			Home About us Contact

Refinement Method (refinement + method)

Distribution by Scientific Domains

Chemistry	42%
Engineering	28%

Selected Abstracts

Numerical solution for consolidation and desiccation of soft soils

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2002
Daniel T. C. Yao
Abstract The consolidation and desiccation behaviour of soft soils can be described by two time-dependent non-linear partial differential equations using the finite strain theory. Analytical solutions do not exist for these governing equations. In this paper, we develop efficient numerical methods and software for finding the numerical solutions. We introduce a semi-implicit time integration scheme, and show numerically that our method converges. In addition, the numerical solution matches well with the experimental result. A boundary refinement method is also developed to improve the convergence and stability for the case of Neumann type boundary conditions. Interface governing equations are derived to maintain the continuity of consolidation and desiccation processes. This is useful because the soil column can undergo desiccation on top and consolidation on the bottom simultaneously. The numerical algorithms has been implemented into a computer program and the results have been verified with centrifuge test results conducted in our laboratory. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Automatic energy conserving space,time refinement for linear dynamic structural problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005
P. Cavin
Abstract In this paper a local space,time automatic refinement method (STAR method) is developed to efficiently solve time-dependent problems using FEM techniques. The automatic process is driven by an energy or a displacement error indicator which controls the precision of the result. The STAR method solves the numerical problem on grids with different mesh size. For the Newmark schemes, a general demonstration, using the energy method, gives the interface conditions between two successive grids which is compatible with the stability of the scheme. Finally, using a linear one-dimensional example, the convergence of the method and the precision of the results are discussed. Copyright © 2005 John Wiley & Sons, Ltd. [source]

The effect of overall discretization scheme on Jacobian structure, convergence rate, and solution accuracy within the local rectangular refinement method

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 8 2001
Beth Anne V. Bennett
Abstract The local rectangular refinement (LRR) solution-adaptive gridding method automatically produces orthogonal unstructured adaptive grids and incorporates multiple-scale finite differences to discretize systems of elliptic governing partial differential equations (PDEs). The coupled non-linear discretized equations are solved simultaneously via Newton's method with a Bi-CGSTAB linear system solver. The grids' unstructured nature produces a nonstandard sparsity pattern within the Jacobian. The effects of two discretization schemes (LRR multiple-scale stencils and traditional single-scale stencils) on Jacobian bandwidth, convergence speed, and solution accuracy are studied. With various point orderings, for two simple problems with analytical solutions, the LRR multiple-scale stencils are seen to: (1) produce Jacobians of smaller bandwidths than those resulting from the traditional single-scale stencils; (2) lead to significantly faster Newton's method convergence than the single-scale stencils; and (3) produce more accurate solutions than the single-scale stencils. The LRR method, including the LRR multiple-scale stencils, is finally applied to an engineering problem governed by strongly coupled, highly non-linear PDEs: a steady-state lean Bunsen flame with complex chemistry, multicomponent transport, and radiation modeling. Very good agreement is observed between the computed flame height and previously published experimental data. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Structural study of ferroelectric and paraelectric phases in PbK2LiNb5O15

PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 11 2004
Y. Gagou
Abstract The structures of PbK2LiNb5O15 showing the ferroelectricity below about 640 K have been studied in the paraelectric and ferroelectric phases by means of synchrotron X-ray powder diffraction. The data are analyzed with a Rietveld refinement method. It is found that the paraelectric structure and the ferroelectric one are of tetragonal and orthorhombic symmetry with P4/mbm and Pba2, respectively. The Pba2 structure gives a polar displacement along c -axis, whose direction is consistent with that deduced from dielectric measurements. The refined chemical occupancies of the cations Pb, K and Nb give the site-situation of these ions in the tunnels with square sections and pentagonal sections in each phase. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Extracting charge density distributions from diffraction data: a model study on urea

ACTA CRYSTALLOGRAPHICA SECTION B, Issue 1 2000
R. Y. De Vries
The quality of the extraction of electron density distributions by means of a multipole refinement method is investigated. Structure factors of the urea crystal have been obtained from an electron density distribution (EDD) resulting from a density function calculation with the CRYSTAL95 package. To account for the thermal motion of the atoms, the stockholder-partioned densities of the atoms have been convoluted with thermal smearing functions, which were obtained from a neutron diffraction experiment. A POP multipole refinement yielded a good fit, R = 0.6%. This disagreement factor is based on magnitudes only. Comparison with the original structure factors gave a disagreement of 0.8% owing to differences in magnitude and phase. The fitted EDD still showed all the characteristics of the interaction density. After random errors corresponding to the experimental situation were added to the structure factors, the refinement was repeated. The fit was R = 1.1%. This time the resulting interaction density was heavily deformed. Repetition with another set of random errors from the same distribution yielded a widely different interaction density distribution. The conclusion is that interaction densities cannot be obtained from X-ray diffraction data on non-centrosymmetric crystals. [source]

Application of normal-mode refinement to X-ray crystal structures at the lower resolution limit

ACTA CRYSTALLOGRAPHICA SECTION D, Issue 7 2009
Fengyun Ni
The structural refinement of large complexes at the lower resolution limit is often difficult and inefficient owing to the limited number of reflections and the frequently high-level structural flexibility. A new normal-mode-based X-ray crystallographic refinement method has recently been developed that enables anisotropic B -factor refinement using a drastically smaller number of thermal parameters than even isotropic refinement. Here, the method has been systematically tested on a total of eight systems in the resolution range 3.0,3.9,Å. This series of tests established the most applicable scenarios for the method, the detailed procedures for its application and the degree of structural improvement. The results demonstrated substantial model improvement at the lower resolution limit, especially in cases in which other methods such as the translation,libration,screw (TLS) model were not applicable owing to the poorly converged isotropic B -factor distribution. It is expected that this normal-mode-based method will be a useful tool for structural refinement, in particular at the lower resolution limit, in the field of X-ray crystallography. [source]

Structural improvement of unliganded simian immunodeficiency virus gp120 core by normal-mode-based X-ray crystallographic refinement

ACTA CRYSTALLOGRAPHICA SECTION D, Issue 4 2009
Xiaorui Chen
The envelope protein gp120/gp41 of simian and human immunodeficiency viruses plays a critical role in viral entry into host cells. However, the extraordinarily high structural flexibility and heavy glycosylation of the protein have presented enormous difficulties in the pursuit of high-resolution structural investigation of some of its conformational states. An unliganded and fully glycosylated gp120 core structure was recently determined to 4.0,Å resolution. The rather low data-to-parameter ratio limited refinement efforts in the original structure determination. In this work, refinement of this gp120 core structure was carried out using a normal-mode-based refinement method that has been shown in previous studies to be effective in improving models of a supramolecular complex at 3.42,Å resolution and of a membrane protein at 3.2,Å resolution. By using only the first four nonzero lowest-frequency normal modes to construct the anisotropic thermal parameters, combined with manual adjustments and standard positional refinement using REFMAC5, the structural model of the gp120 core was significantly improved in many aspects, including substantial decreases in R factors, better fitting of several flexible regions in electron-density maps, the addition of five new sugar rings at four glycan chains and an excellent correlation of the B -factor distribution with known structural flexibility. These results further underscore the effectiveness of this normal-mode-based method in improving models of protein and nonprotein components in low-resolution X-ray structures. [source]