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1.
Soil–structure interaction problems are commonly encountered in geotechnical practice and remarkably characterized with significant material stiffness contrast. When solving the soil–structure interaction problems, the employed Krylov subspace iterative method may converge slowly or even fail, indicating that the adopted preconditioning method may not suit for such problems. The inexact block diagonal preconditioners proposed recently have been shown effective for the soil–structure interaction problems; however, they haven't been exploited to full capabilities. By using the same partition strategy according to the structure elements and soil elements, the partitioned block symmetric successive over‐relaxation preconditioners or partitioned block constraint preconditioners are proposed. Based on two pile‐group foundation problems and a tunnel problem, the proposed preconditioners are evaluated and compared with the available preconditioners for the consolidation analysis and the drained analysis, respectively. In spite of one additional solve associated with the structure block and multiplications with off‐diagonal blocks in the preconditioning step, numerical results reveal that the proposed preconditioners obviously possess better performance than the recently developed inexact block preconditioners. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
2.
Finite element discretization of Biot's consolidation equations can produce a symmetric indefinite system (commonly used in geomechanics) or a non‐symmetric system. While this difference appears to be minor, however, it will require the selection of entirely different Krylov subspace solvers with potentially significant impact on solution efficiency. The former is solved using the symmetric quasi‐minimal residual whereas the latter is solved using the popular bi‐conjugate gradient stabilized. This paper presents an extensive comparison of the symmetric and non‐symmetric forms by varying the time step, size of the spatial domain, choice of physical units, and left versus left–right preconditioning. The generalized Jacobi (GJ) preconditioner is able to handle the non‐symmetric version of Biot's finite element method equation, although there are no practical incentives to do so. The convergence behaviour of GJ‐preconditioned systems and its relation to the spectral condition number or the complete spectrum are studied to clarify the concept of ill‐conditioning within the context of iteration solvers. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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4.
Soil–structure interaction problems are commonly encountered in engineering practice, and the resulting linear systems of equations are difficult to solve due to the significant material stiffness contrast. In this study, a novel partitioned block preconditioner in conjunction with the Krylov subspace iterative method symmetric quasiminimal residual is proposed to solve such linear equations. The performance of these investigated preconditioners is evaluated and compared on both the CPU architecture and the hybrid CPU–graphics processing units (GPU) computing environment. On the hybrid CPU–GPU computing platform, the capability of GPU in parallel implementation and high-intensity floating point operations is exploited to accelerate the iterative solutions, and particular attention is paid to the matrix–vector multiplications involved in the iterative process. Based on a pile-group foundation example and a tunneling example, numerical results show that the partitioned block preconditioners investigated are very efficient for the soil–structure interaction problems. However, their comparative performances may apparently depend on the computer architecture. When the CPU computer architecture is used, the novel partitioned block symmetric successive over-relaxation preconditioner appears to be the most efficient, but when the hybrid CPU–GPU computer architecture is adopted, it is shown that the inexact block diagonal preconditioners embedded with simple diagonal approximation to the soil block outperform the others. 相似文献
5.
Preconditioners in computational geomechanics: A survey 总被引：1，自引：0，他引：1
The finite element (FE) solution of geomechanical problems in realistic settings raises a few numerical issues depending on the actual process addressed by the analysis. There are two basic problems where the linear solver efficiency may play a crucial role: 1. fully coupled consolidation and 2. faulted uncoupled consolidation. A class of general solvers becoming increasingly popular relies on the Krylov subspace (or Conjugate Gradient‐like) methods, provided that an efficient preconditioner is available. For both problems mentioned above, the possible preconditioners include the diagonal scaling (DS), the Incomplete LU decomposition (ILU), the mixed constraint preconditioning (MCP) and the multilevel incomplete factorization (MIF). The development and the performance of these algorithms have been the topic of several recent works. The present paper aims at providing a survey of the preconditioners available to date in computational geomechanics. In particular, a review and a critical discussion of DS, ILU, MCP and MIF are given along with some comparative numerical results. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
6.
The finite element (FE) simulation of large‐scale soil–structure interaction problems (e.g. piled‐raft, tunnelling, and excavation) typically involves structural and geomaterials with significant differences in stiffness and permeability. The symmetric quasi‐minimal residual solver coupled with recently developed generalized Jacobi, modified symmetric successive over‐relaxation (MSSOR), or standard incomplete LU factorization (ILU) preconditioners can be ineffective for this class of problems. Inexact block diagonal preconditioners that are inexpensive approximations of the theoretical form are systematically evaluated for mitigating the coupled adverse effects because of such heterogeneous material properties (stiffness and permeability) and because of the percentage of the structural component in the system in piled‐raft foundations. Such mitigation led the proposed preconditioners to offer a significant saving in runtime (up to more than 10 times faster) in comparison with generalized Jacobi, modified symmetric successive over‐relaxation, and ILU preconditioners in simulating piled‐raft foundations. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
7.
