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Point Distribution (point + distribution)
Selected AbstractsAnalysis of a Distribution of Point Events Using the Network-Based Quadrat MethodGEOGRAPHICAL ANALYSIS, Issue 4 2008Shino Shiode This study proposes a new quadrat method that can be applied to the study of point distributions in a network space. While the conventional planar quadrat method remains one of the most fundamental spatial analytical methods on a two-dimensional plane, its quadrats are usually identified by regular, square grids. However, assuming that they are observed along a network, points in a single quadrat are not necessarily close to each other in terms of their network distance. Using planar quadrats in such cases may distort the representation of the distribution pattern of points on a network. The network-based units used in this article, on the other hand, consist of subsets of the actual network, providing more accurate aggregation of the data points along the network. The performance of the network-based quadrat method is compared with that of the conventional quadrat method through a case study on a point distribution on a network. The ,2 statistic and Moran's I statistic of the two quadrat types indicate that (1) the conventional planar quadrat method tends to overestimate the overall degree of dispersion and (2) the network-based quadrat method derives a more accurate estimate on the local similarity. The article also performs sensitivity analysis on network and planar quadrats across different scales and with different spatial arrangements, in which the abovementioned statistical tendencies are also confirmed. [source] Numerical study of grid distribution effect on accuracy of DQ analysis of beams and plates by error estimation of derivative approximationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2001C. Shu Abstract The accuracy of global methods such as the differential quadrature (DQ) approach is usually sensitive to the grid point distribution. This paper is to numerically study the effect of grid point distribution on the accuracy of DQ solution for beams and plates. It was found that the stretching of grid towards the boundary can improve the accuracy of DQ solution, especially for coarse meshes. The optimal grid point distribution (corresponding to optimal stretching parameter) depends on the order of derivatives in the boundary condition and the number of grid points used. The optimal grid distribution may not be from the roots of orthogonal polynomials. This differs somewhat from the conventional analysis. This paper also proposes a simple and effective formulation for stretching the grid towards the boundary. The error distribution of derivative approximation is also studied, and used to analyze the effect of grid point distribution on accuracy of numerical solutions. Copyright © 2001 John Wiley & Sons, Ltd. [source] A novel finite point method for flow simulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2002M. Cheng Abstract A novel finite point method is developed to simulate flow problems. The mashes in the traditional numerical methods are supplanted by the distribution of points in the calculation domain. A local interpolation based on the properties of Taylor series expansion is used to construct an approximation for unknown functions and their derivatives. An upwind-dominated scheme is proposed to efficiently handle the non-linear convection. Comparison with the finite difference solutions for the two-dimensional driven cavity flow and the experimental results for flow around a cylinder shows that the present method is capable of satisfactorily predicting the flow separation characteristic. The present algorithm is simple and flexible for complex geometric boundary. The influence of the point distribution on computation time and accuracy of results is included. Copyright © 2002 John Wiley & Sons, Ltd. [source] Influence of protrusive tooth contact on tapping point distributionJOURNAL OF ORAL REHABILITATION, Issue 11 2000T. Ueno This study investigated the influence of protrusive tooth contacts (tooth contacts during mandibular protrusion) on the tapping point distribution. Nine healthy subjects volunteered for this study and the protrusive tooth contact pattern, as well as the retrusive tooth contact pattern, was altered on four maxillary occlusal splints. The first splint was adjusted to make the sagittal incisal path of protrusion and retrusion equivalent to that of the natural dentition. The second and third splints had partial and complete elimination of the protrusive tooth contact, respectively. The fourth splint had complete elimination of both protrusive and retrusive tooth contacts. The subjects were asked to use each splint continuously for 1 week. The tapping point distribution was measured on the 7th day after insertion of each splint. The four experimental occlusal conditions were found to have a significant effect on the tapping point distribution. The complete elimination of the protrusive tooth contact caused an anterior tapping point location and an increase in the tapping point area. The former tendency was found to be independent of the presence of the retrusive tooth contact. In conclusion, it was suggested that the protrusive tooth contact plays a significant role in maintaining the consistency and stability of the tapping point. [source] Effektiver Algorithmus zur Lösung von inversen Aufgabenstellungen , Anwendung in der GeomechanikBAUTECHNIK, Issue 7 2006Jörg Meier Dipl.-Ing. Durch den Einsatz von numerischen Modellen für ingenieurtechnische Problemstellungen, wie z. B. der FEM oder der FDM, können zunehmend komplexere Berechnungen in immer kürzerer Zeit bewältigt werden. Gleichzeitig ergibt sich jedoch bei dem Einsatz dieser Werkzeuge der Bedarf an Werten für die verschiedenen Modellparameter, von rein konstitutiven Kennwerten bis hin zu geometrischen Angaben, für deren Bestimmung zunehmend inverse Verfahren Anwendung finden. Bei der Nutzung dieser Methoden ist jedoch , insbesondere bei komplizierten Simulationen , mit sehr langen Berechnungszeiten zu rechnen. Gegenstand dieses Beitrags ist die Vorstellung einer Verfahrensklasse, die eine Abschätzung der Lösung solcher inverser Aufgaben auf der Basis von relativ wenigen Stützstellen ermöglicht. An die Verteilung der Stützstellen werden geringste Anforderungen gestellt, so daß diese wahlweise aus vorhergehenden Simulationen oder auch aus alternativen Quellen stammen können. Im Rahmen dieses Beitrags soll ausgehend von einer Einführung in den theoretischen Ansatz eine Strategie zur Beschleunigung der Lösung von inversen Problemstellungen und Optimierungsaufgaben an einem Beispiel aus dem Gebiet der Geomechanik vorgestellt werden. Effective algorithm for solving inverse problems , geomechanical application. When working with numerical models, it is essential to determine model parameters which are as realistic as possible. Optimization techniques are being employed more and more frequently for solving this task. However, using these methods may lead to very high time costs , in particular, if rather complicated forward calculations are