In this paper,standard and economical cascadic multigrid methods are considered for solving the algebraic systems resulting from the mortar finite element methods. Both cascadic multigrid methods do not need full elli...In this paper,standard and economical cascadic multigrid methods are considered for solving the algebraic systems resulting from the mortar finite element methods. Both cascadic multigrid methods do not need full elliptic regularity,so they can be used to tackle more general elliptic problems.Numerical experiments are reported to support our theory.展开更多
In this paper,we design an efficient domain decomposition(DD)preconditioner for the saddle-point problem resulting from the mixed finite-element discretization of multiscale elliptic problems.By proper equivalent alge...In this paper,we design an efficient domain decomposition(DD)preconditioner for the saddle-point problem resulting from the mixed finite-element discretization of multiscale elliptic problems.By proper equivalent algebraic operations,the original saddle-point system can be transformed to another saddle-point system which can be preconditioned by a block-diagonel matrix efficiently.Actually,the first block of this block-diagonal matrix corresponds to a multiscale H(div)problem,and thus,the direct inverse of this block is unpractical and unstable for the large-scale problem.To remedy this issue,a two-level overlapping DD preconditioner is proposed for this//(div)problem.Our coarse space consists of some velocities obtained from mixed formulation of local eigenvalue problems on the coarse edge patches multiplied by the partition of unity functions and the trivial coarse basis(e.g.,Raviart-Thomas element)on the coarse grid.The condition number of our preconditioned DD method for this multiscale H(div)system is bounded by C(1+务)(1+log4(^)),where 6 denotes the width of overlapping region,and H,h are the typical sizes of the subdomain and fine mesh.Numerical examples are presented to confirm the validity and robustness of our DD preconditioner.展开更多
We develop a monotone ?nite volume method for the time fractional Fokker-Planck equations and theoretically prove its unconditional stability. We show that the convergence rate of this method is of order 1 in the spac...We develop a monotone ?nite volume method for the time fractional Fokker-Planck equations and theoretically prove its unconditional stability. We show that the convergence rate of this method is of order 1 in the space and if the space grid becomes suffciently ?ne, the convergence rate can be improved to order 2.Numerical results are given to support our theoretical ?ndings. One characteristic of our method is that it has monotone property such that it keeps the nonnegativity of some physical variables such as density, concentration,etc.展开更多
In this paper, local multiplicative and additive multilevel methods on adaptively refined meshes are considered for second-order elliptic problems with highly discontinuous coeffi- cients. For the multilevel-precondit...In this paper, local multiplicative and additive multilevel methods on adaptively refined meshes are considered for second-order elliptic problems with highly discontinuous coeffi- cients. For the multilevel-preconditioned system, we study the distribution of its spectrum by using the abstract Schwarz theory. It is proved that, except for a few small eigenval- ues, the spectrum of the preconditioned system is bounded quasi-uniformly with respect to the jumps of the coefficient and the mesh sizes. The convergence rate of multilevel- preconditioned conjugate gradient methods is shown to be quasi-optimal regarding the jumps and the meshes. Numerical experiments are presented to illustrate the theoretical findings.展开更多
In this work, we solve a long-standing open problem： Is it true that the convergence rate of the Lions＇ Robin-Robin nonoverlapping domain decomposition （DD） method can be constant, independent of the mesh size h？...In this work, we solve a long-standing open problem： Is it true that the convergence rate of the Lions＇ Robin-Robin nonoverlapping domain decomposition （DD） method can be constant, independent of the mesh size h？ We closed this old problem with a positive answer. Our theory is also verified by numerical tests.展开更多
In this paper, a local multilevel product algorithm and its additive version are con- sidered for linear systems arising from adaptive nonconforming P1 finite element approx- imations of second order elliptic boundary...In this paper, a local multilevel product algorithm and its additive version are con- sidered for linear systems arising from adaptive nonconforming P1 finite element approx- imations of second order elliptic boundary value problems. The abstract Schwarz theory is applied to analyze the multilevel methods with Jaeobi or Gauss-Seidel smoothers per- formed on local nodes on coarse meshes and global nodes on the finest mesh. It is shown that the local multilevel methods are optimal, i.e., the convergence rate of the multilevel methods is independent of the mesh sizes and mesh levels. Numerical experiments are given to confirm the theoretical results.展开更多
