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1.
Non‐associated flow rule is essential when the popular Mohr–Coulomb model is used to model nonlinear behavior of soil. The global tangent stiffness matrix in nonlinear finite element analysis becomes non‐symmetric when this non‐associated flow rule is applied. Efficient solution of this large‐scale non‐symmetric linear system is of practical importance. The standard Krylov solver for a non‐symmetric solver is Bi‐CGSTAB. The Induced Dimension Reduction [IDR(s)] solver was proposed in the scientific computing literature relatively recently. Numerical studies of a drained strip footing problem on homogenous soil layer show that IDR(s = 6) is more efficient than Bi‐CGSTAB when the preconditioner is the incomplete factorization with zero fill‐in of global stiffness matrix Kep (ILU(0)‐Kep). Iteration time is reduced by 40% by using IDR(s = 6) with ILU(0)‐Kep. To further reduce computational cost, the global stiffness matrix Kep is divided into two parts. The first part is the linear elastic stiffness matrix Ke, which is formed only once at the beginning of solution step. The second part is a low‐rank matrix Δ, which is re‐formed at each Newton–Raphson iteration. Numerical studies show that IDR(s = 6) with this ILU(0)‐Ke preconditioner is more time effective than IDR(s = 6) with ILU(0)‐Kep when the percentage of yielded Gauss points in the mesh is less than 15%. The total computation time is reduced by 60% when all the recommended optimizing methods are used. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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This paper examines the performance of the Jacobi preconditioner when used with two Krylov subspace iterative methods. The number of iterations needed for convergence was shown to be different for drained, undrained and consolidation problems, even for similar condition number. The differences were due to differences in the eigenvalue distribution, which cannot be completely described by the condition number alone. For drained problems involving large stiffness ratios between different material zones, ill‐conditioning is caused by these large stiffness ratios. Since Jacobi preconditioning operates on degrees‐of‐freedom, it effectively homogenizes the different spatial sub‐domains. The undrained problem, modelled as a nearly incompressible problem, is much more resistant to Jacobi preconditioning, because its ill‐conditioning arises from the large stiffness ratios between volumetric and distortional deformational modes, many of which involve the similar spatial domains or sub‐domains. The consolidation problem has two sets of degrees‐of‐freedom, namely displacement and pore pressure. Some of the eigenvalues are displacement dominated whereas others are excess pore pressure dominated. Jacobi preconditioning compresses the displacement‐dominated eigenvalues in a similar manner as the drained problem, but pore‐pressure‐dominated eigenvalues are often over‐scaled. Convergence can be accelerated if this over‐scaling is recognized and corrected for. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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在进行多次外循环更新的增量分析框架下,前一次极小化迭代过程中产生的信息可提供给下一次极小化做预调节。该文在GRAPES全球四维变分同化系统中对极小化算法——L-BFGS算法实施了这种预调节,通过全观测的个例试验和批量试验进行评估,发现进行预调节后L-BFGS算法的收敛效率得到明显提高,而且在1个月的循环试验中表现十分稳定。该工作可以帮助GRAPES全球四维变分同化系统有效减少极小化的迭代次数,有利于满足业务化运行的时效要求。另外,间隔6 h和间隔24 h的两次4DVar分析对应的海森矩阵变化不大,因此,前一时刻极小化过程产生的信息提供给后一时刻的极小化进行预调节也有一定效果。 相似文献
4.
大区域地下水模拟的预优并行GMRES(m)算法研究 总被引:1,自引:1,他引:0
大区域研究区由于涉及范围大、水文地质参数复杂多变,一直是进行地下水数值模拟的热点和难点。针对大区域地下水模拟的特点,在MPI环境中对Krylov子空间GMRES(m)算法的并行性进行分析,提出基于区域分解法的并行实现策略,并对不同的预条件子的加速效果进行比较。数值实验结果表明:并行GMRES(m)算法在求解大区域三维地下水模型时可以显著的加快求解速度,且具有较好的可扩展性。另外,Jacobi预条件子与GMRES算法的组合具有更优的加速比和执行效率,是一种求解大型化、复杂化地下水水流问题的可行方案。 相似文献
5.
The variational assimilation theory is generally based on unbiased observations. In practice, however, almost all observations
suffer from biases arising from observational instruments, radiative transfer operator, precondition of data, and so on. Therefore,
a bias correction scheme is indispensable. The current scheme for radiance bias correction in the GRAPES 3DVar system is an
offline scheme. It is actually a static correction for the radiance bias before the process of cost function minimization.
In consideration of its effects on forecast results, this kind of scheme has some shortcomings. Thus, this study provides
a variational bias correction (VarBC) scheme for the GRAPES 3DVar system following Dee’s idea. In the VarBC scheme, the observation
operator is modified and a new control variable is defined by taking the predictor coefficients as the control parameters.
According to the feature of the GRAPES-3DVAR, an incremental formulation is applied and the original bias correction scheme
is maintained in the actual process of observations. The VarBC is designed to co-exist with the original scheme, because it
is a dynamic revision to the observational operator on the basis of the old method, i.e., it adjusts the model state vector
along with the control parameters to an unbiased state in the process of minimization and the assimilation system remains
consistent with available information automatically. Preliminary experimental results show that the mean departures of background-minus-observation
and analysis-minus-observation are reduced as expected. In a case study of the heavy rainfall that happened in South China
on 11–13 June 2008, the 500-hPa geopotential height is better simulated using the analyzed field from the VarBC as the initial
condition. 相似文献
6.
E. Haber 《Computational Geosciences》2000,4(4):323-336
This paper present a new a mixed finite element method for the simulation of magnetostatic problems with highly discontinuous permeability. The method is derived from the well studied mixed formulation for the div-grad system that is known to be accurate for very large discontinuities. The method robustness is demonstrated on a test model problem. 相似文献
7.
The repeated solution in time of the linear system arising from the finite element integration of coupled consolidation equations is a major computational effort. This system can be written in either a symmetric or an unsymmetric form, thus calling for the implementation of different preconditioners and Krylov subspace solvers. The present paper aims at investigating when either a symmetric or an unsymmetric approach should be better used. The results from a number of representative numerical experiments indicate that a major role in selecting either form is played by the preconditioner rather than by the Krylov subspace method itself. Two other important issues addressed are the size of the time integration step and the possible lumping of the flow capacity matrix. It appears that ad hoc block constrained preconditioners provide the most robust algorithm independently of the time step size, lumping, and symmetry. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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This paper identifies imbalanced columns (or rows) as a significant source of ill‐conditioning in the preconditioned coefficient matrix using the standard Jacobi preconditioner, for finite element solution of Biot's consolidation equations. A simple and heuristic preconditioner is proposed to reduce this source of ill‐conditioning. The proposed preconditioner modifies the standard Jacobi preconditioner by scaling the excess pore pressure degree‐of‐freedoms in the standard Jacobi preconditioner with appropriate factors. The performance of such preconditioner is examined using the symmetric quasi‐minimal residual method. To alleviate storage requirements, element‐by‐element iterative strategies are implemented. Numerical experiment results show that the proposed preconditioner reduces both the number of iteration and CPU execution time significantly as compared with the standard Jacobi preconditioner. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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