Numerical experiments of preconditioned Krylov subspace methods solving the dense non-symmetric systems arising from BEM

Discretization of boundary integral equations leads, in general, to fully populated non-symmetric linear systems of equations. An inherent drawback of boundary element method (BEM) is that, the non-symmetric dense linear systems must be solved. For large-scale problems, the direct methods require expensive computational cost and therefore the iterative methods are perhaps more preferable. This paper studies the comparative performances of preconditioned Krylov subspace solvers as bi-conjugate gradient (Bi-CG), generalized minimal residual (GMRES), conjugate gradient squared (CGS), quasi-minimal residual (QMR) and bi-conjugate gradient stabilized (Bi-CGStab) for the solution of dense non-symmetric systems. Several general preconditioners are also considered and assessed. The results of numerical experiments suggest that the preconditioned Krylov subspace methods are effective approaches solving the large-scale dense non-symmetric linear systems arising from BEM.     

Nodally exact Ritz discretizations of 1D diffusion–absorption and Helmholtz equations by variational FIC and modified equation methods

This article presents the first application of the Finite Calculus (FIC) in a Ritz-FEM variational framework. FIC provides a steplength parametrization of mesh dimensions, which is used to modify the shape functions. This approach is applied to the FEM discretization of the steady-state, one-dimensional, diffusion–absorption and Helmholtz equations. Parametrized linear shape functions are directly inserted into a FIC functional. The resulting Ritz-FIC equations are symmetric and carry a element-level free parameter coming from the function modification process. Both constant- and variable-coefficient cases are studied. It is shown that the parameter can be used to produce nodally exact solutions for the constant coefficient case. The optimal value is found by matching the finite-order modified differential equation (FOMoDE) of the Ritz-FIC equations with the original field equation. The inclusion of the Ritz-FIC models in the context of templates is examined. This inclusion shows that there is an infinite number of nodally exact models for the constant coefficient case. The ingredients of these methods (FIC, Ritz, MoDE and templates) can be extended to multiple dimensions     

Stokes问题一个矩形非协调元逼近

提出了一个新的矩形非协调混合元格式,把它应用于Stokes问题的数值逼近,得到了最优的误差估计.     

用穿透法测量声速时初始点的选择问题

用穿透方法测量岩心或固体的声速时，从测量波形中确定纵波（或横波）的到达时刻（或称初始点）比较困难，当声波的频率比较低时，其误差对测量结果影响比较大。本文用相位分析的方法研究了初始点的选择问题。首先，用各向同性较强、均匀的汉白玉制作标准件，测量其不同传播距离的波形，再用相位补偿的方法得到其传播速度；其次，利用传播速度，可从不同距离的测量波形中确定初始点及其对应的测量系统的时间延迟常数；最后，确定波形的其他位置为初始点时对应的时间延迟常数，因此，我们可以根据实际测量波形的特点选择最佳的初始点，利用其对应的时间延迟常数得到比较精确的声速。模型测量结果表明，初始点位置不同，其对应的测量系统的时间延迟常数也不同，也即测量系统的时间延迟常数是与初始点的选择相对应的。     

用蒙特卡罗法解有压隧洞出口段水流问题

利用不规则游动网格的蒙特卡罗法对有压隧洞出口段水流进行了数值模拟。根据数值计算与模型试验结果的比较，得出具有凸形曲面边界（包括折面底坡）负压区的存在不仅是边界层分离所致，边壁弯曲使过流产生的离心力也是产生负压的重要原因的结论。计算结果表明：蒙特卡罗法灵活简单、结果稳定，计算结果与实测结果吻合较好。     

土石围堰三维有限元渗流分析及防渗措施研究

为了解决上游围堰防渗及绕坝渗漏问题,确定最优防渗方案,对炳灵水电站右岸松动体防渗帷幕的防渗方案进行了三维有限元渗流计算,并对右岸松动体帷幕的防渗范围和灌浆排数进行了敏感性分析。通过多种防渗方案的计算,对右岸松动体的防渗方案做了相应优化,建议了满足设计要求的防渗方案。     

小议变动成本法的合理性

企业对盈亏临界点的计算通常是以变动成本法为基础，但也有以制造成本法为计算基础的，对于这两种成本方法计算的几种盈亏临界点的情况，本文结合案例，通过比较分析认为：盈亏临界点的计算应当以变动成本法为基础更为合理。     

PV module dynamic impedance and its voltage and frequency dependencies

The paper presents a derivation of the dynamic impedance of a PV module. At each bias voltage, the general form of the impedance describes a semicircular locus in the complex impedance plane. Intercepts of each impedance locus yield series, shunt and dynamic resistance of a module. Determinations of the dynamic impedance of a x-Si PV module in the dark with five reverse bias voltages and over a frequency range of 1 Hz to 60 kHz are made. The experimental results validate the derived general form of dynamic impedance.     

Modeling the effect of pigment morphology on the dynamic compression of coating layers using DEM

In the present paper, discrete element method (DEM) was employed to investigate the effect of pigment morphology on packing dynamics and compressive behavior of paper coating layers in calendering process. Spherical, platy, and needle-like particles, representing GCC, delaminated clay, and aragonite PCC pigments, were considered in this study. For each particle shape, the compression of coating structures formed by mono-sized and poly-dispersed pigments were modeled. Stress–strain behavior of the coating layers and in-plane and out-of-plane movements of the pigment particles during the compression were computed under the same maximum compressive stress. Simulation results revealed that the in-plane movements of the pigment particles during compression in the calender nip were small in magnitude (<0.35 μm). These findings help to better understand the smoothening phenomena of coating structures during the calendering process.     

Direct synthesis and catalytic performance of ultralarge pore GaSBA-15 mesoporous molecular sieves with high gallium content

Mesoporous GaSBA-15 molecular sieves with different n_Si/n_Ga ratios have been directly synthesized using Pluronic 123 triblock polymer as a structure-directing agent by pH-adjusting method. The mesoporous materials have been characterized using ICP-AES, XRD, N₂ adsorption, ⁷¹Ga-MAS NMR, SEM and TEM. ICP-AES studies show a high amount of gallium incorporation on the silica pore walls. The structural and textural properties of calcined GaSBA-15 are characterized by XRD and N₂ adsorption. ⁷¹Ga MAS NMR results demonstrate that a high amount of tetrahedral-gallium could be substituted for Si in the framework of SBA-15. TEM and FE-SEM images show the uniform pore diameter and rope-like hexagonal mesoporous structure of GaSBA-15. These GaSBA-15 materials have been used as catalysts for vapour-phase t-butylation of 1,2-dihydroxybenzene (DHB) for selective synthesis of 4-t-butylcatechol (4-TBC) under different reaction conditions. GaSBA-15(10) gave the highest 93.2% conversion of DHB and 95.7% selectivity of 4-TBC as compared with other GaSBA-15 catalysts.