Application of the iterative solution method with Schur complement reduction to mixed finite elements based in a tetrahedral discretization

The iterative solution method for mixed finite element methods is applied to a 3-D domain partitioned with tetrahedral elements. For the particular discretization technique of first partitioning the domain with hexahedral cells, and then subsequently partitioning cells with five tetrahedral elements, a Schur complement decomposition is devised wherein the actual number of equations solved is reduced by 80%. Although this Schur complement reduction requires a fair amount of computational overhead, its application within the iterative solution method can reduce overall solution time by about 44%, depending on closure criterion and other factors.     

求解声波方程的辛可分Runge-Kutta方法

本文基于声波方程的哈密尔顿系统,构造了一种新的保辛数值格式,简称NSPRK方法.该方法在时间上采用二阶辛可分Runge-Kutta方法,空间上采用近似解析离散算子进行离散逼近.针对本文发展的新方法,我们给出了NSPRK方法在一维和二维情况下的稳定性条件、一维数值频散关系以及二维数值误差,并在计算效率方面与传统辛格式和四阶LWC方法进行了比较.最后,我们将本文方法应用于声波在三层各向同性介质和异常体模型中的波传播数值模拟.数值结果表明,本文发展的NSPRK方法能有效压制粗网格或具有强间断情况下数值方法所存在的数值频散,从而极大地提高了计算效率,节省了计算机内存.     

基于改进NAD方法的频率域声波逆时偏移

逆时偏移成像具有高分辨率的特点,在频率域实施能提升偏移成像效率.数值求解波动方程是逆时偏移成像的关键环节,数值算法的优劣直接决定着偏移过程的计算效率与成像结果的质量.本文在频率域近似解析离散化(NAD)方法的基础上通过优化网格差分模板系数构造改进NAD方法,保证数值离散精度的同时可缓解阻抗矩阵的病态程度,以此提高频率域...     

岩土参数随机场离散的三角形单元局部平均法

将不确定性岩土参数建模为随机场而非传统意义上的随机变量,基于随机场的局部平均理论,提出了用于二维随机场离散的三角形单元局部平均法。通过面积坐标变换和高斯数值积分,给出了三角形单元局部平均随机场协方差矩阵的解析计算方法和数值计算方法。采用算例再现了所提方法的分析过程和有效性,并与传统二维随机场四边形单元离散法进行了对比。结果表明:提出的二维随机场三角形单元离散法能与有限元三角形单元离散法完美结合,随机场单元与有限元单元的对应关系清晰,易于随机有限元程序的编制;对于随机场单元的均值,传统四边形单元离散法与所提方法的计算结果相同;对于随机场单元的方差,传统四边形单元离散法计算结果偏小,所提方法显得更加科学、合理。     

水文响应单元空间离散化及SWAT模型改进

水文响应单元(Hydrological Response Units,HRU)是SWAT模型模拟的基本单元,传统方法划分的水文响应单元在空间分布上不连续且难以确定其明确的空间位置,不能反映HRU间的相互作用和进行精确空间分析。利用GIS工具对土地利用和土壤类型数据进行概化处理,提出了HRU空间离散化的方法,实现了水文响应单元在空间上的准确定位。在此基础上,针对SWAT模型中同一子流域所有HRU采取相同延迟的弱点进行改进,并选择太湖地区西苕溪流域对改进的SWAT模型进行水文模拟验证。改进后,校正期港口站Nash效率系数E_NS(Nash-Sutcliffe Efficiency)从0.64提高到0.67,验证期E_NS系数从0.70提高到0.76。研究表明:修正后的SWAT模型更能反映流域的水文特征,可以达到非常好的效果,考虑到HRU距离因素的径流延迟更为准确地刻画径流过程。实现HRU空间离散化将为模型改进和更小尺度的空间分析提供数据基础。     

Spatial discretization of large watersheds and its influence on the estimation of hillslope sediment yield

