An approach of dynamic mesh adaptation for simulating 3‐dimensional unsteady moving‐immersed‐boundary flows

In this paper, we present an approach of dynamic mesh adaptation for simulating complex 3‐dimensional incompressible moving‐boundary flows by immersed boundary methods. Tetrahedral meshes are adapted by a hierarchical refining/coarsening algorithm. Regular refinement is accomplished by dividing 1 tetrahedron into 8 subcells, and irregular refinement is only for eliminating the hanging points. Merging the 8 subcells obtained by regular refinement, the mesh is coarsened. With hierarchical refining/coarsening, mesh adaptivity can be achieved by adjusting the mesh only 1 time for each adaptation period. The level difference between 2 neighboring cells never exceeds 1, and the geometrical quality of mesh does not degrade as the level of adaptive mesh increases. A predictor‐corrector scheme is introduced to eliminate the phase lag between adapted mesh and unsteady solution. The error caused by each solution transferring from the old mesh to the new adapted one is small because most of the nodes on the 2 meshes are coincident. An immersed boundary method named local domain‐free discretization is employed to solve the flow equations. Several numerical experiments have been conducted for 3‐dimensional incompressible moving‐boundary flows. By using the present approach, the number of mesh nodes is reduced greatly while the accuracy of solution can be preserved.     

Studies on basicity of alkali metal catron exchanged β and X zeolites by pyrrole-IR spectroscopy

The strength of basic sites has been measured by pyrrole-IR on alkali metal cation exchanged β and X zeolites, as well as NaOH loaded Naβ. The influence of cation type and the structure of zeolites on their basicity has been studied. The acidic and basic properties of the samples were investigated by NH3-TPD and isopropanol reaction. It was shown that the strength of basic sites on samples could be characterized by the shift of vNH band in the pyrrole-IR spectra. The framework oxygen charges were calculated from the Sanderson electronegativity. The changes in basic properties with various alkali metal cation are consistent with the changes of local oxygen charges of the zeolite framework.     

不完全信息群体决策专家权重的集结

本文对于属性权重信息和属性效用信息都不完全的群体多属性决策问题，通过构造属性值区间和运用系统聚类分析法，对群体决策中的专家进行分类，并确定每位专家的权重．     

Simulation of viscous water column collapse using adapting hierarchical grids

An adaptive hierarchical grid‐based method for predicting complex free surface flows is used to simulate collapse of a water column. Adapting quadtree grids are combined with a high‐resolution interface‐capturing approach and pressure‐based coupling of the Navier–Stokes equations. The Navier–Stokes flow solution scheme is verified for simulation of flow in a lid‐driven cavity at Re=1000. Two approaches to the coupling of the Navier–Stokes equations are investigated as are alternative face velocity and hanging node interpolations. Collapse of a water column as well as collapse of a water column and its subsequent interaction with an obstacle are simulated. The calculations are made on uniform and adapting quadtree grids, and the accuracy of the quadtree calculations is shown to be the same as those made on the equivalent uniform grids. Results are in excellent agreement with experimental and other numerical data. A sharp interface is maintained at the free surface. The new adapting quadtree‐based method achieves a considerable saving in the size of the computational grid and CPU time in comparison with calculations made on equivalent uniform grids. Copyright © 2005 John Wiley & Sons, Ltd.     

Stereological simulations of asymmetric polymerization in channels of bile acid inclusion compounds: A detailed analysis of the monomer arrangements in the channels

We studied simulations by computer graphics to estimate the steric mechanism of the asymmetric polymerization of prochiral diene monomers in channels of inclusion compounds of steroidal bile acids, such as deoxycholic acid (DCA) and cholic acid. We applied a hierarchization method to interpret the crystal structures of bile acids, clarifying that the chiral host molecules associated to form characteristic 2₁-helical assemblies with uneven surfaces. A detailed analysis of the uneven channels in a close-packing state indicated that there were many possible arrangements of the monomers in the channels. The plausible arrangements in the channel could explain a previous study, which showed that the polymerization in the DCA channel yielded chiral polymers with a predominant configuration from prochiral diene monomers, such as 2-methyl-trans-1,3-pentadiene. On the basis of such simulation studies of the arrangements of guest monomers in the channel, we examined a plausible steric mechanism for asymmetric inclusion polymerization. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4648–4655, 2004     