Oxide nanostructures grown on noble metal surfaces are often highly active in many reactions,in which the oxide/metal interfaces play an important role.In the present work,we studied the surface structures of Fe Ox-on...Oxide nanostructures grown on noble metal surfaces are often highly active in many reactions,in which the oxide/metal interfaces play an important role.In the present work,we studied the surface structures of Fe Ox-on-Pt and Ni Ox-on-Pt catalysts and their activity to CO oxidation reactions using both model catalysts and supported nanocatalysts.Although the active Fe O1x structure is stabilized on the Pt surface in a reductive reaction atmosphere,it is prone to change to an Fe O2x structure in oxidative reaction gases and becomes deactivated.In contrast,a Ni O1x surface structure supported on Pt is stable in both reductive and oxidative CO oxidation atmospheres.Consequently,CO oxidation over the Ni O1x-on-Pt catalyst is further enhanced in the CO oxidation atmosphere with an excess of O2.The present results demonstrate that the stability of the active oxide surface phases depends on the stabilization effect of the substrate surface and is also related to whether the oxide exhibits a variable oxidation state.展开更多
CeO_(2)/g-C_(3)N_(4)photocatalysts have attracted tremendous attention in the photocatalytic degradation of organic pollutants.The design and construction of highly active CeO_(2)/g-C_(3)N_(4)photocatalysts without ha...CeO_(2)/g-C_(3)N_(4)photocatalysts have attracted tremendous attention in the photocatalytic degradation of organic pollutants.The design and construction of highly active CeO_(2)/g-C_(3)N_(4)photocatalysts without harsh conditions are still challenging.Herein,highly dispersed CeO_(2-x)nanoparticles with rich oxygen vacancies were successfully precipitated on the surface of g-C_(3)N_(4)under mild conditions.The fabricated CeO_(2-x)/g-C_(3)N_(4)exhibits remarkable activity and stability for photocatalytic degradation of MO pollutant.The optimal rate constant of MO degradation over CeO_(2-x)/g-C_(3)N_(4)is about 0.031 min^(-1),which is three times higher than that of g-C_(3)N_(4).A negligible activity decrease is observed after three cycling runs.The enhanced catalytic performance can be ascribed to the excellent dispersion of CeO_(2-x)with rich oxygen vacancies that benefit O_(2)adsorption and visible light absorption.In addition,the proper band alignment between CeO_(2-x)and gC_(3)N_(4)is conducive to the highly efficient separation of photogenerated electron-hole pairs.展开更多
Based on the stochastic market demand, this paper considers the order decision-making strategies of the supply chain by introducing statement strategies. Consequently, the time-variant variance in the demands of the m...Based on the stochastic market demand, this paper considers the order decision-making strategies of the supply chain by introducing statement strategies. Consequently, the time-variant variance in the demands of the market is incorporated into the model. The retailer simultaneously determines the purchase time （i.e., lead time） and order quantity, and the manufacturer determines the statement strategy and the reserved profit rate. The results show that the no overtime statement strategy can induce the retailer to place more orders in advance by limiting the available order quantity within the available time. Finally, we also adopt numerical examples to support the conclusion of this paper.展开更多
This short article is the epilog of the 11 preceding papers in this issue of JCM.All contributions are authored by participants of the 6th Sino-German Workshop on Computational and Applied Mathematics at Shanghai.
基金supported by the National Basic Research Program of China under the grant 2005CB321701the National Science Foundation(NSF) of China(10731060)111 project(B08018)
文摘In this paper,standard and economical cascadic multigrid methods are considered for solving the algebraic systems resulting from the mortar finite element methods. Both cascadic multigrid methods do not need full elliptic regularity,so they can be used to tackle more general elliptic problems.Numerical experiments are reported to support our theory.
文摘In this paper,we design an efficient domain decomposition(DD)preconditioner for the saddle-point problem resulting from the mixed finite-element discretization of multiscale elliptic problems.By proper equivalent algebraic operations,the original saddle-point system can be transformed to another saddle-point system which can be preconditioned by a block-diagonel matrix efficiently.Actually,the first block of this block-diagonal matrix corresponds to a multiscale H(div)problem,and thus,the direct inverse of this block is unpractical and unstable for the large-scale problem.To remedy this issue,a two-level overlapping DD preconditioner is proposed for this//(div)problem.Our coarse space consists of some velocities obtained from mixed formulation of local eigenvalue problems on the coarse edge patches multiplied by the partition of unity functions and the trivial coarse basis(e.g.,Raviart-Thomas element)on the coarse grid.The condition number of our preconditioned DD method for this multiscale H(div)system is bounded by C(1+务)(1+log4(^)),where 6 denotes the width of overlapping region,and H,h are the typical sizes of the subdomain and fine mesh.Numerical examples are presented to confirm the validity and robustness of our DD preconditioner.
基金supported by National Natural Science Foundation of China (Grant Nos. 11571053, 11671302, 51239001 and 91647118)
文摘We develop a monotone ?nite volume method for the time fractional Fokker-Planck equations and theoretically prove its unconditional stability. We show that the convergence rate of this method is of order 1 in the space and if the space grid becomes suffciently ?ne, the convergence rate can be improved to order 2.Numerical results are given to support our theoretical ?ndings. One characteristic of our method is that it has monotone property such that it keeps the nonnegativity of some physical variables such as density, concentration,etc.
