Evaluation of pairwise distances among orthogonal grid points in hypercube

2017 ◽  
Author(s):  
Václav Sadílek ◽  
Miroslav Vořechovský ◽  
Magdalena Šmídová
Keyword(s):  
Orthogonal Grid ◽  
Grid Points

A New Method of Orthogonal Grid Generation

2011 ◽  
Vol 130-134 ◽  
pp. 757-760
Author(s):  
K. Ma ◽  
W.L. Wei
Keyword(s):  
Control Function ◽  
Grid Generation ◽  
Test Problems ◽  
Point Distribution ◽  
Good Balance ◽  
Orthogonal Grid ◽  
Finite Difference Discretization ◽  
Grid Points ◽  
Generating System ◽  
Difference Discretization

A method for orthogonal grid generation is presented. The generating system is based on solution of a system of partial differential equations with finite difference discretization. The influence of the number of grid points, type of boundary, and intensity of the grid quality control function and grid properties are investigated. Specification of both boundary point distribution on all sides is used. The proposed method is applied to various test problems£¬which shows this method provides a good balance between controlling grid orthogonality and cell aspect ratio.

Research on Nearly Orthogonal Two-Dimensional Grid Generation

2011 ◽  
Vol 130-134 ◽  
pp. 2981-2984
Author(s):  
B.L. Su ◽  
W.L. Wei
Keyword(s):  
Control Function ◽  
Grid Generation ◽  
Moving Boundaries ◽  
Test Problems ◽  
Point Distribution ◽  
Orthogonal Grid ◽  
Finite Difference Discretization ◽  
Grid Points ◽  
Generating System ◽  
Difference Discretization

A method for nearly orthogonal grid generation is presented in this study. The generating system is based on solution of a system of partial differential equations with finite difference discretization. The influence of the number of grid points, type of boundary, and intensity of the grid quality control function and grid properties are investigated. Specification of both boundary point distribution on all sides and moving boundaries is used. The proposed method is applied to various test problems£¬which shows this method provides a good balance between controlling grid orthogonality and cell aspect ratio.

Research on Grid Generation

2012 ◽  
Vol 170-173 ◽  
pp. 3691-3694
Author(s):  
Y. L. Liu ◽  
Y. Bai ◽  
X.J. Zhao ◽  
W.L. Wei ◽  
K. Ma
Keyword(s):  
Control Function ◽  
Grid Generation ◽  
Test Problems ◽  
Point Distribution ◽  
Good Balance ◽  
Orthogonal Grid ◽  
Finite Difference Discretization ◽  
Grid Points ◽  
Generating System ◽  
Difference Discretization

A method for orthogonal grid generation is presented. The generating system is based on solution of a system of partial differential equations with finite difference discretization. The influence of the number of grid points, type of boundary, and intensity of the grid quality control function and grid properties are investigated. Specification of both boundary point distribution on all sides is used. The proposed method is applied to various test problems，which shows this method provides a good balance between controlling grid orthogonality and cell aspect ratio.

On the construction of orthogonal curvilinear grids for regional oceanic modeling: algorithm and user guide

2020 ◽  
Vol 48 (4) ◽  
pp. 45-111
Author(s):  
A. F. Shepetkin
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Elliptic Problem ◽  
Software Package ◽  
Conformal Transformation ◽  
Iterative Procedure ◽  
Geometric Shape ◽  
Curvilinear Grids ◽  
Grid Points ◽  
Grid Nodes

A new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a “compile-once - use forever” software package. It is based on the numerical solution of the inverse problem by an iterative procedure -- finding such distribution of grid points along its perimeter, so that the conformal transformation of the perimeter into a rectangle turns this distribution into uniform one. The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure. Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving an elliptic problem. It is shown that it was possible to obtain the exact orthogonality of the perimeter at the corners of the grid, to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes about both directions are equal to each other.

ADAPTAÇÃO E APLICAÇÃO DE MÉTODOS DE INTELIGÊNCIA COMPUTACIONAL PARA A ESTIMAÇÃO DE UMA FONTE DE POLUENTES EM ESTUÁRIOS

Engevista ◽  
2014 ◽  
Vol 17 (2) ◽  
pp. 152
Author(s):  
Radael De Souza Parolin ◽  
Pedro Paulo Gomes Watts Rodrigues ◽  
Antônio J. Silva Neto
Keyword(s):  
Computational Intelligence ◽  
Computational Models ◽  
Source Position ◽  
Iterative Search ◽  
Contaminant Source ◽  
Resources Management ◽  
Search Spaces ◽  
Grid Points ◽  
Computational Intelligence Methods

