A matrix equation solved in an eddy current analysis,??-??method based on a domain decomposition method becomes a complex symmetric system.In general,iterative method is used as the solver.Convergence of iterative met...A matrix equation solved in an eddy current analysis,??-??method based on a domain decomposition method becomes a complex symmetric system.In general,iterative method is used as the solver.Convergence of iterative method in an interface problem is improved by increasing an accuracy of a solution of an iterative method of a subdomain problem.However,it is difficult to improve the convergence by using a small convergence criterion in the subdomain problem.Therefore,authors propose a method to introduce double-double precision into the interface problem and the subdomain problem.This proposed method improves the convergence of the interface problem.In this paper,first,we describe proposed method.Second,we confirm validity of the method by using Team Workshop Problem 7,standard model for eddy current analysis.Finally,we show effectiveness of the method from two numerical results.展开更多
A domain decomposition algorithm coupling the finite element and the boundary element was presented. It essentially involves subdivision of the analyzed domain into sub-regions being independently modeled by two metho...A domain decomposition algorithm coupling the finite element and the boundary element was presented. It essentially involves subdivision of the analyzed domain into sub-regions being independently modeled by two methods, i.e., the finite element method （FEM） and the boundary element method （BEM）. The original problem was restored with continuity and equilibrium conditions being satisfied on the interface of the two sub-regions using an iterative algorithm. To speed up the convergence rate of the iterative algorithm, a dynamically changing relaxation parameter during iteration was introduced. An advantage of the proposed algorithm is that the locations of the nodes on the interface of the two sub-domains can be inconsistent. The validity of the algorithm is demonstrated by the consistence of the results of a numerical example obtained by the proposed method and those by the FEM, the BEM and a present finite element-boundary element （FE-BE） coupling method.展开更多
Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations...Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.展开更多
In this paper, we shall study the domain decomposition techniques for the finite element probability computational methods. These techniques provide a theoretical basis for parallel probability computational methods.
INTERNODES is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into two or several disjoint subdomains. It exploits two intergrid ...INTERNODES is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into two or several disjoint subdomains. It exploits two intergrid interpolation operators, one for transfering the Dirichlet trace across the interfaces, and the other for the Neumann trace. In this paper, in every subdomain the original problem is discretized by either the finite element method (FEM) or the spectral element method (SEM or hp-FEM), using a priori non-matching grids and piecewise polynomials of different degrees. Other discretization methods, however, can be used. INTERNODES can also be applied to heterogeneous or multiphysics problems, that is, problems that feature different differential operators inside adjacent subdomains. For instance, in this paper we apply the INTERNODES method to a Stokes- Darcy coupled problem that models the filtration of fluids in porous media. Our results highlight the flexibility of the method as well as its optimal rate of convergence with respect to the grid size and the polynomial degree.展开更多
We consider, in this paper, the trace averaging domain decomposition method for the second order self-adjoint elliptic problems discretized by a class of nonconforming finite elements, which is only continuous at the ...We consider, in this paper, the trace averaging domain decomposition method for the second order self-adjoint elliptic problems discretized by a class of nonconforming finite elements, which is only continuous at the nodes of the quasi-uniform mesh. We show its geometric convergence and present the dependence of the convergence factor on the relaxation factor, the subdomain diameter H and the mesh parameter h. In essence;, this method is equivalent to the simple iterative method for the preconditioned capacitance equation. The preconditioner implied in this iteration is easily invertible and can be applied to preconditioning the capacitance matrix with the condition number no more than O((1 + In H/h)max(1 + H-2, 1 + In H/h)).展开更多
