In this paper,the two level additive Schwarz algorithm of mixed finite element.dts-cretization of Inharmonic problem is presented,the rate of convergenece is obtained.Moreover,the two level multiplicative Schwarz algo...In this paper,the two level additive Schwarz algorithm of mixed finite element.dts-cretization of Inharmonic problem is presented,the rate of convergenece is obtained.Moreover,the two level multiplicative Schwarz algorithm is considered.展开更多
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
Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the add...Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.展开更多
In this paper, a new Schwarz method called restricted additive Schwarz method （RAS） is presented and analyzed for a kind of nonlinear complementarity problem （NCP）. The method is proved to be convergent by using w...In this paper, a new Schwarz method called restricted additive Schwarz method （RAS） is presented and analyzed for a kind of nonlinear complementarity problem （NCP）. The method is proved to be convergent by using weighted maximum norm. Besides, the effect of overlap on RAS is also considered. Some preliminary numerical results are reported to compare the performance of RAS and other known methods for NCP.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.
Schwarz method is put forward to solve second order backward stochastic di erential equations(2BSDEs)in this work.We will analyze uniqueness,convergence,stability and optimality of the proposed method.Moreover,several...Schwarz method is put forward to solve second order backward stochastic di erential equations(2BSDEs)in this work.We will analyze uniqueness,convergence,stability and optimality of the proposed method.Moreover,several simulation results are presented to demonstrate the e ectiveness;several applications of the 2BSDEs are investigated.It is concluded from these results that the proposed the method is powerful to calculate the 2BSDEs listing from the nancial engineering.展开更多
In this paper the Schwarz alternating method for a fourth-order elliptic variational inequality problem is considered by way of the equivalent form, and the geometric convergence is obtained on two subdomains.
Finite Element Method (FEM), when applied to solve problems, has faced some challenges over the years, such as time consumption and the complexity of assumptions. In particular, the making of assumptions has had a sig...Finite Element Method (FEM), when applied to solve problems, has faced some challenges over the years, such as time consumption and the complexity of assumptions. In particular, the making of assumptions has had a significant influence on the accuracy of the method, making it mandatory to carry out sensitivity analysis. The sensitivity analysis helps to identify the level of impact the assumptions have on the method. However, sensitivity analysis via FEM can be very challenging. A priori error estimation, an integral part of FEM, is a basic mathematical tool for predicting the accuracy of numerical solutions. By understanding the relationship between the mesh size, the order of basis functions, and the resulting error, practitioners can effectively design and apply FEM to solve complex Partial Differential Equations (PDEs) with confidence in the reliability of their results. Thus, the coercive property and A priori error estimation based on the L1 formula on a mesh in time and the Mamadu-Njoseh basis functions in space are investigated for a linearly distributed time-order fractional telegraph equation with restricted initial conditions. For this purpose, we constructed a mathematical proof of the coercive property for the fully discretized scheme. Also, we stated and proved a cardinal theorem for a priori error estimation of the approximate solution for the fully discretized scheme. We noticed the role of the restricted initial conditions imposed on the solution in the analysis of a priori error estimation.展开更多
基金The research was supported by the Doctoral Point Foundation of China Universities and by State Major Key Project for Basic Research of China.
文摘In this paper,the two level additive Schwarz algorithm of mixed finite element.dts-cretization of Inharmonic problem is presented,the rate of convergenece is obtained.Moreover,the two level multiplicative Schwarz algorithm is considered.
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supported by the National Natural Science Foundation of China (No. 10671154)the Na-tional Basic Research Program (No. 2005CB321703)the Science and Technology Foundation of Guizhou Province of China (No. [2008]2123)
文摘Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.
基金The authors would like to thank the anonymous referees for their valuable suggestions and comments, which improved the paper greatly. The work was supported by Natural Science Foundation of Guangdong Province,China （Grant No.S2012040007993） and Educational Commission of Guangdong Province, China （Grant No. 2012LYM_0122）, NNSF of China （Grand No.11126147）, NNSF of China （Grand No.11201197） and NNSF of China （Grand No.11271069）.
文摘In this paper, a new Schwarz method called restricted additive Schwarz method （RAS） is presented and analyzed for a kind of nonlinear complementarity problem （NCP）. The method is proved to be convergent by using weighted maximum norm. Besides, the effect of overlap on RAS is also considered. Some preliminary numerical results are reported to compare the performance of RAS and other known methods for NCP.
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.
文摘Schwarz method is put forward to solve second order backward stochastic di erential equations(2BSDEs)in this work.We will analyze uniqueness,convergence,stability and optimality of the proposed method.Moreover,several simulation results are presented to demonstrate the e ectiveness;several applications of the 2BSDEs are investigated.It is concluded from these results that the proposed the method is powerful to calculate the 2BSDEs listing from the nancial engineering.
文摘In this paper the Schwarz alternating method for a fourth-order elliptic variational inequality problem is considered by way of the equivalent form, and the geometric convergence is obtained on two subdomains.
文摘Finite Element Method (FEM), when applied to solve problems, has faced some challenges over the years, such as time consumption and the complexity of assumptions. In particular, the making of assumptions has had a significant influence on the accuracy of the method, making it mandatory to carry out sensitivity analysis. The sensitivity analysis helps to identify the level of impact the assumptions have on the method. However, sensitivity analysis via FEM can be very challenging. A priori error estimation, an integral part of FEM, is a basic mathematical tool for predicting the accuracy of numerical solutions. By understanding the relationship between the mesh size, the order of basis functions, and the resulting error, practitioners can effectively design and apply FEM to solve complex Partial Differential Equations (PDEs) with confidence in the reliability of their results. Thus, the coercive property and A priori error estimation based on the L1 formula on a mesh in time and the Mamadu-Njoseh basis functions in space are investigated for a linearly distributed time-order fractional telegraph equation with restricted initial conditions. For this purpose, we constructed a mathematical proof of the coercive property for the fully discretized scheme. Also, we stated and proved a cardinal theorem for a priori error estimation of the approximate solution for the fully discretized scheme. We noticed the role of the restricted initial conditions imposed on the solution in the analysis of a priori error estimation.