The quality of a given water body can be assessed through the analysis of a number of indicators. Mathematical and computational models can be built to simulate the behavior of these indicators (observable variables), in such a way that different scenarios can be generated, supporting decisions regarding water resources management. In this study, the transport of a conservative contaminant in an estuarine environment is simulated in order to identify the position and intensity of the contaminant source. For this, it was formulated an inverse problem, which was solved through computational intelligence methods. This approach required adaptations to these methods, which had to be modified to relate the source position to the discrete mesh points of the domain. In this context, two adaptive techniques were developed. In one, the estimated points are projected to the grid points, and in the other, points are randomly selected in the iterative search spaces of the methods. The results showed that the methodology here developed has a strong potential in water bodies’ management and simulation.

scholarly journals Image-based textile decoding

2020 ◽  
pp. 1-14
Author(s):  
Siqiang Chen ◽  
Masahiro Toyoura ◽  
Takamasa Terada ◽  
Xiaoyang Mao ◽  
Gang Xu
Keyword(s):  
Deep Learning ◽  
Grid Point ◽  
Intermediate Representation ◽  
Training Set ◽  
Binary Matrix ◽  
The Matrix ◽  
Correct Pattern ◽  
Grid Points ◽  
Textile Fabric ◽  
Direct Correspondence

A textile fabric consists of countless parallel vertical yarns (warps) and horizontal yarns (wefts). While common looms can weave repetitive patterns, Jacquard looms can weave the patterns without repetition restrictions. A pattern in which the warps and wefts cross on a grid is defined in a binary matrix. The binary matrix can define which warp and weft is on top at each grid point of the Jacquard fabric. The process can be regarded as encoding from pattern to textile. In this work, we propose a decoding method that generates a binary pattern from a textile fabric that has been already woven. We could not use a deep neural network to learn the process based solely on the training set of patterns and observed fabric images. The crossing points in the observed image were not completely located on the grid points, so it was difficult to take a direct correspondence between the fabric images and the pattern represented by the matrix in the framework of deep learning. Therefore, we propose a method that can apply the framework of deep learning viau the intermediate representation of patterns and images. We show how to convert a pattern into an intermediate representation and how to reconvert the output into a pattern and confirm its effectiveness. In this experiment, we confirmed that 93% of correct pattern was obtained by decoding the pattern from the actual fabric images and weaving them again.

A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations

2020 ◽  
Vol 21 (7-8) ◽  
pp. 683-691
Author(s):  
Phumlani G. Dlamini ◽  
Vusi M. Magagula
Keyword(s):  
Collocation Method ◽  
Three Dimensional ◽  
Linearization Method ◽  
High Accuracy ◽  
Time Variable ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Burgers Equations ◽  
Grid Points ◽  
Linearization Techniques

AbstractIn this paper, we introduce the multi-variate spectral quasi-linearization method which is an extension of the previously reported bivariate spectral quasi-linearization method. The method is a combination of quasi-linearization techniques and the spectral collocation method to solve three-dimensional partial differential equations. We test its applicability on the (2 + 1) dimensional Burgers’ equations. We apply the spectral collocation method to discretize both space variables as well as the time variable. This results in high accuracy in both space and time. Numerical results are compared with known exact solutions as well as results from other papers to confirm the accuracy and efficiency of the method. The results show that the method produces highly accurate solutions and is very efficient for (2 + 1) dimensional PDEs. The efficiency is due to the fact that only few grid points are required to archive high accuracy. The results are portrayed in tables and graphs.

The Use of Subgrid Transport Equations in a Three-Dimensional Model of Atmospheric Turbulence

1973 ◽  
Vol 95 (3) ◽  
pp. 429-438 ◽  
Author(s):  
J. W. Deardorff
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Transport Equations ◽  
Subgrid Scale ◽  
Reynolds Stresses ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Truncation Errors ◽  
Subgrid Scales ◽  
Grid Points

A three-dimensional numerical model of turbulence in an atmospheric boundary layer has been revised to utilize subgrid transport equations for the subgrid Reynolds stresses and fluxes rather than subgrid eddy coefficients. It was applied to a daytime boundary layer over heated ground in a region of horizontal area 8km square and 2km deep, utilizing 40×40×40 grid points. The constraints involved in selecting four important subgrid closure constants are discussed in some detail, along with maintenance of realizability on the subgrid scale. The results indicate that the subgrid transport equations produce subgrid Reynolds stresses and fluxes which realistically simulate the transfer of larger scale variance to subgrid scales, provided truncation errors due to advective terms are not too large. They also show the superiority of this method over the use of (nonstability dependent) nonlinear eddy coefficients in maintaining the sharpness of the inversion base which lies above the mixed layer.

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