在导弹类金属-介质复合目标电磁散射特性求解过程中,采用常规迭代求解方法存在难以收敛以及内迭代边界积分区域重复求解的问题。针对该问题,在传统有限元边界积分区域分解法(finite element boundary integral domain decomposition met...在导弹类金属-介质复合目标电磁散射特性求解过程中,采用常规迭代求解方法存在难以收敛以及内迭代边界积分区域重复求解的问题。针对该问题,在传统有限元边界积分区域分解法(finite element boundary integral domain decomposition method,FE-BI-DDM)的基础上,采用了更为灵活的多区多求解器的方法(multi domain multi solver method,MDMSM)。该方法对导弹类金属-介质复合目标中难以收敛的金属区域,使用快速直接求逆的方法求解,由于可以使用独立的网格模型进行电磁建模,避免了内迭代部分的模型重复建立过程,从而大幅减少了整体模型求解时间。实验结果表明:所提方法可以在相同计算精度的条件下,以不过多增加内存空间为前提,大幅缩短了导弹类目标的金属-介质复合模型的电磁求解时间。该方法为开展导弹类目标特性分析提供了一条可行的技术途径。展开更多
In this study, for the purpose of improving the efficiency and accuracy of numerical simulation of massive concrete, the symmetric successive over relaxation-preconditioned conjugate gradient method （SSOR-PCGM） with...In this study, for the purpose of improving the efficiency and accuracy of numerical simulation of massive concrete, the symmetric successive over relaxation-preconditioned conjugate gradient method （SSOR-PCGM） with an improved iteration format was derived and applied to solution of large sparse symmetric positive definite linear equations in the computational process of the finite element analysis. A three-dimensional simulation program for massive concrete was developed based on SSOR-PCGM with an improved iteration format. Then, the programs based on the direct method and SSOR-PCGM with an improved iteration format were used for computation of the Guandi roller compacted concrete （RCC） gravity dam and an elastic cube under free expansion. The comparison and analysis of the computational results show that SSOR-PCGM with the improved iteration format occupies much less physical memory and can solve larger-scale problems with much less computing time and flexible control of accuracy.展开更多
岩土工程规模大,加上岩土介质复杂的特性,使得当前有限元数值模拟在时间和精确度上很难达到工程要求。研究了在普通 PC 机群上实现的大规模并行有限元方法,以更好地发挥有限元在岩土工程中的应用。组建了Windows 下 PC 机群并行系统。...岩土工程规模大,加上岩土介质复杂的特性,使得当前有限元数值模拟在时间和精确度上很难达到工程要求。研究了在普通 PC 机群上实现的大规模并行有限元方法,以更好地发挥有限元在岩土工程中的应用。组建了Windows 下 PC 机群并行系统。采用“分而治之”的并行策略实现有限元并行,并实现了存储局部化。采用基于区域分解预处理技术的并行共轭梯度法来实现方程组的求解。集成以上方法,用 C++开发了并行有限元程序ParallelGeoFEM。对水布垭地下厂房进行了三维有限元并行模拟,得到了较好的加速比。结果表明,基于区域分解的并行有限元方法可以实现岩土工程大规模快速精细的模拟。展开更多
文摘A matrix equation solved in an eddy current analysis,??-??method based on a domain decomposition method becomes a complex symmetric system.In general,iterative method is used as the solver.Convergence of iterative method in an interface problem is improved by increasing an accuracy of a solution of an iterative method of a subdomain problem.However,it is difficult to improve the convergence by using a small convergence criterion in the subdomain problem.Therefore,authors propose a method to introduce double-double precision into the interface problem and the subdomain problem.This proposed method improves the convergence of the interface problem.In this paper,first,we describe proposed method.Second,we confirm validity of the method by using Team Workshop Problem 7,standard model for eddy current analysis.Finally,we show effectiveness of the method from two numerical results.
基金Project supported by China Postdoctoral Science Foundation (No.2004036145)
文摘A domain decomposition algorithm coupling the finite element and the boundary element was presented. It essentially involves subdivision of the analyzed domain into sub-regions being independently modeled by two methods, i.e., the finite element method （FEM） and the boundary element method （BEM）. The original problem was restored with continuity and equilibrium conditions being satisfied on the interface of the two sub-regions using an iterative algorithm. To speed up the convergence rate of the iterative algorithm, a dynamically changing relaxation parameter during iteration was introduced. An advantage of the proposed algorithm is that the locations of the nodes on the interface of the two sub-domains can be inconsistent. The validity of the algorithm is demonstrated by the consistence of the results of a numerical example obtained by the proposed method and those by the FEM, the BEM and a present finite element-boundary element （FE-BE） coupling method.
基金Project supported by the National Natural Science Foundation of China(No.11001061)the Science and Technology Foundation of Guizhou Province of China(No.[2008]2123)
文摘Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.
