The deferred correction(DeC)is an iterative procedure,characterized by increasing the accuracy at each iteration,which can be used to design numerical methods for systems of ODEs.The main advantage of such framework i...The deferred correction(DeC)is an iterative procedure,characterized by increasing the accuracy at each iteration,which can be used to design numerical methods for systems of ODEs.The main advantage of such framework is the automatic way of getting arbitrarily high order methods,which can be put in the Runge-Kutta(RK)form.The drawback is the larger computational cost with respect to the most used RK methods.To reduce such cost,in an explicit setting,we propose an efcient modifcation:we introduce interpolation processes between the DeC iterations,decreasing the computational cost associated to the low order ones.We provide the Butcher tableaux of the new modifed methods and we study their stability,showing that in some cases the computational advantage does not afect the stability.The fexibility of the novel modifcation allows nontrivial applications to PDEs and construction of adaptive methods.The good performances of the introduced methods are broadly tested on several benchmarks both in ODE and PDE contexts.展开更多
Tornado codes have been used in the error control of data transmission in IP network. The efficiency of this erasure codes is critically affected by the short cycles in its bipartite graph. To remove this effect, two ...Tornado codes have been used in the error control of data transmission in IP network. The efficiency of this erasure codes is critically affected by the short cycles in its bipartite graph. To remove this effect, two algorithms are introduced: (1) while generating the graph, the cycle eliminating algorithm is used to reduce the number of the short cycles in it; (2) in the decoding algorithm, cycles that are inevitably in the graph are used to remove decoding efficiency degradation. The simulation results show that they have a better performance than that of general tornado codes.展开更多
文摘The deferred correction(DeC)is an iterative procedure,characterized by increasing the accuracy at each iteration,which can be used to design numerical methods for systems of ODEs.The main advantage of such framework is the automatic way of getting arbitrarily high order methods,which can be put in the Runge-Kutta(RK)form.The drawback is the larger computational cost with respect to the most used RK methods.To reduce such cost,in an explicit setting,we propose an efcient modifcation:we introduce interpolation processes between the DeC iterations,decreasing the computational cost associated to the low order ones.We provide the Butcher tableaux of the new modifed methods and we study their stability,showing that in some cases the computational advantage does not afect the stability.The fexibility of the novel modifcation allows nontrivial applications to PDEs and construction of adaptive methods.The good performances of the introduced methods are broadly tested on several benchmarks both in ODE and PDE contexts.
基金Supported by the National Natural Science Foundation of China(No.61072030) & Huawei Technologies Foundation
文摘Tornado codes have been used in the error control of data transmission in IP network. The efficiency of this erasure codes is critically affected by the short cycles in its bipartite graph. To remove this effect, two algorithms are introduced: (1) while generating the graph, the cycle eliminating algorithm is used to reduce the number of the short cycles in it; (2) in the decoding algorithm, cycles that are inevitably in the graph are used to remove decoding efficiency degradation. The simulation results show that they have a better performance than that of general tornado codes.
