The nonoverlapping domain decomposition method for parabolic partialdifferential equation on general domain is considered. A kind of domain decompositionthat uses the finite element procedure is given. The problem ove...The nonoverlapping domain decomposition method for parabolic partialdifferential equation on general domain is considered. A kind of domain decompositionthat uses the finite element procedure is given. The problem over the domains can beimplemented on parallel computer. Convergence analysis is also presented.展开更多
In this paper,we consider the cascadic multigrid method for a parabolic type equation.Backward Euler approximation in time and linear finite element approximation in space are employed.A stability result is establishe...In this paper,we consider the cascadic multigrid method for a parabolic type equation.Backward Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some conditions on the smoother.Using new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter,these conditions are verified for a number of popular smoothers.Optimal error bound sare derived for both smooth and non-smooth data.Iteration strategies guaranteeing both the optimal accuracy and the optimal complexity are presented.展开更多
文摘The nonoverlapping domain decomposition method for parabolic partialdifferential equation on general domain is considered. A kind of domain decompositionthat uses the finite element procedure is given. The problem over the domains can beimplemented on parallel computer. Convergence analysis is also presented.
基金the National Science Foundation(Grant Nos.DMS0409297,DMR0205232,CCF-0430349)US National Institute of Health-National Cancer Institute(Grant No.1R01CA125707-01A1)+2 种基金the National Natural Science Foundation of China(Grant No.10571172)the National Basic Research Program(Grant No.2005CB321704)the Youth's Innovative Program of Chinese Academy of Sciences(Grant Nos.K7290312G9,K7502712F9)
文摘In this paper,we consider the cascadic multigrid method for a parabolic type equation.Backward Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some conditions on the smoother.Using new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter,these conditions are verified for a number of popular smoothers.Optimal error bound sare derived for both smooth and non-smooth data.Iteration strategies guaranteeing both the optimal accuracy and the optimal complexity are presented.
