Regular Rectangular Grid Research Articles

Addressing incomplete tile phenomena in image tiling: Introducing the grid six-intersection model

Abstract With the continuous development of Earth Observation technology, resolution of imagery and gridded data has significantly increased, leading to a rapid increase in data volume. To efficiently acquire and analyze these vast amounts of imagery and gridded data, image tiling technology has been developed to effectively access data of interested areas. Tiling technology divides large-scale image data into smaller tiles, providing fast, accurate, and efficient access support for imagery and gridded data. The spatial grid model, as the foundational framework of the new generation of geographic spatial information, plays a critical role in the retrieval, integration, services, and applications of imagery and gridded data resources. When tiling image data based on the spatial grid model, it always generates both complete and incomplete tiles. Particularly, when conducting image tile retrieval using the same rule-based grid in the retrieval area, incomplete tile phenomena along the boundary regions of the retrieved images often occur, resulting in gaps within the retrieval area. To tackle this issue, in this study, we present a new topological model called the Grid Six-Intersection Model (G-6IM), specifically designed for regular rectangular grids, to accurately represent boundary issues in image tiling. Through a practical case study, we demonstrate the effectiveness and practical application potential of the proposed G-6IM model, providing new insights and guidance for the improvement and optimization of imagery and gridded data tiling technology.

A METHOD TO DEFINE A CELL SIZE OF REGULAR NETWORK FOR INFRASTRUCTURAL TERRITORY ZONING WITH PURPOSE OF FOREST FIRE PROTECTION

Infrastructural projects at regional scale are ones of the important components of modern digital economy. In relation to the forestry, the main objects that determine infrastructural load of the territory in the forestry are the networks of fire stations and forest roads with settlements and public roads. A method to define a cell size of a regular uniform rectangular grid based on the pixel size of MODIS-based vegetation raster is described. It is based on the statistics of number of settlements, fire stations and road sections, as well as road sections lengths. Exploratory regression was used to choose a cell size with a number of forest fires as a dependent variable and number of settlements, road segments and fires stations as independent variables. It was found that the most optimal size of regular grid cell for Krasnoyark Region (Kray) is 24 km2. Paper’s findings could be used in climate and economic projects to estimate infrastructural load.

МОДЕЛИРОВАНИЕ ЦВЕТЕНИЯ ВОДЫ В КУЙБЫШЕВСКОМ ВОДОХРАНИЛИЩЕ В ГОДЫ С РАЗЛИЧНЫМ РЕЖИМОМ РЕГУЛИРОВАНИЯ СТОКА

The article studies the influence that the dynamics of currents have on algal blooms in the Kuibyshev Reservoir in the conditions of an unsteady flow regime. One of the ways to improve the ecological condition of the reservoir is to reduce cyanobacteria blooms by increasing the flow rate during the maximum warming of the water. The hydrodynamics of the aquatic environment is considered as a regulatory factor that reduces the negative effects of eutrophication and improves the quality of water in the reservoir. The author performed full-scale hydroecological observations in the summer periods of 2016 and 2017 and made model calculations of the dynamics of currents and spatial distribution of phytoplankton in the water area of the Kuibyshev Reservoir. As a result, the dependence of the chlorophyll a index (Chl a) on the flow regulation regime was established. The proposed model is based on the equations of long-wave hydrodynamics, known as the shallow-water equations, the equations of convective transport and development of the components of the ecosystem, which is implemented in the author’s software environment VOLNA. The model is constructed for the near-dam water area on a regular rectangular grid with a step of 200 m. The model was verified on the basis of data from field observations, and the quality of the calculations performed was evaluated. It has been found that the phytoplankton biomass index (Chl a) is related to the water flow velocity non-linearly and varies according to a power law. The conducted studies give reason to believe that the intensity of cyanobacteria blooms largely depends not on the water content of the year, but on the intra-annual redistribution of runoff.

