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Efficient GOCE satellite gravity field recovery based on least-squares using QR decomposition 总被引:3,自引:0,他引:3
We develop and apply an efficient strategy for Earth gravity field recovery from satellite gravity gradiometry data. Our approach
is based upon the Paige-Saunders iterative least-squares method using QR decomposition (LSQR). We modify the original algorithm
for space-geodetic applications: firstly, we investigate how convergence can be accelerated by means of both subspace and
block-diagonal preconditioning. The efficiency of the latter dominates if the design matrix exhibits block-dominant structure.
Secondly, we address Tikhonov-Phillips regularization in general. Thirdly, we demonstrate an effective implementation of the
algorithm in a high-performance computing environment. In this context, an important issue is to avoid the twofold computation
of the design matrix in each iteration. The computational platform is a 64-processor shared-memory supercomputer. The runtime
results prove the successful parallelization of the LSQR solver. The numerical examples are chosen in view of the forthcoming
satellite mission GOCE (Gravity field and steady-state Ocean Circulation Explorer). The closed-loop scenario covers 1 month
of simulated data with 5 s sampling. We focus exclusively on the analysis of radial components of satellite accelerations
and gravity gradients. Our extensions to the basic algorithm enable the method to be competitive with well-established inversion
strategies in satellite geodesy, such as conjugate gradient methods or the brute-force approach. In its current development
stage, the LSQR method appears ready to deal with real-data applications. 相似文献
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We present preconditioned non‐linear conjugate gradient algorithms as alternatives to the Gauss‐Newton method for frequency domain full‐waveform seismic inversion. We designed two preconditioning operators. For the first preconditioner, we introduce the inverse of an approximate sparse Hessian matrix. The approximate Hessian matrix, which is highly sparse, is constructed by judiciously truncating the Gauss‐Newton Hessian matrix based on examining the auto‐correlation and cross‐correlation of the Jacobian matrix. As the second preconditioner, we employ the approximation of the inverse of the Gauss‐Newton Hessian matrix. This preconditioner is constructed by terminating the iteration process of the conjugate gradient least‐squares method, which is used for inverting the Hessian matrix before it converges. In our preconditioned non‐linear conjugate gradient algorithms, the step‐length along the search direction, which is a crucial factor for the convergence, is carefully chosen to maximize the reduction of the cost function after each iteration. The numerical simulation results show that by including a very limited number of non‐zero elements in the approximate Hessian, the first preconditioned non‐linear conjugate gradient algorithm is able to yield comparable inversion results to the Gauss‐Newton method while maintaining the efficiency of the un‐preconditioned non‐linear conjugate gradient method. The only extra cost is the computation of the inverse of the approximate sparse Hessian matrix, which is less expensive than the computation of a forward simulation of one source at one frequency of operation. The second preconditioned non‐linear conjugate gradient algorithm also significantly saves the computational expense in comparison with the Gauss‐Newton method while maintaining the Gauss‐Newton reconstruction quality. However, this second preconditioned non‐linear conjugate gradient algorithm is more expensive than the first one. 相似文献
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Due to complex dynamics inherent in the physical models, numerical formulation of subsurface and overland flow coupling can be challenging to solve. ParFlow is a subsurface flow code that utilizes a structured grid discretization in order to benefit from fast and efficient structured solvers. Implicit coupling between subsurface and overland flow modes in ParFlow is obtained by prescribing an overland boundary condition at the top surface of the computational domain. This form of implicit coupling leads to the activation and deactivation of the overland boundary condition during simulations where ponding or drying events occur. This results in a discontinuity in the discrete system that can be challenging to resolve. Furthermore, the coupling relies on unstructured connectivities between the subsurface and surface components of the discrete system, which makes it challenging to use structured solvers to effectively capture the dynamics of the coupled flow. We present a formulation of the discretized algebraic system that enables the use of an analytic form of the Jacobian for the Newton–Krylov solver, while preserving the structured properties of the discretization. An effective multigrid preconditioner is extracted from the analytic Jacobian and used to precondition the Jacobian linear system solver. We compare the performance of the new solver against one that uses a finite difference approximation to the Jacobian within the Newton–Krylov approach, previously used in the literature. Numerical results explores the effectiveness of using the analytic Jacobian for the Newton–Krylov solver, and highlights the performance of the new preconditioner and its cost. The results indicate that the new solver is robust and generally outperforms the solver that is based on the finite difference approximation to the Jacobian, for problems where the overland boundary condition is activated and deactivated during the simulation. A parallel weak scaling study highlights the efficiency of the new solver. 相似文献
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本文改进并验证了大地电磁测深数据的三维反演算法和并行计算程序,程序对计算机物理内存和CPU速度及数量要求较低,使普通家用机进行三维反演计算成为可能.本文在Newman和Alumbaugh(2000)提出的三维非线性共轭梯度算法和Rodi和Mackie(2001)给出的大地电磁场二维NLCG反演预处理方法的基础上实现了大地电磁场NLCG三维反演算法,改进了的预处理方法,将反演计算对初始模型的依赖性降到最低,并且通过理论模型验证了程序的正确性,并根据日本KAYABE地区实测数据的反演结果验证了算法的实用性. 相似文献
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GRAPeS三维变分同化系统的理想试验 总被引:43,自引:13,他引:43
文中介绍了一种新的、适合格点模式的三维变分同化方案GRAPeS 3DVAR。该方案采用相互独立的流函数、非平衡速度势函数、非平衡位势和水汽作为分析变量。通过变量变换对目标函数进行预调节 ,不仅避免了直接计算背景误差协方差逆矩阵的困难 ,而且改善了Hessian矩阵的性状 ,提高了收敛速度。采用EOF分解方法 ,将三维分析变量投影到垂直摸态上 ,分解成为二维场 ;水平方向采用数字 (递归 )滤波器代替矩阵运算 ,实现和简化了方案的求解。此外 ,还考虑了质量场和风场之间的平衡约束关系。理想试验结果表明 ,GRAPeS 3DVAR能够正确地反映多变量之间相互作用关系 ,收敛迅速 ,分析结果合理 相似文献
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Review of the algebraic linear methods and parallel implementation in numerical simulation of groundwater flow 下载免费PDF全文
The desire to increase spatial and temporal resolution in modeling groundwater system has led to the requirement for intensive computational ability and large memory space. In the course of satisfying such requirement, parallel computing has played a core role over the past several decades. This paper reviews the parallel algebraic linear solution methods and the parallel implementation technologies for groundwater simulation. This work is carried out to provide guidance to enable modelers of groundwater systems to make sensible choices when developing solution methods based upon the current state of knowledge in parallel computing. 相似文献
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