Quantitative Comparison of REAPDOR and TRAPDOR Experiments by Numerical Simulations and Determination of H–Al Distances in Zeolites

Quantitative H–Al distances in acid sites of two zeolites with MFI and IFR framework topology were obtained by numerical simulation of ¹H{²⁷Al} rotational echo adiabatic passage double resonance (REAPDOR) experiments. A ²⁷Al offset-dependent data set yields for each resolved ¹H NMR line a corresponding nuclear electric quadrupole coupling constant of the neighboring ²⁷Al site. This information is used for analyzing a second data set for on-resonance irradiation, where the dipolar evolution time (number of rotor cycles) was varied, to yield the ¹H–²⁷Al dipolar coupling constant. Numerical simulations indicate that the REAPDOR method does not depend significantly on the polar angles, defining the orientation of the electric field gradient tensor of ²⁷Al with respect to the Al–H dipolar vector. In contrast, the transfer of populations in double resonance sequence is sensitive to these angles, and it can be thus used to measure them.     

Uniform estimate of the constant in the strengthened CBS inequality for anisotropic non‐conforming FEM systems

Preconditioners based on various multilevel extensions of two‐level finite element methods (FEM) lead to iterative methods which have an optimal order computational complexity with respect to the size of the system. Such methods were first presented in Axelsson and Padiy (SIAM. J. Sci. Stat. Comp. 1990; 20 :1807) and Axelsson and Vassilevski (Numer. Math. 1989; 56 :157), and are based on (recursive) two‐level splittings of the finite element space. The key role in the derivation of optimal convergence rate estimates is played by the constant γ in the so‐called Cauchy–Bunyakowski–Schwarz (CBS) inequality, associated with the angle between the two subspaces of the splitting. It turns out that only existence of uniform estimates for this constant is not enough but accurate quantitative bounds for γ have to be found as well. More precisely, the value of the upper bound for γ∈(0,1) is part of the construction of various multilevel extensions of the related two‐level methods. In this paper, an algebraic two‐level preconditioning algorithm for second‐order elliptic boundary value problems is constructed, where the discretization is done using Crouzeix–Raviart non‐conforming linear finite elements on triangles. An important point to make is that in this case the finite element spaces corresponding to two successive levels of mesh refinements are not nested. To handle this, a proper two‐level basis is considered, which enables us to fit the general framework for the construction of two‐level preconditioners for conforming finite elements and to generalize the method to the multilevel case. The major contribution of this paper is the derived estimates of the related constant γ in the strengthened CBS inequality. These estimates are uniform with respect to both coefficient and mesh anisotropy. To our knowledge, the results presented in the paper are the first such estimates for non‐conforming FEM systems. Copyright © 2004 John Wiley & Sons, Ltd.     

Field-of-values analysis of preconditioned iterative methods for nonsymmetric elliptic problems

Summary. The convergence rate of Krylov subspace methods for the solution of nonsymmetric systems of linear equations, such as GMRES or FOM, is studied. Bounds on the convergence rate are presented which are based on the smallest real part of the field of values of the coefficient matrix and of its inverse. Estimates for these quantities are available during the iteration from the underlying Arnoldi process. It is shown how these bounds can be used to study the convergence properties, in particular, the dependence on the mesh-size and on the size of the skew-symmetric part, for preconditioners for finite element discretizations of nonsymmetric elliptic boundary value problems. This is illustrated for the hierarchical basis and multilevel preconditioners which constitute popular preconditioning strategies for such problems. Received May 3, 1996     

Accelerating Galerkin BEM for linear elasticity using adaptive cross approximation

The adaptive cross approximation (ACA) algorithm (Numer. Math. 2000; 86 :565–589; Computing 2003; 70 (1):1–24) provides a means to compute data‐sparse approximants of discrete integral formulations of elliptic boundary value problems with almost linear complexity. ACA uses only few of the original entries for the approximation of the whole matrix and is therefore well‐suited to speed up existing computer codes. In this article we extend the convergence proof of ACA to Galerkin discretizations. Additionally, we prove that ACA can be applied to integral formulations of systems of second‐order elliptic operators without adaptation to the respective problem. The results of applying ACA to boundary integral formulations of linear elasticity are reported. Furthermore, we comment on recent implementation issues of ACA for non‐smooth boundaries. Copyright © 2006 John Wiley & Sons, Ltd.