基金This research is supported by the Foundation of Education Committee of Henan Province.
文摘In this paper, we shall study the domain decomposition techniques for the finite element probability computational methods. These techniques provide a theoretical basis for parallel probability computational methods.
文摘INTERNODES is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into two or several disjoint subdomains. It exploits two intergrid interpolation operators, one for transfering the Dirichlet trace across the interfaces, and the other for the Neumann trace. In this paper, in every subdomain the original problem is discretized by either the finite element method (FEM) or the spectral element method (SEM or hp-FEM), using a priori non-matching grids and piecewise polynomials of different degrees. Other discretization methods, however, can be used. INTERNODES can also be applied to heterogeneous or multiphysics problems, that is, problems that feature different differential operators inside adjacent subdomains. For instance, in this paper we apply the INTERNODES method to a Stokes- Darcy coupled problem that models the filtration of fluids in porous media. Our results highlight the flexibility of the method as well as its optimal rate of convergence with respect to the grid size and the polynomial degree.
文摘We consider, in this paper, the trace averaging domain decomposition method for the second order self-adjoint elliptic problems discretized by a class of nonconforming finite elements, which is only continuous at the nodes of the quasi-uniform mesh. We show its geometric convergence and present the dependence of the convergence factor on the relaxation factor, the subdomain diameter H and the mesh parameter h. In essence;, this method is equivalent to the simple iterative method for the preconditioned capacitance equation. The preconditioner implied in this iteration is easily invertible and can be applied to preconditioning the capacitance matrix with the condition number no more than O((1 + In H/h)max(1 + H-2, 1 + In H/h)).
文摘在导弹类金属-介质复合目标电磁散射特性求解过程中,采用常规迭代求解方法存在难以收敛以及内迭代边界积分区域重复求解的问题。针对该问题,在传统有限元边界积分区域分解法(finite element boundary integral domain decomposition method,FE-BI-DDM)的基础上,采用了更为灵活的多区多求解器的方法(multi domain multi solver method,MDMSM)。该方法对导弹类金属-介质复合目标中难以收敛的金属区域,使用快速直接求逆的方法求解,由于可以使用独立的网格模型进行电磁建模,避免了内迭代部分的模型重复建立过程,从而大幅减少了整体模型求解时间。实验结果表明:所提方法可以在相同计算精度的条件下,以不过多增加内存空间为前提,大幅缩短了导弹类目标的金属-介质复合模型的电磁求解时间。该方法为开展导弹类目标特性分析提供了一条可行的技术途径。
基金supported by the National Natural Science Foundation of China (Grant No.50808066)
文摘In this study, for the purpose of improving the efficiency and accuracy of numerical simulation of massive concrete, the symmetric successive over relaxation-preconditioned conjugate gradient method （SSOR-PCGM） with an improved iteration format was derived and applied to solution of large sparse symmetric positive definite linear equations in the computational process of the finite element analysis. A three-dimensional simulation program for massive concrete was developed based on SSOR-PCGM with an improved iteration format. Then, the programs based on the direct method and SSOR-PCGM with an improved iteration format were used for computation of the Guandi roller compacted concrete （RCC） gravity dam and an elastic cube under free expansion. The comparison and analysis of the computational results show that SSOR-PCGM with the improved iteration format occupies much less physical memory and can solve larger-scale problems with much less computing time and flexible control of accuracy.
文摘岩土工程规模大,加上岩土介质复杂的特性,使得当前有限元数值模拟在时间和精确度上很难达到工程要求。研究了在普通 PC 机群上实现的大规模并行有限元方法,以更好地发挥有限元在岩土工程中的应用。组建了Windows 下 PC 机群并行系统。采用“分而治之”的并行策略实现有限元并行,并实现了存储局部化。采用基于区域分解预处理技术的并行共轭梯度法来实现方程组的求解。集成以上方法,用 C++开发了并行有限元程序ParallelGeoFEM。对水布垭地下厂房进行了三维有限元并行模拟,得到了较好的加速比。结果表明,基于区域分解的并行有限元方法可以实现岩土工程大规模快速精细的模拟。