involved. In this paper, we present a class of methods that allows estimating the solution of this kind of optimization problems based on relatively few sampling points. We put very weak constraints on the sampling point distribution; hence, they may be taken from previous forward calculations as well as from alternative sources. Starting from an introduction into the theoretical approach, a strategy for speeding up inverse optimization problems is introduced which is illustrated by an example geomechanics. [source] Analysis of a Distribution of Point Events Using the Network-Based Quadrat MethodGEOGRAPHICAL ANALYSIS, Issue 4 2008Shino Shiode This study proposes a new quadrat method that can be applied to the study of point distributions in a network space. While the conventional planar quadrat method remains one of the most fundamental spatial analytical methods on a two-dimensional plane, its quadrats are usually identified by regular, square grids. However, assuming that they are observed along a network, points in a single quadrat are not necessarily close to each other in terms of their network distance. Using planar quadrats in such cases may distort the representation of the distribution pattern of points on a network. The network-based units used in this article, on the other hand, consist of subsets of the actual network, providing more accurate aggregation of the data points along the network. The performance of the network-based quadrat method is compared with that of the conventional quadrat method through a case study on a point distribution on a network. The ,2 statistic and Moran's I statistic of the two quadrat types indicate that (1) the conventional planar quadrat method tends to overestimate the overall degree of dispersion and (2) the network-based quadrat method derives a more accurate estimate on the local similarity. The article also performs sensitivity analysis on network and planar quadrats across different scales and with different spatial arrangements, in which the abovementioned statistical tendencies are also confirmed. [source] Towards automatic structured multiblock mesh generation using improved transfinite interpolationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008C. B. AllenArticle first published online: 4 OCT 200 Abstract The quality of any numerical flowfield solution is inextricably linked to the quality of the mesh used. It is normally accepted that structured meshes are of higher quality than unstructured meshes, but are much more difficult to generate and, furthermore, for complex topologies a multiblock approach is required. This is the most resource-intensive approach to mesh generation, since block structures, mesh point distributions, etc., need to be defined before the generation process, and so is seldom used in an industrial design loop, particularly where a novice user may be involved. This paper considers and presents two significant advances in multiblock mesh generation: the development of a fast, robust, and improved quality interpolation-based generation scheme and a fully automatic multiblock optimization and generation method. A volume generation technique is presented based on a form of transfinite interpolation, but modified to include improved orthogonality and spacing control and, more significantly, an aspect ratio-based smoothing algorithm that removes grid crossover and results in smooth meshes even for discontinuous boundary distributions. A fully automatic multiblock generation scheme is also presented, which only requires surface patch(es) and a target number of mesh cells. Hence, all user input is removed from the process, and a novice user is able to obtain a high-quality mesh in a few minutes. It also means the code can be run in batch mode, or called as an external function, and so is ideal for incorporation into a design or optimization loop. To demonstrate the power and efficiency of the code, multiblock meshes of up to 256 million cells are presented for wings and rotors in hover and forward flight. Copyright © 2007 John Wiley & Sons, Ltd. [source] Stable high-order finite-difference methods based on non-uniform grid point distributionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2008Miguel Hermanns Abstract It is well known that high-order finite-difference methods may become unstable due to the presence of boundaries and the imposition of boundary conditions. For uniform grids, Gustafsson, Kreiss, and Sundström theory and the summation-by-parts method provide sufficient conditions for stability. For non-uniform grids, clustering of nodes close to the boundaries improves the stability of the resulting finite-difference operator. Several heuristic explanations exist for the goodness of the clustering, and attempts have been made to link it to the Runge phenomenon present in polynomial interpolations of high degree. By following the philosophy behind the Chebyshev polynomials, a non-uniform grid for piecewise polynomial interpolations of degree q,N is introduced in this paper, where N + 1 is the total number of grid nodes. It is shown that when q=N, this polynomial interpolation coincides with the Chebyshev interpolation, and the resulting finite-difference schemes are equivalent to Chebyshev collocation methods. Finally, test cases are run showing how stability and correct transient behaviours are achieved for any degree q Simple modifications for stabilization of the finite point methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005B. Boroomand Abstract A stabilized version of the finite point method (FPM) is presented. A source of instability due to the evaluation of the base function using a least square procedure is discussed. A suitable mapping is proposed and employed to eliminate the ill-conditioning effect due to directional arrangement of the points. A step by step algorithm is given for finding the local rotated axes and the dimensions of the cloud using local average spacing and inertia moments of the points distribution. It is shown that the conventional version of FPM may lead to wrong results when the proposed mapping algorithm is not used. It is shown that another source for instability and non-monotonic convergence rate in collocation methods lies in the treatment of Neumann boundary conditions. Unlike the conventional FPM, in this work the Neumann boundary conditions and the equilibrium equations appear simultaneously in a weight equation similar to that of weighted residual methods. The stabilization procedure may be considered as an interpretation of the finite calculus (FIC) method. The main difference between the two stabilization procedures lies in choosing the characteristic length in FIC and the weight of the boundary residual in the proposed method. The new approach also provides a unique definition for the sign of the stabilization terms. The reasons for using stabilization terms only at the boundaries is discussed and the two methods are compared. Several numerical examples are presented to demonstrate the performance and convergence of the proposed methods. Copyright © 2005 John Wiley & Sons, Ltd. [source]
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