文摘In this paper, local multiplicative and additive multilevel methods on adaptively refined meshes are considered for second-order elliptic problems with highly discontinuous coeffi- cients. For the multilevel-preconditioned system, we study the distribution of its spectrum by using the abstract Schwarz theory. It is proved that, except for a few small eigenval- ues, the spectrum of the preconditioned system is bounded quasi-uniformly with respect to the jumps of the coefficient and the mesh sizes. The convergence rate of multilevel- preconditioned conjugate gradient methods is shown to be quasi-optimal regarding the jumps and the meshes. Numerical experiments are presented to illustrate the theoretical findings.
文摘In this work, we solve a long-standing open problem： Is it true that the convergence rate of the Lions＇ Robin-Robin nonoverlapping domain decomposition （DD） method can be constant, independent of the mesh size h？ We closed this old problem with a positive answer. Our theory is also verified by numerical tests.
基金Acknowledgements. The work of the first author was supported by the National Basic Research Program under the Grant 2011CB30971 and National Science Foundation of China （11171335）. The work of the second author was supported by the National Natural Science Foundation of China （Grant No. 11201394） and the Fundamental Research Funds for the Central Universities （Grant No. 2012121003）.
文摘In this paper, a local multilevel product algorithm and its additive version are con- sidered for linear systems arising from adaptive nonconforming P1 finite element approx- imations of second order elliptic boundary value problems. The abstract Schwarz theory is applied to analyze the multilevel methods with Jaeobi or Gauss-Seidel smoothers per- formed on local nodes on coarse meshes and global nodes on the finest mesh. It is shown that the local multilevel methods are optimal, i.e., the convergence rate of the multilevel methods is independent of the mesh sizes and mesh levels. Numerical experiments are given to confirm the theoretical results.
基金financially supported by the National Natural Science Foundation of China(21222305,11079005,20923001)the National Basic Research Program of China(2011CBA00503,2013CB933100)
文摘Oxide nanostructures grown on noble metal surfaces are often highly active in many reactions,in which the oxide/metal interfaces play an important role.In the present work,we studied the surface structures of Fe Ox-on-Pt and Ni Ox-on-Pt catalysts and their activity to CO oxidation reactions using both model catalysts and supported nanocatalysts.Although the active Fe O1x structure is stabilized on the Pt surface in a reductive reaction atmosphere,it is prone to change to an Fe O2x structure in oxidative reaction gases and becomes deactivated.In contrast,a Ni O1x surface structure supported on Pt is stable in both reductive and oxidative CO oxidation atmospheres.Consequently,CO oxidation over the Ni O1x-on-Pt catalyst is further enhanced in the CO oxidation atmosphere with an excess of O2.The present results demonstrate that the stability of the active oxide surface phases depends on the stabilization effect of the substrate surface and is also related to whether the oxide exhibits a variable oxidation state.
基金Project supported by the Guangdong Provincial Education Department Special Project of Key Research Areas(2020ZDZX2066)the Innovation Team of Universities of Guangdong Province(2020KCXTD011)+2 种基金the Engineering Research Center of Universities of Guangdong Province(2019GCZX002)the Guangdong Key Laboratory for Hydrogen Energy Technologies(2018B030322005)Guangdong Basic and Applied Basic Research Foundation(2019A1515110586,2019A1515110534)。
文摘CeO_(2)/g-C_(3)N_(4)photocatalysts have attracted tremendous attention in the photocatalytic degradation of organic pollutants.The design and construction of highly active CeO_(2)/g-C_(3)N_(4)photocatalysts without harsh conditions are still challenging.Herein,highly dispersed CeO_(2-x)nanoparticles with rich oxygen vacancies were successfully precipitated on the surface of g-C_(3)N_(4)under mild conditions.The fabricated CeO_(2-x)/g-C_(3)N_(4)exhibits remarkable activity and stability for photocatalytic degradation of MO pollutant.The optimal rate constant of MO degradation over CeO_(2-x)/g-C_(3)N_(4)is about 0.031 min^(-1),which is three times higher than that of g-C_(3)N_(4).A negligible activity decrease is observed after three cycling runs.The enhanced catalytic performance can be ascribed to the excellent dispersion of CeO_(2-x)with rich oxygen vacancies that benefit O_(2)adsorption and visible light absorption.In addition,the proper band alignment between CeO_(2-x)and gC_(3)N_(4)is conducive to the highly efficient separation of photogenerated electron-hole pairs.
基金supported by the National Nature Science Foundation of China under Grant Numbers 71071059,71001041 and 71172075
文摘Based on the stochastic market demand, this paper considers the order decision-making strategies of the supply chain by introducing statement strategies. Consequently, the time-variant variance in the demands of the market is incorporated into the model. The retailer simultaneously determines the purchase time （i.e., lead time） and order quantity, and the manufacturer determines the statement strategy and the reserved profit rate. The results show that the no overtime statement strategy can induce the retailer to place more orders in advance by limiting the available order quantity within the available time. Finally, we also adopt numerical examples to support the conclusion of this paper.
文摘This short article is the epilog of the 11 preceding papers in this issue of JCM.All contributions are authored by participants of the 6th Sino-German Workshop on Computational and Applied Mathematics at Shanghai.
