Additive Schwarz algorithms for solving the discrete problems of twrvside obstacle problems are proposed. The monotone convergence of the algorithms is established for M-matrix and the h-independent convergence rate i...Additive Schwarz algorithms for solving the discrete problems of twrvside obstacle problems are proposed. The monotone convergence of the algorithms is established for M-matrix and the h-independent convergence rate is proved for S-matrix. The so-called finite step convergence for coincident components is discussed for nondegenerate discreted problems.展开更多
The industry-standard constrained pressure residual(CPR)algorithm is often able to effectively improve the robustness behavior and the convergence speed of linear iterations for isothermal reservoir simulation.In this...The industry-standard constrained pressure residual(CPR)algorithm is often able to effectively improve the robustness behavior and the convergence speed of linear iterations for isothermal reservoir simulation.In this paper,we present and study an improved extension of CPR to the constrained pressure-temperature residual(CPTR)version for non-isothermal reservoir problems in heterogeneous porous media.In the proposed preconditioner,the corresponding approximations for the inverse of matrices are computed under a domain decomposition framework by using the restricted additive Schwarz(RAS)algorithm,to equally deal with the coupled thermalpressure-saturation reservoir system and highly exploit the parallelism of supercomputer platforms.Moreover,we introduce and develop a family of multilevel CPTR preconditioners with suitable coarse grid corrections,to further improve the applicability of this two-stage preconditioner for large-scale computation.Numerical results for strong heterogeneous flow problems show that the new approach can dramatically improve the convergence of linear iterations,and demonstrate the superiority of CPTR over the commonly used RAS preconditioners.The parallel scalability of the non-isothermal reservoir simulator is also studied versus a supercomputer with tens of thousands of processors.展开更多
In this paper,we establish a new algorithm to the non-overlapping Schwarz domain decomposition methods with changing transmission conditions for solving one dimensional advection reaction diffusion problem.More precis...In this paper,we establish a new algorithm to the non-overlapping Schwarz domain decomposition methods with changing transmission conditions for solving one dimensional advection reaction diffusion problem.More precisely,we first describe the new algorithm and prove the convergence results under several natural assumptions on the sequences of parameters which determine the transmission conditions.Then we give a simple method to estimate the new value of parameters in each iteration.The interesting advantage of our method is that one may update the better parameters in each iteration to save the computational cost for optimizing the parameters after many steps.Finally some numerical experiments are performed to show the behavior of the convergence rate for the new method.展开更多
Two kinds of Schwarz type domain decomposition methods are introduced to solve thegeneral selfadjoint second order parabolic partial differential equstions, and the dependence ofconvergence rate of these algorithms on...Two kinds of Schwarz type domain decomposition methods are introduced to solve thegeneral selfadjoint second order parabolic partial differential equstions, and the dependence ofconvergence rate of these algorithms on parameters of time-step and space-mesh is also analyzed.The convergence, independent of the iteration times at each time-level, of the approximate solution is proved and a priori optimal L2 error estimates are given.展开更多
The convergence rate of a generalized additive Schwarz algorithm for solving boundary value problems of elliptic partial differential equations is studied. A quantitative analysis of the convergence rate is given for ...The convergence rate of a generalized additive Schwarz algorithm for solving boundary value problems of elliptic partial differential equations is studied. A quantitative analysis of the convergence rate is given for the model Dirichlet problem. It will be shown that a greater acceleration of the algorithm can be obtained by choosing the parameter suitably. Some numerical tests are also presented in this paper.展开更多
Focuses on a study which presented monotonic iterative algorithms for solving quasicomplementarity problem (QCP). Details on the sequential complementarity problem (CP) algorithm; Information on the supersolution and ...Focuses on a study which presented monotonic iterative algorithms for solving quasicomplementarity problem (QCP). Details on the sequential complementarity problem (CP) algorithm; Information on the supersolution and subsolution of CP to QCP; Equation of Schwarz algorithm.展开更多
Partition property plays a central role in domain decomposition methods. Existing theory essentially assumes certain ellipticity. We prove the partition property for prod lems without ellipticity which are of practica...Partition property plays a central role in domain decomposition methods. Existing theory essentially assumes certain ellipticity. We prove the partition property for prod lems without ellipticity which are of practical importance. Example applications include implicit schemes applied to degenerate parabolic partial differential equations arising from superconductors, superfluids and liquid crystals. With this partition property, Schwarz algorithms can be applied to general non-elliptic problems with an h-independent optimal convergence rate. Application to the time-dependent Ginzburg-Landau model of superconductivity is illustrated and numerical results are presented.展开更多
An efficient iteration-by-subdomain method (known as the Schwarz alternating algorithm) for incompressible viscous/inviscid coupled model is presented. Appropriate spectral collocation approximations are proposed. The...An efficient iteration-by-subdomain method (known as the Schwarz alternating algorithm) for incompressible viscous/inviscid coupled model is presented. Appropriate spectral collocation approximations are proposed. The convergence analysis show that the iterative algorithms converge with a rate independent of the polynomial degree used.展开更多
Domain decomposition method and multigrid method can be unified in the framework of the space decomposition method. This paper has obtained a new result on the convergence rate of the space decomposition method, which...Domain decomposition method and multigrid method can be unified in the framework of the space decomposition method. This paper has obtained a new result on the convergence rate of the space decomposition method, which can be applied to some nonuniformly elliptic problems.展开更多
文摘Additive Schwarz algorithms for solving the discrete problems of twrvside obstacle problems are proposed. The monotone convergence of the algorithms is established for M-matrix and the h-independent convergence rate is proved for S-matrix. The so-called finite step convergence for coincident components is discussed for nondegenerate discreted problems.