Well-balanced numerical method for atmospheric flow equations with gravity

We are interested in simulating gravitationally stratified atmospheric flows governed by the compressible Euler equations in irregular domains. In such simulations, one of the challenges arises when the computations are conducted on a Cartesian grid. The use of regular rectangular grids that intersect with the irregular boundaries leads to the generation of arbitrarily small and highly distorted computational cells adjacent to the boundaries of the domain. The appearance of such cells may affect both the stability and efficiency of the numerical method and therefore require special attention.In order to overcome this difficulty, we introduce a structured quadrilateral mesh, which is designed for the irregular domain at hand, and solve the studied atmospheric flow equations using a second-order central-upwind scheme. In addition, the resulting numerical method is developed to provide a well-balanced discretization of the underlying system. The latter is achieved by rewriting the governing equations in terms of equilibrium variables representing perturbations of the known background equilibrium state. The proposed method is tested in a number of numerical experiments, including the buoyant bubble rising and interacting with an (zeppelin) obstacle and the Lee wave generation due to topography. The obtained numerical results demonstrate high resolution and robustness of the proposed computational approach.

Application of the automatic code generation and symbolic computation techniques to numerical solution of PDE problems

A software package for the numerical solution of systems of linear and nonlinear partial differential equations by grid methods is presented, which combines symbolic computations and automatic code generation techniques. Discretization of differential equations is carried out by the methods of finite volumes and finite differences on two-dimensional and three-dimensional regular rectangular grids. The solution of the systems of nonlinear algebraic equations obtained as a result of discretization is performed by Newton’s method with employment of third-party SLAE solvers. The generated code can exploit shared and distributed memory parallelisms and take advantage of heterogeneous computations. The results of the numerical solutions of two sample CFD problems of the fluid flow generation in a cylindrical cavity filled with electrically conductive liquid driven the by traveling and rotating magnetic fields are presented.

Evaluation of Nearshore QuikSCAT 4.1 and ERA-5 Wind Stress and Wind Stress Curl Fields over Eastern Boundary Currents

Fields of coastal wind stress and wind stress curl in the 10–100 km next to the land control the processes of upwelling and downwelling of nutrients and water properties that are vital to highly productive coastal marine ecosystems. Here we ask the question: Do the present surface wind stress products from a satellite-borne scatterometer (QuikSCAT) and an atmospheric reanalysis model (ERA-5) systematically overestimate the magnitude of wind speed and stress in the 10–50 km next to the coast? We compare QuikSCAT wind speed retrievals to the relatively unused wind speed retrievals from satellite altimeters, which are able to approach closer to the coast than scatterometers without land reflections, due to their smaller radar footprints. Altimeter data on tracks approaching and crossing the coast indicate that the increases in coastal QuikSCAT wind speed values and ERA-5 coastal wind stress values are unrealistic. For analyses of wind speed and stress requiring high accuracy, especially those involving wind stress curl, we suggest considering individual Level 2B scatterometer wind retrievals as suspect at distances of 10 km and less from the coast, along with use of the Poor Coastal Processing flag. We found that similar increases in wind stress values next to the coast in gridded ERA-5 fields are not due to errors in the model physics or wind speeds. They are created during the interpolation of wind stress from the original model grid to a regular rectangular grid. We recommend that researchers who are analyzing wind stress and wind stress curl should calculate wind stress themselves from the gridded ERA-5 vector wind speed fields, rather than using the interpolated model wind stress or curl fields.

Elastic Reverse-Time Migration with Complex Topography

Migration is an important step in seismic data processing for oil and gas exploration. The accuracy of migration directly affects the accuracy of subsequent oil and gas reservoir characterization. Reverse-time migration is one of the most accurate migration methods at present. Multi-wave and multicomponent seismic data contain more P- and S-wave information. Making full use of multi-wave and multicomponent seismic data can offer more information about underground structure and lithology, as well as improve the accuracy of seismic exploration. Elastic reverse-time migration (ERTM) has no dip restriction and can be applied to image multi-wave and multicomponent seismic data in complex structural areas and some special lithology structures. However, the surface topography of complex regions has an influence on wavefield and seriously degrades the quality of ERTM’s migration results. We developed a new ERTM method to migrate multi-wave and multicomponent seismic data in the region with complex surface topography. We first fill the layers between the highest and lowest undulating surface with near-surface elastic parameters in a complex topography model to obtain a new model with a horizontal surface. This allows the finite difference (FD) method based on the regular rectangular grid to be used to numerically solve elastic wave equations in the model with complex topography. The decoupled wave equations are used to generate source P- and S-waves and receiver P- and S-waves to reduce crosstalk artefacts in ERTM. A topography-related filter is further used to remove the influence of surface topography on migration results. The scalar imaging condition is also applied to generate PP and PS migration images. Some numerical examples with different complex topographies demonstrate that our proposed ERTM method can remove the influence of complex topography on ERTM’s images and effectively generate high-quality ERTM images.

