Based on two-grid discretizations, in this paper, some new local and parallel finite element algorithms are proposed and analyzed for the stationary incompressible Navier- Stokes problem. These algorithms are motivate...Based on two-grid discretizations, in this paper, some new local and parallel finite element algorithms are proposed and analyzed for the stationary incompressible Navier- Stokes problem. These algorithms are motivated by the observation that for a solution to the Navier-Stokes problem, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedure. One major technical tool for the analysis is some local a priori error estimates that are also obtained in this paper for the finite element solutions on general shape-regular grids.展开更多
Some new local and parallel finite element algorithms are proposed and analyzed in this paper for eigenvalue problems. With these algorithms, the solution of an eigenvalue problem on a fine grid is reduced to the solu...Some new local and parallel finite element algorithms are proposed and analyzed in this paper for eigenvalue problems. With these algorithms, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a relatively coarse grid together with solutions of some linear algebraic systems on fine grid by using some local and parallel procedure. A theoretical tool for analyzing these algorithms is some local error estimate that is also obtained in this paper for finite element approximations of eigenvectors on general shape-regular grids.展开更多
By combination of iteration methods with the partition of unity method(PUM),some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD)with different physical parameters are pre...By combination of iteration methods with the partition of unity method(PUM),some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD)with different physical parameters are presented and analyzed.These algorithms are highly efficient.At first,a global solution is obtained on a coarse grid for all approaches by one of the iteration methods.By parallelized residual schemes,local corrected solutions are calculated on finer meshes with overlapping sub-domains.The subdomains can be achieved flexibly by a class of PUM.The proposed algorithm is proved to be uniformly stable and convergent.Finally,one numerical example is presented to confirm the theoretical findings.展开更多
In this paper,a multiscale model is developed for the mass functionally graded(FG)beam-fluid system to investigate its static and dynamic responses based on 3D printed porous beam free vibration tests,which are determ...In this paper,a multiscale model is developed for the mass functionally graded(FG)beam-fluid system to investigate its static and dynamic responses based on 3D printed porous beam free vibration tests,which are determined by two aspects.At the microstructural level,the gradient variation is realized by arbitrary distribution of matrix pores,and the effective moduli under specific distribution are obtained using the micromechanics homogenization theory.In the meantime,at the structural level,the mechanical responses of FG porous beams subjected to mass loading are considered in a static fluid environment.Then,the explicit expressions of local finite-element(FE)expressions corresponding to the static and dynamic responses are given in the appendices.The present results are validated against numerical and experimental results from the literature and mechanical tests of 3D printed structures,with good agreement generally obtained,giving credence to the present model.On this basis,a comprehensive parametric study is carried out,with a particular focus on the effects of boundary conditions,fluid density,and slenderness ratio on the bending and vibration of FG beams with several different gradations.展开更多
基金The first author was partially subsidized by the NSF of China 10371095. The third author was partially supported by the National Science Foundation of China under the grant 10425105 and the National Basic Research Program under the grant 2005CB321704.
文摘Based on two-grid discretizations, in this paper, some new local and parallel finite element algorithms are proposed and analyzed for the stationary incompressible Navier- Stokes problem. These algorithms are motivated by the observation that for a solution to the Navier-Stokes problem, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedure. One major technical tool for the analysis is some local a priori error estimates that are also obtained in this paper for the finite element solutions on general shape-regular grids.
基金Partially supported by NSF DMS-0074299 through Penn State and Center for Computational Mathematics and Applications, The Pennsylvania State University.Subsidized by the Special Funds for Major State Basic Research Projects, and also partially supported
文摘Some new local and parallel finite element algorithms are proposed and analyzed in this paper for eigenvalue problems. With these algorithms, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a relatively coarse grid together with solutions of some linear algebraic systems on fine grid by using some local and parallel procedure. A theoretical tool for analyzing these algorithms is some local error estimate that is also obtained in this paper for finite element approximations of eigenvectors on general shape-regular grids.
基金supported by the National Natural Science Foundation of China(Grant Nos.12071404,12271465,12026254)by the Young Elite Scientist Sponsorship Program by CAST(Grant No.2020QNRC001)+3 种基金by the China Postdoctoral Science Foundation(Grant No.2018T110073)by the Natural Science Foundation of Hunan Province(Grant No.2019JJ40279)by the Excellent Youth Program of Scientific Research Project of Hunan Provincial Department of Education(Grant No.20B564)by the International Scientific and Technological Innovation Cooperation Base of Hunan Province for Computational Science(Grant No.2018WK4006).
文摘By combination of iteration methods with the partition of unity method(PUM),some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD)with different physical parameters are presented and analyzed.These algorithms are highly efficient.At first,a global solution is obtained on a coarse grid for all approaches by one of the iteration methods.By parallelized residual schemes,local corrected solutions are calculated on finer meshes with overlapping sub-domains.The subdomains can be achieved flexibly by a class of PUM.The proposed algorithm is proved to be uniformly stable and convergent.Finally,one numerical example is presented to confirm the theoretical findings.
基金supported by the National Key Research and Development Program of China(No.2020YFA0711700)the National Natural Science Foundation of China(No.12322206,No.52378158,No.12302205)ZJU-ZCCC Institute of Collaborative Innovation(No.ZDJG2021002).
文摘In this paper,a multiscale model is developed for the mass functionally graded(FG)beam-fluid system to investigate its static and dynamic responses based on 3D printed porous beam free vibration tests,which are determined by two aspects.At the microstructural level,the gradient variation is realized by arbitrary distribution of matrix pores,and the effective moduli under specific distribution are obtained using the micromechanics homogenization theory.In the meantime,at the structural level,the mechanical responses of FG porous beams subjected to mass loading are considered in a static fluid environment.Then,the explicit expressions of local finite-element(FE)expressions corresponding to the static and dynamic responses are given in the appendices.The present results are validated against numerical and experimental results from the literature and mechanical tests of 3D printed structures,with good agreement generally obtained,giving credence to the present model.On this basis,a comprehensive parametric study is carried out,with a particular focus on the effects of boundary conditions,fluid density,and slenderness ratio on the bending and vibration of FG beams with several different gradations.