基金supported by the National Natural Science Foundation of China(No.12131002 and No.11971006)Shenzhen Science and Technology Program(No.JCYJ20210324130801003)+2 种基金Guangdong Basic and Applied Basic Research Foundation(No.2022A1515010147)Changsha science and technology bureau(No.kh2301001)The fourth author also greatly thanks for the support from King Abdullah University of Science and Technology(KAUST)through the grants BAS/1/1351-01 and URF/1/4074-01.
文摘The industry-standard constrained pressure residual(CPR)algorithm is often able to effectively improve the robustness behavior and the convergence speed of linear iterations for isothermal reservoir simulation.In this paper,we present and study an improved extension of CPR to the constrained pressure-temperature residual(CPTR)version for non-isothermal reservoir problems in heterogeneous porous media.In the proposed preconditioner,the corresponding approximations for the inverse of matrices are computed under a domain decomposition framework by using the restricted additive Schwarz(RAS)algorithm,to equally deal with the coupled thermalpressure-saturation reservoir system and highly exploit the parallelism of supercomputer platforms.Moreover,we introduce and develop a family of multilevel CPTR preconditioners with suitable coarse grid corrections,to further improve the applicability of this two-stage preconditioner for large-scale computation.Numerical results for strong heterogeneous flow problems show that the new approach can dramatically improve the convergence of linear iterations,and demonstrate the superiority of CPTR over the commonly used RAS preconditioners.The parallel scalability of the non-isothermal reservoir simulator is also studied versus a supercomputer with tens of thousands of processors.
文摘In this paper,we establish a new algorithm to the non-overlapping Schwarz domain decomposition methods with changing transmission conditions for solving one dimensional advection reaction diffusion problem.More precisely,we first describe the new algorithm and prove the convergence results under several natural assumptions on the sequences of parameters which determine the transmission conditions.Then we give a simple method to estimate the new value of parameters in each iteration.The interesting advantage of our method is that one may update the better parameters in each iteration to save the computational cost for optimizing the parameters after many steps.Finally some numerical experiments are performed to show the behavior of the convergence rate for the new method.
文摘Two kinds of Schwarz type domain decomposition methods are introduced to solve thegeneral selfadjoint second order parabolic partial differential equstions, and the dependence ofconvergence rate of these algorithms on parameters of time-step and space-mesh is also analyzed.The convergence, independent of the iteration times at each time-level, of the approximate solution is proved and a priori optimal L2 error estimates are given.
基金This work was supported by 973 project granted 2004CB719402 and national nature science foundation granted 10371035. We would like to thank the anonymous referees for their invaluable comments and suggestions, We would like also to thank the State Key Laboratory of Advanced Design and Manufacture for Vehicle Body of Hunan University since the work was done while the authors were working there.
文摘The convergence rate of a generalized additive Schwarz algorithm for solving boundary value problems of elliptic partial differential equations is studied. A quantitative analysis of the convergence rate is given for the model Dirichlet problem. It will be shown that a greater acceleration of the algorithm can be obtained by choosing the parameter suitably. Some numerical tests are also presented in this paper.
文摘Focuses on a study which presented monotonic iterative algorithms for solving quasicomplementarity problem (QCP). Details on the sequential complementarity problem (CP) algorithm; Information on the supersolution and subsolution of CP to QCP; Equation of Schwarz algorithm.
基金This work was supported in part by Hong Kong RGC DAG93/94 SC10, Competitive Earmarked ResearchGrant HKUST593/94E and the speci
文摘Partition property plays a central role in domain decomposition methods. Existing theory essentially assumes certain ellipticity. We prove the partition property for prod lems without ellipticity which are of practical importance. Example applications include implicit schemes applied to degenerate parabolic partial differential equations arising from superconductors, superfluids and liquid crystals. With this partition property, Schwarz algorithms can be applied to general non-elliptic problems with an h-independent optimal convergence rate. Application to the time-dependent Ginzburg-Landau model of superconductivity is illustrated and numerical results are presented.
文摘An efficient iteration-by-subdomain method (known as the Schwarz alternating algorithm) for incompressible viscous/inviscid coupled model is presented. Appropriate spectral collocation approximations are proposed. The convergence analysis show that the iterative algorithms converge with a rate independent of the polynomial degree used.
基金the National Natural Science Foundation of China (No.19771034).
文摘Domain decomposition method and multigrid method can be unified in the framework of the space decomposition method. This paper has obtained a new result on the convergence rate of the space decomposition method, which can be applied to some nonuniformly elliptic problems.