Development of a method of extended cells for the formulation of boundary conditions in numerical integration of gas dynamics equations in the domains of a curvilinear shape

A method of extended cells for the formulation of boundary conditions in the numerical integration of the Euler equations in domains with curvilinear boundaries for the cases of one-dimensional and two-dimensional compressible gas flows has been proposed in this study. The proposed method is based on the use of the explicit Godunov type finite volume method on a regular rectangular Cartesian grid. The essence of the extended cell method is that when integrating the basic equations of gas dynamics in a fractional cell, numerical fluxes are calculated through the sides of the new extended cell. This new cell is constructed tangentially to the curved boundary and has a size no less than the cell size in the regular domain. Parameters inside the new cell are calculated as mean integral values over the area of the neighboring regular cells included in it. In this case, when choosing a time step in accordance with the Courant condition, the stability of the method in the main computational domain is preserved both when integrating fractional cells and when integrating regular cells. Thanks to this approach, the proposed method has low requirements for computing resources, the ability to generalize for three-dimensional space and increase the order of accuracy without major modifications of the algorithm. To test the proposed method, solutions were obtained for the generally accepted test problems of gas dynamics: normal and double Mach reflection of a shock wave from a plane wall. The choice of the time step was made in accordance with the Courant condition in regular finite volumes. The results obtained have made it possible to assess the convergence of the proposed method and their comparison with the results of calculations using other methods have shown a good quantitative and qualitative agreement

SIMULATION RESULTS OF SPECKLE SUPPRESSION IN RADAR WITH SYNTHETIC APERTURE

The disadvantage of (RLI) radar images obtained with a single-channel radar station is the presence of speckle that leads to intensity flashes increasing the number of false alarms when detecting point targets. Therefore, the detection and target distinguishing by their reflective capability (using the energy characteristics of the signal) is not effective enough. In polarimetric radar stations the formation of each image element is carried out by the output signals of four receiving channels. Joint processing of these signals allows minimizing speckle without reducing the resolution capability. The paper presents the results of the computer simulation of the suppression methods of the image speckle obtained in the polarized radar stations with the synthesized antenna aperture. The first one uses the norm of the backscattering matrix as a parameter of the intensity of the reflected signal resolution from the i-th element. The incoherent addition of the intensities obtained by sequential overview of the space with several rays is carried out in the second one. Both of these methods can be applied together. The block diagram of such processing for one strip of range is given. The computer simulation of the three-rayed suppression method of the image speckle obtained in the radar stations with the synthesized antenna aperture is carried out. As a model of the reflecting surface a random diffraction grating formed by a set of independent reflectors located at the nodes of a regular rectangular grid with a step of 1 m is chosen. In this connection the image of the grating is formed as an incoherent sum of three images obtained at different angles. The results show that the speckle effect reduces even at angular changes of the order of degree units.

Цифровая топографическая аэрофотокамера – средство измерений

The difference between the topographic digital aerial cameras and the analogue ones are analyzed. The first one allows considering a digital aerial camera as a means of measurement. A regular rectangular grid of pixels of digital aerial cameras image sensor is a two-dimensional scale with divisions equal to the physical size of the pixel. It allows determining the position of interest points of the image in the coordinate system of a matrix of pixels, the axis of which is directed along rows and columns of the matrix. Wherein the measured value for aerial cameras, should be considered as the coordinates of the vector pointing from the perspective center to the point of interest in the coordinate system of aerial cameras, the beginning of which is located at the front nodal point of the lens, and the Sz axis is directed along the principal ray. Exactly they are directly used in the solutions of photogrammetric tasks for determination of coordinates of the locality object point. The accuracy of the result of determining the coordinates depends on the accuracy of the coordinates of a direction vector and the accuracy of the exterior orientation parameters of aerial cameras (the image). Metrological characteristics of digital topographic aerial cameras should be considered measurement range (the frame size in pixels and pixel size) and the error of a measuring instrument (the error of the coordinates of a direction vector) as the accuracy characteristics and the parameters of calibration of aerial cameras, allowing to determine the measured values according to indications of measurements with estimates of the errors of the calibration parameters.

