Matrix analysis on additive Schwarz methods as preconditioners is given in this paper. Both cases of with and without coarse mesh are considered. It is pointed out that an advantage of matrix analysis is to obtain mor...Matrix analysis on additive Schwarz methods as preconditioners is given in this paper. Both cases of with and without coarse mesh are considered. It is pointed out that an advantage of matrix analysis is to obtain more exact upper hound. Our numerical tests access the estimations.展开更多
It is well known the order of preconditioned matrix by using additive Schwarz methods. In order to estimate the resulted PCG iteration counts, the related leading term brfore the order is given in this paper.
In the past few years,the number of processor cores of top ranked supercomputers has increased drastically.It is challenging to design efficient parallel algorithms that offer such a high degree of parallelism,especia...In the past few years,the number of processor cores of top ranked supercomputers has increased drastically.It is challenging to design efficient parallel algorithms that offer such a high degree of parallelism,especially for certain time-dependent problems because of the sequential nature of“time”.To increase the degree of parallelization,some parallel-in-time algorithms have been developed.In this paper,we give an overview of some recently introduced parallel-in-time methods,and present in detail the class of space-time Schwarz methods,including the standard and the restricted versions,for solving parabolic partial differentialequations.Some numerical experiments carried out on a parallel computer with a large number of processor cores for three-dimensional problems are given to show the parallel scalability of the methods.In the end of the paper,we provide a comparison of the parallel-in-time algorithms with a traditional algorithm that is parallelized only in space.展开更多
文摘Matrix analysis on additive Schwarz methods as preconditioners is given in this paper. Both cases of with and without coarse mesh are considered. It is pointed out that an advantage of matrix analysis is to obtain more exact upper hound. Our numerical tests access the estimations.
基金This work was partly supported by National Natural Science Foundation of China and Laboratory LSEC.
文摘It is well known the order of preconditioned matrix by using additive Schwarz methods. In order to estimate the resulted PCG iteration counts, the related leading term brfore the order is given in this paper.
基金supported by the National Key R&D Program of China 2016YFB0200601the Shenzhen basic research grant JCYJ20160331193229720,JCYJ20170307165328836,JCYJ20170818153840322NSFC 11701133,61531166003,11726636.
文摘In the past few years,the number of processor cores of top ranked supercomputers has increased drastically.It is challenging to design efficient parallel algorithms that offer such a high degree of parallelism,especially for certain time-dependent problems because of the sequential nature of“time”.To increase the degree of parallelization,some parallel-in-time algorithms have been developed.In this paper,we give an overview of some recently introduced parallel-in-time methods,and present in detail the class of space-time Schwarz methods,including the standard and the restricted versions,for solving parabolic partial differentialequations.Some numerical experiments carried out on a parallel computer with a large number of processor cores for three-dimensional problems are given to show the parallel scalability of the methods.In the end of the paper,we provide a comparison of the parallel-in-time algorithms with a traditional algorithm that is parallelized only in space.
