In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,t...In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.展开更多
In this paper,we established a class of parallel algorithm for solving low-rank tensor completion problem.The main idea is that N singular value decompositions are implemented in N different processors for each slice ...In this paper,we established a class of parallel algorithm for solving low-rank tensor completion problem.The main idea is that N singular value decompositions are implemented in N different processors for each slice matrix under unfold operator,and then the fold operator is used to form the next iteration tensor such that the computing time can be decreased.In theory,we analyze the global convergence of the algorithm.In numerical experiment,the simulation data and real image inpainting are carried out.Experiment results show the parallel algorithm outperform its original algorithm in CPU times under the same precision.展开更多
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)+2 种基金Basic Research Plan of Shanxi Province(202203021211129)Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)。
文摘In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.
基金Supported by National Nature Science Foundation(12371381)Nature Science Foundation of Shanxi(202403021222270)。
文摘In this paper,we established a class of parallel algorithm for solving low-rank tensor completion problem.The main idea is that N singular value decompositions are implemented in N different processors for each slice matrix under unfold operator,and then the fold operator is used to form the next iteration tensor such that the computing time can be decreased.In theory,we analyze the global convergence of the algorithm.In numerical experiment,the simulation data and real image inpainting are carried out.Experiment results show the parallel algorithm outperform its original algorithm in CPU times under the same precision.