The focus of this work is efficient solution methods for mixed finite element models of variably saturated fluid flow through
deformable porous media. In particular, we examine preconditioning techniques to accelerate the convergence of implicit Newton–Krylov
solvers. We highlight an approach in which preconditioners are built from block-factorizations of the coupled system. The
key result of the work is the identification of effective preconditioners for the various sub-problems that appear within
the block decomposition. We use numerical examples drawn from both linear and nonlinear hydromechanical models to test the
robustness and scalability of the proposed methods. Results demonstrate that an algebraic multigrid variant of the block preconditioner
leads to mesh-independent convergence, good parallel efficiency, and insensitivity to the material parameters of the medium. 相似文献
8.
为了研究复杂地电模型的航空瞬变电磁法全波形响应特征,需要开发考虑发射波形的三维数值模拟算法。本研究基于非结构四面体网格和位移逆Krylov子空间(Shift-and-Invert Krylov,简称SAI Krylov)方法,采用基于电偶极子离散的场源处理方法模拟场源,在时间域进行计算实现了全波形航空瞬变电磁法矢量有限元三维数值模拟。使用均匀半空间模型在阶跃波、半正弦波、三角波和梯形波激发下的全波形解析解、VTEM实际激发波形的后推欧拉算法计算结果,检验了本研究开发的数值模拟算法的正确性。设计地表起伏异常体模型,计算和分析了航空瞬变电磁响应特征。开发的基于位移逆Krylov子空间的全波形航空瞬变电磁法三维数值模拟算法适合模拟复杂地电模型的响应,具有较高的计算精度。 相似文献
9.
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
10.
George Zyvoloski 《国际地质力学数值与分析法杂志》1983,7(1):75-86
Two finite element algorithms suitable for long term simulation of geothermal reservoirs are presented. Both methods use a diagonal mass matrix and a Newton iteration scheme. The first scheme solves the 2N unsymmetric algebraic equations resulting from the finite element discretization of the equations governing the flow of heat and mass in porous media by using a banded equation solver. The second method, suitable for problems in which the transmissibility terms are small compared to the accumulation terms, reduces the set of N equations for the Newton corrections to a symmetric system. Comparison with finite difference schemes indicates that the proposed algorithms are competitive with existing methods. 相似文献
11.
Stress‐driven integration strategies and m‐AGC tangent operator for Perzyna viscoplasticity and viscoplastic relaxation: application to geomechanical interfaces 
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下载免费PDF全文 The paper proposes a stress‐driven integration strategy for Perzyna‐type viscoplastic constitutive models, which leads also to a convenient algorithm for viscoplastic relaxation schemes. A generalized trapezoidal rule for the strain increment, combined with a linearized form of the yield function and flow rules, leads to a plasticity‐like compliance operator that can be explicitly inverted to give an algorithmic tangent stiffness tensor also denoted as the m‐AGC tangent operator. This operator is combined with the stress‐prescribed integration scheme, to obtain a natural error indicator that can be used as a convergence criterion of the intra‐step iterations (in physical viscoplasticity), or to a variable time‐step size in viscoplastic relaxation schemes based on a single linear calculation per time step. The proposed schemes have been implemented for an existing zero‐thickness interface constitutive model. Some numerical application examples are presented to illustrate the advantages of the new schemes proposed. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
12.
Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection–diffusion
PDEs coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each
grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper, a global
solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies
the Newton–Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated
in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that
one be able to solve chemical equilibrium problems (and compute derivatives) without having to know the solution method. An
additional advantage of the Newton–Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times
vector product. The proposed method is tested on the MoMaS reactive transport benchmark. 相似文献
13.
Clint N. Dawson Héctor Klíe Mary F. Wheeler Carol S. Woodward 《Computational Geosciences》1997,1(3-4):215-249
A new parallel solution technique is developed for the fully implicit three‐dimensional two‐phase flow model. An expandedcell‐centered finite difference scheme which allows for a full permeability tensor is employed for the spatial discretization, and backwardEuler is used for the time discretization. The discrete systems are solved using a novel inexact Newton method that reuses the Krylov information generated by the GMRES linear iterative solver. Fast nonlinear convergence can be achieved by composing inexact Newton steps with quasi‐Newton steps restricted to the underlying Krylov subspace. Furthermore, robustness and efficiency are achieved with a line‐search backtracking globalization strategy for the nonlinear systems and a preconditioner for each coupled linear system to be solved. This inexact Newton method also makes use of forcing terms suggested by Eisenstat and Walker which prevent oversolving of the Jacobian systems. The preconditioner is a new two‐stage method which involves a decoupling strategy plus the separate solutions of both nonwetting‐phase pressure and saturation equations. Numerical results show that these nonlinear and linear solvers are very effective. 相似文献
14.