(Re-) Meshing using interpolative mapping and control point optimization

Abstract This work proposes a simple and fast approach for re-meshing the surfaces of smooth-featured geometries prior to CFD analysis. The aim is to improve mesh quality and thus the convergence and accuracy of the CFD analysis. The method is based on constructing an interpolant based on the geometry shape and then mapping a regular rectangular grid to the shape of the original geometry using that interpolant. Depending on the selected interpolation algorithm the process takes from less than a second to several minutes. The main interpolant discussed in this article is a Radial Basis Function with cubic spline basis, however other algorithms are also compared. The mesh can be optimized further using active (flexible) control points and optimization algorithms. A range of objective functions are discussed and demonstrated. The difference between re-interpolated and original meshes produces a metric function which is indicative of the mesh quality. It is shown that the method works for flat 2D surfaces, 3D surfaces and volumes. Highlights RBF Map is created between key points on an arbitrary shape and an ideal equivalent. The rest of the points are recreated using reverse transformation to the original. Control points are automatically selected based on k-mean clustering. Optimization of the control points position based on desired mesh quality metrics. The method is shown to work both on 2D and 3D shapes as well as 3D surfaces.

Generalization of Magnetostatic Method of Moments for Thin Layers with Regular Rectangular Grids

Generalization of Magnetostatic Method of Moments for Thin Layers with Regular Rectangular Grids

An Efficient Low Storage and Memory Treatment of Gridded Interaction Fields for Simulations of Macromolecular Association.

Computer simulations of molecular systems often make use of regular rectangular grids with equidistant spacing to store information on their molecular interaction fields, e.g., electrostatic potential. These grids provide an easy way to store the data as they do not require any particular specification of the structure of the data. However, such grids may easily become large, and the storage and memory demands may become so high that calculations become infeasible. To overcome this problem, we show here how the data structure DT-Grid can be adapted and applied to efficiently represent macromolecular interaction grids by exploiting the nonuniformity of information on the grid; at the same time, this data structure ensures fast random data access. We demonstrate use of the DT-Grid data structure for potential of mean force and Brownian dynamics simulations of protein-surface binding and macromolecular association with the SDA software. We further demonstrate that the DT-Grid structure enables systems of large size, such as a viral capsid, and high resolution grids to be handled that are beyond current computational feasibility.

ColDICE: A parallel Vlasov–Poisson solver using moving adaptive simplicial tessellation

Resolving numerically Vlasov–Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincaré invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli [65–67] generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a “warm” dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.

Adaptive Finite Difference Methods for Nonlinear Elliptic and Parabolic Partial Differential Equations with Free Boundaries

Monotone finite difference methods provide stable convergent discretizations of a class of degenerate elliptic and parabolic partial differential equations (PDEs). These methods are best suited to regular rectangular grids, which leads to low accuracy near curved boundaries or singularities of solutions. In this article we combine monotone finite difference methods with an adaptive grid refinement technique to produce a PDE discretization and solver which is applied to a broad class of equations, in curved or unbounded domains which include free boundaries. The grid refinement is flexible and adaptive. The discretization is combined with a fast solution method, which incorporates asynchronous time stepping adapted to the spatial scale. The framework is validated on linear problems in curved and unbounded domains. Key applications include the obstacle problem and the one-phase Stefan free boundary problem.

NUMERICAL STUDIES ON FLAT SLAB STRCTURES SUPPORTED ON NON-RECTANGULAR GRIDS

Construction of flat slab structures has increased enormously in recent times. Well established procedures are available in the literature and codes for the analysis, design and detailing of flat slab structures supported on regular rectangular column grids. However, these structures pose a greater challenge to the designers, when they are supported on non-rectangular column grids. Use of non- rectangular column grids is often necessitated in the modern context, due to varied parking requirements, floor wise variation of building plans, site constraints etc. Besides, the seismic performance of flat slab structures has been the subject of interest for the researchers over the years. Though their works established the behavior of flat slabs supported on regular rectangular grids to a greater extent, the seismic behavior of flat slab structure supported on non-rectangular grids, still needs detailed investigations. Lack of adequate information in literature and non availability of standard specifications in codes on these types & structures indicate the immediate necessity for such investigations. This paper presents the inferences of extensive numerical investigations on a chosen flat slab structure for possible shifting, breaking and new formations of column strips with the variation in the position of an interior column, which makes the regular rectangular grids into non- rectangular. The sensitivity of the structure is explored by varying the position of an interior column. The variation of moments and shears in column strips in the flat slab under static and dynamic loads are observed and are also plotted. Further, a 10 storeyed flat slab structure is analysed and the results are studied to know the effect of staggering a column of a rectangular grid, on the moments in chosen (corner, side and interior) columns, under both static and dynamic loads. Results reveal that there is every need to consider the effect of non rectangularity column grids on the formation of column strips, moments and shears in column strips, the detailing of reinforcement in column strips and also the moments in the columns of such flat slab structures.

