Subdivision Approach Research Articles

The impact of grid partitioning on the convergence efficiency of tree-based Bayesian inversion

Abstract Bayesian inversion commonly employs the rj-MCMC sampling algorithm for global search, but it is known for its low efficiency. To enhance sampling efficiency in multidimensional subspaces, advanced model parameterization methods are required. Hawkins proposed a tree-based model parameterization using wavelet basis functions, which leverages the tree structure to subdivide the subsurface model. This paper examines the impact of logarithmic interval subdivision of the subsurface and a combination of shallow uniform subdivision with deep logarithmic interval subdivision on sampling efficiency. The results indicate that the combined approach of shallow uniform subdivision and deep logarithmic interval subdivision leads to faster convergence in the inversion process.

Energy management based on coalitionnal game subdivision applied to energy communities

The energy transition requires rethinking how we produce and consume energy. Energy communities (EC) provide a recent legal framework for sharing energy, aiming to reduce energy bills and the environmental footprint of their participants. One of the challenges is adapting economic models to this technological upheaval. In this context, cooperative games, based on game theory, are valuable tools for modeling energy management through cooperation. However, despite their promising characteristics, cooperative games are limited by their computational complexity. The required computation time to solve cooperative games increases exponentially with the number of participants, restricting their application in energy management. This paper aims to propose a solution to apply cooperative game theory tools to larger communities using a multidisciplinary approach. For this purpose, a game subdivision approach based on the specific properties of energy communities is proposed. This methodology will be shown to be efficient in terms of computation time. While the game theory concepts are depreciated by limiting computing time, the sub-games method can become an interesting tool in energy management. Advantages and drawbacks in terms of energy management and game theory are discussed in this paper.

Enhanced curve representations using piecewise non-linear binary subdivision scheme

This study presents a piecewise non-linear binary subdivision scheme based on a four-point linear binary subdivision scheme. This scheme is first transformed into a piecewise linear subdivision scheme and then into a piecewise non-linear subdivision scheme. The non-linear subdivision approach removes artifacts and distortions from limit curves, producing better continuous curves. The study demonstrates that this technique is a workable technique for producing smooth curves, especially when avoiding bends, distortion, and oscillation.

A comprehensive study of subdivision collocation method for Burgers’ equation

This study explores the use of subdivision schemes to efficiently solve Burgers’ equation. Burgers’ equation is a fundamental fluid dynamics equation that describes the nonlinear behavior of fluid flow. This type of nonlinear equation is difficult to solve analytically, which makes the numerical solution an important tool. The subdivision collocation method (SCM) converts Burgers’ equation into a system of algebraic linear equations using the quasilinearization technique. The results of this study demonstrate that the proposed approach yields accurate numerical solutions for Burgers’ equation. Additionally, the subdivision approach is computationally efficient and requires fewer computational resources than existing numerical methods, making it a promising tool for solving Burgers’ equation in practical applications. Overall, this study provides valuable insights into the approximate solution of Burgers’ equation by implementing subdivision schemes.

Subdivision-based IGA Coupled EIEQ Method for the Cahn–Hilliard Phase-Field Model of Homopolymer Blends on Complex Surfaces

In this paper, we construct an IGA-EIEQ coupling scheme to solve the phase-field model of homopolymer blends on complex subdivision surfaces, in which the total free energy contains a gradient entropy with a concentration-dependent de-Gennes type coefficient and a non-linear logarithmic Flory–Huggins type potential. Based on the EIEQ method, we develop a fully-discrete numerical scheme with the superior properties of linearity, unconditional energy stability, and second-order time accuracy. All we need to do with this fourth-order system is to solve some constant-coefficient elliptic equations by applying a new nonlocal splitting techniqueWe then provide detailed proof of the unconditional energy stability and the practical implementation process. Subdivision approaches show a robust and elegant description of the models with arbitrary topology. Subdivision basis functions serve to define the geometry of the models and represent the numerical solutions. Subdivision-based IGA approach provides us with a good candidate for solving the phase-field model on complex surfaces. We successfully demonstrate the unity of employing subdivision basis functions to describe the geometry and simulate the dynamical behaviors of the phase-field models on surfaces with arbitrary topology. This coupling strategy combining the subdivision-based IGA method and the EIEQ method could be extended to a lot of gradient flow models with complex nonlinearities on complex surfaces.

MV-CDN: Multi-Visual Collaborative Deep Network for Change Detection of Double-Temporal Hyperspectral Images

Since individual neural networks have limited deep expressiveness and effectiveness, many learning frameworks face difficulties in the availability and balance of sample selection. As a result, in change detection, it is difficult to upgrade the hit rate of a high-performance model on both positive and negative pixels. Therefore, supposing that the sacrificed components coincide perfectly with the important evaluation objectives, such as positives, it would lose more than gain. To address this issue, in this paper, we propose a multi-visual collaborative deep network (MV-CDN) served by three collaborative network members that consists of three subdivision approaches, the CDN with one collaborator (CDN-C), CDN with two collaborators (CDN-2C), and CDN with three collaborators (CDN-3C). The purpose of the collaborator is to re-evaluate the feature elements in the network transmission, and thus to translate the group-thinking into a more robust field of vision. We use three sets of public double-temporal hyperspectral images taken by the AVIRIS and HYPERION sensors to show the feasibility of the proposed schema. The comparison results have confirmed that our proposed schema outperforms the existing state-of-the-art algorithms on the three tested datasets, which demonstrates the broad adaptability and progressiveness of the proposal.

Image sub-division and quadruple clipped adaptive histogram equalization (ISQCAHE) for low exposure image enhancement.