在三维电阻率的正演计算中往往涉及到快速、准确求解大型线性方程纽Ax=b的问题。通过采用有限差分法来构造出求解点电源三维地电场的大型稀疏对称线性方程组。并引入Lanczos迭代技术，构造出三对角阵方程组，然后采用正交分解法进行求解，它是Krylov子空间方法中的一种。与传统迭代算法相比，它占用内存少，收敛速度快且稳定。针对大型稀疏矩阵及MATLAB语言的特点，采用简单记录矩阵的非零元素值及其所在行、列值的方法存储大型稀疏矩阵，可大大节省机器内存，提高运算速度。理论分析和计算实例显示，此算法是地电三维正演计算的有效方法，为下一步的反演计算打好基础。 相似文献
15.
The transport of chemically reactive solutes (e.g. surfactants, CO2 or dissolved minerals) is of fundamental importance to a wide range of applications in oil and gas reservoirs such as enhanced
oil recovery and mineral scale formation. In this work, we investigate exponential time integrators, in conjunction with an
upwind weighted finite volume discretisation in space, for the efficient and accurate simulation of advection–dispersion processes
including non-linear chemical reactions in highly heterogeneous 3D oil reservoirs. We model sub-grid fluctuations in transport
velocities and uncertainty in the reaction term by writing the advection–dispersion–reaction equation as a stochastic partial
differential equation with multiplicative noise. The exponential integrators are based on the variation of constants solution
and solve the linear system exactly. While this is at the expense of computing the exponential of the stiff matrix representing
the finite volume discretisation, the use of real Léja point or the Krylov subspace technique to approximate the exponential
makes these methods competitive compared to standard finite difference-based time integrators. For the deterministic system,
we investigate two exponential time integrators, the second-order accurate exponential Euler midpoint (EEM) scheme and exponential
time differencing of order one (ETD1). All our numerical examples demonstrate that our methods can compete in terms of efficiency
and accuracy compared with standard first-order semi-implicit time integrators when solving (stochastic) partial differential
equations that model mixing and chemical reactions in 3D heterogeneous porous media. Our results suggest that exponential
time integrators such as the ETD1 and EEM schemes could be applied to typical 3D reservoir models comprising tens to hundreds
of thousands unknowns. 相似文献
16.
Zhendong Shan Daosheng Ling Zhinan Xie Liping Jing Yongqiang Li 《国际地质力学数值与分析法杂志》2019,43(13):2184-2199
One-dimensional transient wave propagation in a saturated single-layer porous medium with a fluid surface layer is studied in this paper. An analytical solution for a special case with a dynamic permeability coefficient kf → ∞ and a semianalytical solution for a general case with an arbitrary dynamic permeability coefficient are presented. The eigenfunction expansion and precise time step integration methods are employed. The solution is presented in series form, and thus, the long-term dynamic responses of saturated porous media with small permeability coefficients can be easily computed. We first transform the nonhomogeneous boundary conditions into homogeneous boundary conditions, and then we obtain the eigenvalues and orthogonal eigenfunctions of the fluid–solid system. Finally, the solutions in the time domain are developed. As the model is one dimensional, geometric attenuation is absent, and only the attenuation in the saturated porous medium is considered. We can apply this model to analyse the influences of different seabed types on the propagation of acoustic waves in the fluid layer, which is very important in ocean acoustics and ocean seismic. This solution can also be employed to validate the accuracies of various numerical methods. 相似文献
17.
The double‐spike approach for correction of instrumental mass bias in mass spectrometry data is well established. However, there is very little consistency within the scientific community in terms of double‐spike data reduction. Double‐spike solutions require computer calculation, using either geometric or algebraic approaches, and are often performed using spreadsheet calculations that vary from group to group and between isotope systems. Here, we present IsoSpike, a generalised computer procedure for the processing of double‐spike mass spectrometry data, built as an add‐on for the Iolite data‐reduction package ( www.iolite.org.au ). Use of this software permits visualisation of mass spectrometry data in a time window, and rigorous treatment and screening of data. Additionally, IsoSpike uses an integration‐by‐integration approach where the double‐spike calculations are performed on every integration within an analysis, providing straightforward quantification of uncertainties on double‐spike‐corrected isotope ratios. The advantages of this approach over traditional methods are discussed here. Platinum stable isotope data are presented as an example data set, although the procedure is applicable to any double‐spike system. IsoSpike is freely available from www.isospike.org . 相似文献
18.