Application of the implicit particle filter to a model of nearshore circulation

The implicit particle filter is applied to a stochastically forced shallow water model of nearshore flow, and found to produce reliable state estimates with tens of particles. The state vector of this model consists of a height anomaly and two horizontal velocity components at each point on a 128 × 98 regular rectangular grid, making for a state dimension O(104). The particle filter was applied to the model with two parameter choices representing two distinct dynamical regimes, and performed well in both. Demands on computing resources were manageable. Simulations with as many as a hundred particles ran overnight on a modestly configured workstation. In this case of observations defined by a linear function of the state vector, taken every time step of the numerical model, the implicit particle filter is equivalent to the optimal importance filter, i.e., at each step any given particle is drawn from the density of the system conditioned jointly upon observations and the state of that particle at the previous time. Even in this ideal case, the sample occasionally collapses to a single particle, and resampling is necessary. In those cases, the sample rapidly reinflates, and the analysis never loses track. In both dynamical regimes, the ensembles of particles deviated significantly from normality.

Comparison of measuring strategies for the 3-D electrical resistivity imaging of tumuli

Artificial erected hills like tumuli, mounds, barrows and kurgans comprise monuments of the past human activity and offer opportunities to reconstruct habitation models regarding the life and customs during their building period. These structures also host features of archeological significance like architectural relics, graves or chamber tombs. Tumulus exploration is a challenging geophysical problem due to the complex distribution of the subsurface physical properties, the size and burial depth of potential relics and the uneven topographical terrain. Geoelectrical methods by means of three-dimensional (3-D) inversion are increasingly popular for tumulus investigation. Typically data are obtained by establishing a regular rectangular grid and assembling the data collected by parallel two-dimensional (2-D) tomographies. In this work the application of radial 3-D mode is studied, which is considered as the assembly of data collected by radially positioned Electrical Resistivity Tomography (ERT) lines. The relative advantages and disadvantages of this measuring mode over the regular grid measurements were investigated and optimum ways to perform 3-D ERT surveys for tumuli investigations were proposed. Comparative test was performed by means of synthetic examples as well as by tests with field data. Overall all tested models verified the superiority of the radial mode in delineating bodies positioned at the central part of the tumulus while regular measuring mode proved superior in recovering bodies positioned away from the center of the tumulus. The combined use of radial and regular modes seems to produce superior results in the expense of time required for data acquisition and processing.

On limit state displacements of regular rectangular twistless grids

While elastic analysis remains the cornerstone of standard design techniques for space structures under service conditions, performance based procedures could further enhance their effectiveness up to prescribed target limits. Performance-based plastic design appears to be the quintessential method of design for space structures composed of flexural members, such as steel and reinforced concrete grillages, interconnected vierendeel girders, moment frames, etc. The current contribution presents a general technique for the estimation of maximum plastic displacements of twistless, orthotropic grillages of regular formation with any combination of boundary support conditions, along the sides of a parallelogram, and subjected to monotonically increasing distribution of continuous normal nodal forces.

Numerical method for the bone regeneration model, defined within the evolving 2D axisymmetric physical domain

A numerical algorithm, used to obtain a solution for a peri-implant osseointegration model is constructed. The model is formulated in terms of a system of three nonlinear coupled time-dependent advection–diffusion–reaction equations, which are defined within the irregular two dimensional physical domain, which evolves in time. The embedded boundary method and the level set function, which is approximated on the fixed regular rectangular grid, are used to track the changes of the irregular geometry of the physical domain. The method of lines is applied to separate the discretizations in time and in space. The advection, diffusion and reaction terms are discretized separately by means of the cell-centered finite volume method. The exact solution of the Riemann problem for the nonstrictly hyperbolic system without genuine nonlinearity, is obtained. An approach for the determination of the gradients of the unknown variables on the edges of the irregular control volumes is proposed. The explicit second order trapezoidal rule is used for the time integration, since it allows to maintain positivity of the solution, which is critical for the considered problem. Some results of the numerical simulations are presented. Contact and distance osteogenesis are predicted for micro-rough and smooth implants.