The combined use of water erosion models and geographic information systems has facilitated soil loss estimation at the watershed scale. Tools such as the Geo‐spatial interface for the Water Erosion Prediction Project (GeoWEPP) model provide a convenient spatially distributed soil loss estimate but require discretization to identify hillslopes and channels. In GeoWEPP, the TOpographic PArameteriZation (TOPAZ) model is used as an automated procedure to extract a watershed boundary, hillslopes and channels from a digital elevation model (DEM). Previous studies in small watersheds have shown that the size of the hillslopes and the channel distribution affect the model estimates, but in large watersheds, the effects on the soil loss estimates have yet to be tested. Therefore, the objective of this study was to evaluate the effect of discretization on the hillslope sediment yield estimates using GeoWEPP in two large watersheds (>10 km²). The watersheds were selected and discretized varying the TOPAZ parameters [critical source area (CSA) and minimum source channel length (MSCL)] in a 30‐m resolution digital elevation model. The drainage networks built with TOPAZ were compared with each other using the drainage density index. The results showed that the discretization affected hillslope sediment yield estimates and their spatial distribution more than the total runoff. The drainage density index and the hillslope sediment yield were proportional but inversely related; thus, soil loss estimates were highly affected by the spatial discretization. As a result of this analysis, a method to choose the CSA and MSCL values that generates the greatest fraction of hillslopes having profile lengths less than 200 m was developed. This slope length condition is particularly crucial when using the WEPP and GeoWEPP models, in order for them to produce realistic estimates of sheet and rill erosion. Finally, and as a result of this analysis, a more reliable method was developed for selecting the TOPAZ channel network parameters (CSA and MSCL). Copyright © 2015 John Wiley & Sons, Ltd.     

Monotonicity conditions for control volume methods on uniform parallelogram grids in homogeneous media

Control volume methods are frequently used in porous media flow. This article gives an example on how one method, the Multipoint Flux Approximation method (MPFA), fails to satisfy the maximum principle for strong anisotropies or grid skewnesses, and develops conditions for when the monotonicity property holds for uniform parallelogram grids in homogeneous media. The conditions developed are applicable to any nine-point scheme in 2D or 27-point scheme in 3D, and is useful when the method produces a system matrix which is not an M-matrix.     

基于Weka平台的C4.5算法在影像分类中的应用

遥感图像分类是从复杂的地物类型中提取有效类别信息的过程。在研究区地物类型较为复杂的情况下,借助计算机对遥感数据进行类别预测可以提高分类效率和准确率。本文基于Weka平台,利用决策树C4.5算法构造分类模型,进而对未知类别数据进行预测。实验分析表明,基于Weka平台利用决策树C4.5算法对遥感图像分类是可行且有效的,且分类精度较高。     

The role of iron in tetrahedrite and tennantite determined by Rietveld refinement of neutron powder diffraction data

Rietveld refinement of neutron powder diffraction data on four samples of synthetic, iron-bearing tetrahedrite (Cu_12?xFe_xSb₄S₁₃) with x = 0.28, 0.69, 0.91, 2.19 and four samples of synthetic tennantite (Cu_12?xFe_xAs₄S₁₃) with x = 0.33, 0.38, 0.86, 1.5 indicate unambiguously that iron is incorporated into tetrahedral M1 (12d) sites and not into triangular M2 (12e) sites in the cubic crystal structure (space group I $ \ifmmode\expandafter\bar\else\expandafter\=\fi{4} Rietveld refinement of neutron powder diffraction data on four samples of synthetic, iron-bearing tetrahedrite (Cu_12−xFe_xSb₄S₁₃) with x = 0.28, 0.69, 0.91, 2.19 and four samples of synthetic tennantite (Cu_12−xFe_xAs₄S₁₃) with x = 0.33, 0.38, 0.86, 1.5 indicate unambiguously that iron is incorporated into tetrahedral M1 (12d) sites and not into triangular M2 (12e) sites in the cubic crystal structure (space group I 3 m). The refinement results also confirm that M2 is a split (24g), flat-pyramidal site situated statistically on both sides of the S1−S1–S2 triangle. In tetrahedrite, this split is about 0.6 ?, in tennantite about 0.7 ?. Trends in bond lengths and magnitude of the M2 split were evaluated by means of linear regression with Fe concentration as the independent variable.