport problem in three dimensions that takes place in the soil of waste disposals. Such problem is modeled by a diffusion-dominated equation. The solution of this eq...In this work the authors simulate a contaminant transport problem in three dimensions that takes place in the soil of waste disposals. Such problem is modeled by a diffusion-dominated equation. The solution of this equation is addressed by using mixed finite element method for the spatial discretization of the equation. The resulting linear algebraic system is handled by an iterative domain decomposition procedure. This procedure is naturally parallelizable, and permits to implement computational codes in distributed memory machines in order to save on CPU time. Numerical results of the serial and parallel codes were compared with experimental results, and their performance measures were evaluated. The results indicate that the parallelizable procedure is an efficient tool for performing simulations of the problem.展开更多
This article discusses computational methods for the numerical simulation of unsteady Bingham visco-plastic flow. These methods are based on time-discretization by operator-splitting and take advantage of a characteri...This article discusses computational methods for the numerical simulation of unsteady Bingham visco-plastic flow. These methods are based on time-discretization by operator-splitting and take advantage of a characterization of the solutions involving some kind of Lagrange multipliers. The full discretization is achieved by combining the above operator-splitting methods with finite element approximations, the advection being treated by a wave-like equation 'equivalent' formulation easier to implement than the method of characteristics or high order upwinding methods. The authors illustrate the methodology discussed in this article with the results of numerical experiments concerning the simulation of wall driven cavity Bingham flow in two dimensions.展开更多
This paper considers the variational discretization for the constrained optimal control problem governed by linear parabolic equations.The state and co-state are approximated by RaviartThomas mixed finite element spac...This paper considers the variational discretization for the constrained optimal control problem governed by linear parabolic equations.The state and co-state are approximated by RaviartThomas mixed finite element spaces,and the authors do not discretize the space of admissible control but implicitly utilize the relation between co-state and control for the discretization of the control.A priori error estimates are derived for the state,the co-state,and the control.Some numerical examples are presented to confirm the theoretical investigations.展开更多
A combination of the classical Newton Method and the multigrid method, i.e., a Newton multigrid method is given for solving quasilinear parabolic equations discretized by finite elements. The convergence of the algori...A combination of the classical Newton Method and the multigrid method, i.e., a Newton multigrid method is given for solving quasilinear parabolic equations discretized by finite elements. The convergence of the algorithm is obtained for only one step Newton iteration per level. The asymptotically computational cost for quasilinear parabolic problems is O（NNk） similar to multigrid method for linear parabolic problems.展开更多
In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic ...In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic regularization of the resulting variational problem, and the time discretization by operator-splitting of an initial value problem associated with the Euler-Lagrange equations of the regularized variational problem. A low-order finite element discretization is advocated since it is well-suited to the low regularity of the solutions. Numerical experiments show that the method sketched above can capture efficiently the extremal solutions of various two-dimensional test problems and that it has also the ability of handling easily domains with curved boundaries.展开更多
文摘In this work the authors simulate a contaminant transport problem in three dimensions that takes place in the soil of waste disposals. Such problem is modeled by a diffusion-dominated equation. The solution of this equation is addressed by using mixed finite element method for the spatial discretization of the equation. The resulting linear algebraic system is handled by an iterative domain decomposition procedure. This procedure is naturally parallelizable, and permits to implement computational codes in distributed memory machines in order to save on CPU time. Numerical results of the serial and parallel codes were compared with experimental results, and their performance measures were evaluated. The results indicate that the parallelizable procedure is an efficient tool for performing simulations of the problem.
文摘This article discusses computational methods for the numerical simulation of unsteady Bingham visco-plastic flow. These methods are based on time-discretization by operator-splitting and take advantage of a characterization of the solutions involving some kind of Lagrange multipliers. The full discretization is achieved by combining the above operator-splitting methods with finite element approximations, the advection being treated by a wave-like equation 'equivalent' formulation easier to implement than the method of characteristics or high order upwinding methods. The authors illustrate the methodology discussed in this article with the results of numerical experiments concerning the simulation of wall driven cavity Bingham flow in two dimensions.
基金supported by the National Natural Science Foundation of Chinaunder Grant No.11271145Foundation for Talent Introduction of Guangdong Provincial University+3 种基金Fund for the Doctoral Program of Higher Education under Grant No.20114407110009the Project of Department of Education of Guangdong Province under Grant No.2012KJCX0036supported by Hunan Education Department Key Project 10A117the National Natural Science Foundation of China under Grant Nos.11126304 and 11201397
文摘This paper considers the variational discretization for the constrained optimal control problem governed by linear parabolic equations.The state and co-state are approximated by RaviartThomas mixed finite element spaces,and the authors do not discretize the space of admissible control but implicitly utilize the relation between co-state and control for the discretization of the control.A priori error estimates are derived for the state,the co-state,and the control.Some numerical examples are presented to confirm the theoretical investigations.
基金This research is supported by the National Natural Science Foundation of China(10471011).
文摘A combination of the classical Newton Method and the multigrid method, i.e., a Newton multigrid method is given for solving quasilinear parabolic equations discretized by finite elements. The convergence of the algorithm is obtained for only one step Newton iteration per level. The asymptotically computational cost for quasilinear parabolic problems is O（NNk） similar to multigrid method for linear parabolic problems.
基金supported by the National Science Foundation(No.DMS-0913982)
文摘In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic regularization of the resulting variational problem, and the time discretization by operator-splitting of an initial value problem associated with the Euler-Lagrange equations of the regularized variational problem. A low-order finite element discretization is advocated since it is well-suited to the low regularity of the solutions. Numerical experiments show that the method sketched above can capture efficiently the extremal solutions of various two-dimensional test problems and that it has also the ability of handling easily domains with curved boundaries.
