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Large‐scale simulations of flow in deformable porous media require efficient iterative methods for solving the involved systems of linear algebraic equations. Construction of efficient iterative methods is particularly challenging in problems with large jumps in material properties, which is often the case in geological applications, such as basin evolution at regional scales. The success of iterative methods for this type of problems depends strongly on finding effective preconditioners. This paper investigates how the block‐structured matrix system arising from single‐phase flow in elastic porous media should be preconditioned, in particular for highly discontinuous permeability and significant jumps in elastic properties. The most promising preconditioner combines algebraic multigrid with a Schur complement‐based exact block decomposition. The paper compares numerous block preconditioners with the aim of providing guidelines on how to formulate efficient preconditioners. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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K. Kusaka K. Hagiya M. Ohmasa Y. Okano M. Mukai K. Iishi N. Haga 《Physics and Chemistry of Minerals》2001,28(3):150-166
The structures of Ca2CoSi2O7, Ca2MgSi2O7, and Ca2(Mg0.55Fe0.45)Si2O7 have been determined in the temperature range between 297 and 773 K with arbitrary intervals. The structures of the incommensurate
phase of the three compounds are characterized by the presence of the six-, seven-, and eight-coordinated Ca–O polyhedra and
of the bundles along the c-axes consisting of four arrays of the six-coordinated Ca–O polyhedra and an array of T1O4 (T1: Co, Mg, or Mg–Fe) tetrahedra in the structures. The number of bundles in each material decreases at elevated temperatures.
The incommensurate phase undergoes a phase transition into the normal phase at 493 K in Ca2CoSi2O7, at 360 K in Ca2MgSi2O7, and at 510 K in Ca2(Mg0.55Fe0.45)Si2O7. The features of the structures of the normal phase are almost the same as those found in the basic structures (the averaged
structures of the incommensurate structures), and this fact implies that the characteristics of the structures, such as the
six-coordinated Ca–O polyhedra or fragments of the bundles, should be partially preserved at higher temperatures both in the
incommensurate structures and also in the structures of the normal phase. Analyses of anisotropic displacement parameters
clarified that disorder of the modulation waves is developed in the structures at higher temperatures. The evolution of a
disorder in the structures was ascertained by observation of the circular diffuse streaks in the vicinity of the transition
temperature between the incommensurate and normal phases.
Received: 3 July 2000 / Accepted: 26 October 2000 相似文献
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Nonphysical pressure oscillations are observed in finite element calculations of Biot's poroelastic equations in low‐permeable media. These pressure oscillations may be understood as a failure of compatibility between the finite element spaces, rather than elastic locking. We present evidence to support this view by comparing and contrasting the pressure oscillations in low‐permeable porous media with those in low‐compressible porous media. As a consequence, it is possible to use established families of stable mixed elements as candidates for choosing finite element spaces for Biot's equations. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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Pietro Passerini Marta Marcucci Giovanni Sguazzoni Leonardo Zan Abdourahman Omar Haga 《地学学报》1991,3(6):607-618
Slickenside studies in regions of crustal spreading such as Iceland and the Afar Depression, East Africa, reveal that a significant number of faults parallel and close to rift axes are strike-slip rather than normal. Therefore, the pattern of brittle deformation in these regions does not conform to the classic two-dimensional schemes of oceanic tectonics and pre-oceanic rifting. Dip-slip and strike-slip faulting presumably alternated along or in the vicinity of spreading axes, indicate a varying stress field and a combination of transverse and longitudinal movements. In Iceland, strike-slip faults parallel to rifts are observed both west and east of the rift system as well as in a median area between overlapping rifts; the mechanisms proposed for their origin include accommodation of oblique convergence or divergence of crustal sections due to variations of spreading directions along axis and the interaction of overlapping rifts. In the Afar Depression this kind of fault is recorded west of the rift of Asal and can be imputed to reflect an interaction among rifts in the vicinity of the Afar triple junction. Rift-parallel strike-slip faults cannot however be assumed to be a feature of all crustal spreading axes due to the peculiarity of the examined regions: both of them are hot-spot areas and the Afar Depression lies at a triple junction. 相似文献
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Joachim Berdal Haga Harald Osnes Hans Petter Langtangen 《Computational Geosciences》2012,16(3):723-734
Large-scale simulations of coupled flow in deformable porous media require iterative methods for solving the systems of linear
algebraic equations. Construction of efficient iterative methods is particularly challenging in problems with large jumps
in material properties, which is often the case in realistic geological applications, such as basin evolution at regional
scales. The success of iterative methods for such problems depends strongly on finding effective preconditioners with good
parallel scaling properties, which is the topic of the present paper. We present a parallel preconditioner for Biot’s equations
of coupled elasticity and fluid flow in porous media. The preconditioner is based on an approximation of the exact inverse
of the two-by-two block system arising from a finite element discretisation. The approximation relies on a highly scalable
approximation of the global Schur complement of the coefficient matrix, combined with generally available state-of-the-art
multilevel preconditioners for the individual blocks. This preconditioner is shown to be robust on problems with highly heterogeneous
material parameters. We investigate the weak and strong parallel scaling of this preconditioner on up to 512 processors and
demonstrate its ability on a realistic basin-scale problem in poroelasticity with over eight million tetrahedral elements. 相似文献
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A loop flare that occurred on 22 April 1993 near the disk center is examined using the Yohkoh Hard X-ray Telescope (HXT). We specifically looked into the faint early phase of the flare prior to the start of the strong impulsive phase. The pre-impulsive phase, though weak in intensity, is expected to contain essential clues to the mechanism of loop flares according to the causality principle, but it has not received attention previously, probably due to the insufficient dynamic range and cadence of observations by the instruments on earlier satellites. Observations with Yohkoh/HXT can clarify what occurs in this phase. This flare, like many other flares of this type, shows a relatively weak emission with a smooth and gradual increase during this pre-impulsive phase, followed by impulsive bursts, and then turns into a smooth decay phase without impulsive bursts. First, we found that the spectrum for the initial smooth rise part is consistent with a thin-thermal source at a temperature around 80 MK. Imaging of this phase in the HXT/L and M bands shows a single source between the footpoint sources that will come up in the impulsive phase following this phase, suggesting that this hyperhot source is located at a high part of the loop between the footpoints, since this flare takes a form of a loop. Furthermore, as we go up to the earliest times of the flare before this `hyperhot' source phase, two fainter sources are found near the footpoint sources that will appear later in the impulsive phase. The spectra of these sources at this earliest time of the flare, in contrast to the `hyperhot' source, cannot be determined from the HXT because the instrument was not in flare mode, and HXT/M1, M2, and H-band data are, unfortunately, not available at this very initial time. We can guess, however, that they are also of thermal character because the time profile is smooth without any spikes just as in the following `hyperhot' thermal phase, and in the post-impulsive `superhot' thermal phase coming up much later. These findings suggest that there is an important, and probably dynamic, early phase in loop flares that has been unnoticed in the still dark pre-impulsive phase, because the very early footpoint sources change into the loop top source in a matter of 20–30 s, comparable to the dynamic Alfvén time scale. Some implications of our new findings are discussed. 相似文献
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