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考虑用GMRES方法求解多右端非对称位移方程组(A-σjI)x^(j)=b^(j),1≤j≤p。基于Smith的求解多右端方程组的种子投影思想,提出了求解上述位移方程组的GMRES种子投影方法,利用种子方程组产生的Krylov子空间来求近似解。本文给出了近似解的误差界,最后数值结果显示了该方法的有效性。 相似文献
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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
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GMRES方法在大型离岸结构水弹性分析中的应用 总被引:1,自引:1,他引:1
使用GMRES方法求解了大型离岸结构水弹性分析所获得的复系数线性方程组,并按照向后误差分析的方法,给出了它的终止准则。数值试验表明对于所考虑的问题,GMRES方法优于直接方法。 相似文献
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Added mass and damping coefficients are very important in hydrodynamic analysis of naval structures. In this paper, a double submerged inclined plates with ‘/ \’ configuration is firstly considered. By use of the boundary element method (BEM) based on Green function with the wave term, the radiation problem of this special type structure is investigated. The added mass and damping coefficients due to different plate lengths and inclined angles are obtained. The results show that: the added mass and damping coefficients for sway are the largest. Heave is the most sensitive mode to inclined angles. The wave frequencies of the maximal added mass and damping coefficients for sway and roll are the same. 相似文献
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The boundary-volume integral equation numerical technique can be a powerful tool for piecewise heterogeneous media, but it is limited to small problems or low frequencies because of great computational cost. Therefore, a restarted GMRES method is applied to solve large-scale boundary-volume scattering problems in this paper to overcome the computational barrier. The iterative method is firstly applied to responses of dimensionless frequency to a semicircular alluvial valley filled with sediments, compared with the standard Gaussian elimination method. Then the method is tested by a heterogeneous multilayered model to show its applicability. Numerical experiments indicate that the preconditioned GMRES method can significantly improve computational efficiency especially for large Earth models and high frequencies, but with a faster convergence for the left diagonal preconditioning. 相似文献
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For wave propagation simulation in piecewise heterogeneous media, Gaussian-elimination-based full-waveform solutions to the generalized Lippmann–Schwinger integral equation (GLSIE) are highly accurate, but involved with extremely time-consuming computations because of the very large size of the resulting boundary–volume integral equation matrix to be inverted. Several flexible approximations to the GLSIE are scaled in an iterative way to adapt numerical solutions to the smoothness of heterogeneous media in terms of incident wavelengths, with a great saving of computing time and memory. Among various typical iterative schemes to the GLSIE matrix, the generalized minimal residual method (GMRES) is an efficient approach to reduce the computational intensity to some degree. The most efficient approximation can be obtained using a Born series, as an alternative iterative solution, to both the boundary-scattering and volume-scattering waves, leading to the Born-series approximation (BSA) scheme and the improved Born-series approximation (IBSA) scheme. These iteration schemes are validated by dimensionless frequency responses to a heterogeneous semicircular alluvial valley, and then applied to a heterogeneous multilayered model by calculating synthetic seismograms to evaluate approximation accuracies. Numerical experiments, compared with the full-waveform numerical solution, indicate that the convergence rates of these methods decrease gradually with increasing velocity perturbations. The comparison also shows that the BSA scheme has a faster convergence than the GMRES method for velocity perturbations less than 10 percent, but converges slowly and even hardly achieves convergence for velocity perturbations greater than 15 percent. The IBSA scheme gives a superior performance over the other methods, with the least iterations to achieve the necessary convergence. 相似文献
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面元法的快速算法与B样条高阶方法综述 总被引:1,自引:0,他引:1
介绍了面元法的快速算法及B样条高阶方法的发展概况,对快速多极算法及预修正快速傅里叶变换方法做了详细的介绍,指出了这些方法今后的发展方向。 相似文献
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