Projection, or conjugate gradient like, methods are becoming increasingly popular for the efficient solution of large sparse sets of unsymmetric indefinite equations arising from the numerical integration of (initial) boundary value problems. One such problem is soil consolidation coupling a flow and a structural model, typically solved by finite elements (FE) in space and a marching scheme in time (e.g. the Crank–Nicolson scheme). The attraction of a projection method stems from a number of factors, including the ease of implementation, the requirement of limited core memory and the low computational cost if a cheap and effective matrix preconditioner is available. In the present paper, biconjugate gradient stabilized (Bi‐ CGSTAB) is used to solve FE consolidation equations in 2‐D and 3‐D settings with variable time integration steps. Three different nodal orderings are selected along with the preconditioner ILUT based on incomplete triangular factorization and variable fill‐in. The overall cost of the solver is made up of the preconditioning cost plus the cost to converge which is in turn related to the number of iterations and the elementary operations required by each iteration. The results show that nodal ordering affects the perfor mance of Bi‐CGSTAB. For normally conditioned consolidation problems Bi‐CGSTAB with the best ILUT preconditioner may converge in a number of iterations up to two order of magnitude smaller than the size of the FE model and proves an accurate, cost‐effective and robust alternative to direct methods. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
19.
Martin G. LOCKLEY LI Jianjun LI Rihui Masaki MATSUKAWA Jerald D. HARRIS XING Lida 《《地质学报》英文版》2013,87(1):1-20
<正>"Splitting" and "lumping" are perpetual problems in vertebrate,especially dinosaur, ichnotaxonomy.Chinese dinosaur ichnotaxonomy,which began in 1940,provides a series of interesting case studies,highlighting the dual problems of historical and dubious ichnotaxonomy. Chinese Mesozoic tetrapod track types have been placed into 63 ichnospecies(one Triassic,28 Jurassic,and 34 Cretaceous),exclusive of other,non-type ichnospecies or ichnotaxa identified from China.Fifty-two(～83%) of these 63 tetrapod ichnospecies were placed in monospecific ichnogenera. At the ichnogenus level,we prune—either by recognizing nomina dubia or by synonymy—17 from the list of 53 dinosaurian ichnogenera(a 32%reduction),leaving 36 ichnotaxa that we consider valid. Most of the cuts affect Jurassic theropod ichnotaxa,which are reduced from 23 to only nine because most ichnogenera are subjective junior synonyms of Grallator and Eubrontes.Fewer Chinese Cretaceous ichnotaxa(only six of 21 ichnogenera) are obvious nomina dubia or subjective synonyms, suggesting greater east Asian endemism during this time.Because ichnospecies differences are subtle, we provisionally retain ichnospecies as valid pending detailed comparative analyses of congeneric ichnospecies.This synthesis is long overdue and is necessary to address problems of historical and provincial ichnotaxonomy,which severely hamper comparisons of tetrapod ichnofaunas in space and time. 相似文献
20.
Effective bulk composition changes due to cooling: a model predicting complexities in retrograde reaction textures 总被引：11，自引：1，他引：11
Kurt Stüwe 《Contributions to Mineralogy and Petrology》1997,129(1):43-52
Diffusive processes are a strong function of temperature. Thus, during cooling of rocks, mineral grains may develop zoning
profiles as successively larger parts of the grain “close” to the diffusive exchange with the rock. One of the consequences
of this process is that, during cooling, successively larger parts of zoned minerals (depending on grain size) are effectively
removed from the reacting part of the rock volume. Thus, the effective bulk composition of metamorphic rocks changes during
cooling and the rate of its change will be a function of grain size. Because the sequence of metamorphic reactions seen by
a given rock is a strong function of its bulk composition, this process may have the consequence that two rocks of identical overall bulk composition, but of different grain size, may experience a different sequence of reactions. Qualitatively identical peak paragenesis may therefore react to form qualitatively different retrograde reaction textures. The model is applied to examples in the pelitic system. There, garnet is usually the slowest
diffusing phase developing zoning profiles during cooling and the effective removal of garnet from the reacting rock volume
will cause changes of the effective bulk composition. It is shown that, during cooling of pelitic rocks from amphibolite facies
conditions, typical aluminous peak parageneses of garnet-muscovite-kyanite ± biotite may react to form either staurolite,
chlorite or muscovite (or different combinations thereof), depending on grain size. During cooling from the granulite facies,
aluminous peak parageneses of garnet-cordierite-sillimanite may form biotite, either on the expense of cordierite or garnet,
also depending on grain size. The two examples are illustrated with a series of reaction textures reported for amphibolite
and granulite terrains in the literature.
Received: 12 March 1996 / Accepted: 7 April 1997 相似文献