In this paper, a novel image sub-division and quadruple clipped adaptive histogram equalization (ISQCAHE) technique is proposed for the enhancement of low exposure images. The proposed method involves, computation of the histogram which includes a new approach of image sub-division, enhancement controlling mechanism, modification of probability density function (PDF) and histogram equalization (HE). The original histogram is segmented into sub-histograms based on exposure threshold and mean, to preserve the brightness and entropy. Then, individual sub-histogram is clipped separately to control the enhancement rate. For enhancing the visual quality, HE is applied to individual sub-histogram using the modified PDF. The experimental results show that, the proposed ISQCAHE method avoids the unpleasant artifacts effectively and provide a natural appearance to the enhanced image. It is simple, adaptive and performs superior than other techniques in terms of visual quality, absolute mean brightness error, entropy, Natural image quality evaluation, brightness preservation, structure similarity index measure and feature similarity index measure.

Formula omitted]-B-splines non-stationary subdivision schemes for grids of arbitrary topology design

This paper proposes a new class of B-spline-like functions that blend trigonometric and hyperbolic functions. A new family of non-stationary subdivision schemes of order k≥3 has been built using the refinement of these B-splines. The schemes yield a Ck−2 limit curve that represents the spline. A tensor-product subdivision approach is used to produce a limit surface from an initial mesh with regular vertices. For extraordinary vertices, new rules are proposed. Except at extraordinary points, where they are C1 continuous, the scheme generates Ck−2 continuous limit surfaces. The proposed scheme is a particular case of many well-known curve and surface subdivision schemes. Some examples are given to demonstrate how well the new schemes perform in generating various shapes of limit curves and surfaces.

Dividing a Sphere Hierarchically into a Large Number of Spherical Pentagons Using Equal Area or Equal Length Optimization

Dividing a 2-dimensional sphere uniformly into a large number of spherical polygons is a challenging mathematical problem, which has been studied across many disciplines due to its important practical applications. Most sphere subdivisions are achieved using spherical triangles, quadrangles, or a combination of hexagons and pentagons. However, spherical pentagons, which may create elegant configurations, remain under-explored. This study presents a new sphere subdivision method to generate a large number of spherical pentagons based on successively subdividing a module of an initial spherical dodecahedron. The new method can conveniently control the shapes of generated spherical pentagons through specified design parameters. Two optimization problems have been investigated: (I) dividing a sphere into spherical pentagons of equal area; (II) minimizing the number of different arc lengths used in the pentagonal subdivision. A variety of examples are presented to demonstrate the effectiveness of the new method. This study shows that treating the mathematical challenge of dividing a sphere uniformly into a large number of spherical polygons as an optimization problem can effectively obtain equal area or equal length sphere subdivisions. Furthermore, considering additional constraints on the optimization problem may achieve sphere subdivisions of specific characteristics. • A new sphere subdivision method is developed to generate a large number of spherical pentagons. • The subdivision approach is performed locally and hierarchically on a module of a spherical dodecahedron. • The mathematical challenge of dividing a sphere uniformly is treated as an optimization problem. • Optimization algorithms are used to achieve sphere subdivisions of specific characteristics.

Achieving high sensing resolution using a Microwave Photonic Signal generated by a laser diode with a control cavity

Laser diodes (LDs) experiencing external optical feedback (OF) are known to demonstrate complex nonlinear dynamics and found various applications. Typical sensing configuration using an LD with OF is called optical feedback interferometry (OFI) that can produce an interferometric-like fringe signal (called OFI fringe) with a fringe resolution as half laser wavelength for displacement measurement. This work uses a dual-cavity OFI and operates the LD at Period-One (P1) state. By optimal configuration for such system, a microwave photonic (MWP) signal can be generated in oscillation form at a very high frequency with its amplitude modulated by an OFI fringe signal. The high frequency component contained in the MWP signal is used for subdivision of an OFI fringe to greatly improve sensing resolution. Both simulation and experiment are conducted to confirm the proposed approach for OFI fringe subdivision.

Investigation of Atom-Bond Connectivity Indices of Line Graphs Using Subdivision Approach

A topological index is a numerical measure that characterises the whole structure of a graph. Based on vertex degrees, the idea of an atom-bond connectivity A B C index was introduced in chemical graph theory. Later, different versions of the ABC index were created, and some of these indices were recently designed. In this paper, we present the edge version of the atom-bond connectivity A B C e index, edge version of the multiplicative atom-bond connectivity A B C I I e index, and atom-bond connectivity temperature ( A B C T ) index for the line graph of subdivision graph of tadpole graph T n , k , ladder graph L n , and wheel graph W n + 1 . Numerical simulation has also been shown for some novel families of atom-bond connectivity index comparing the three types of indices which can be useful for QSAR and QSPR studies.

Gravity field forward modelling using tesseroids accelerated by Taylor series expansion and symmetry relations

SUMMARY In this study, we developed a new method that can significantly accelerate the forward modelling of gravity fields generated by large-scale tesseroids while keeping the computational accuracy as high as possible. The cost of the high efficiency is that the method only works under the assumptions that (1) all tesseroids in the same latitude band have the same horizontal dimension, (2) the computation points are located at the same surface level and aligned with the horizontal centres of tesseroids and (3) each tesseroid has a constant or linearly varying density. The new method first integrates the kernel function of the Newton’s volume integral analytically in the radial direction to eliminate its dependence on the vertical dimension of the tesseroid, and then expands the integrated kernel function into a Taylor series up to a certain order. Because the Taylor series expansion term of the integrated kernel function is an odd or even function of the difference between the longitudes of the tesseroid and computation point, there exist shifting or swapping symmetry relations among the gravity field of tesseroids. Consequently, the shifting or swapping symmetry is extended to the tesseroids with unequal vertical dimensions. Numerical experiments using the spherical shell model are conducted to verify the effectiveness of the new method. The results show that the computational speed of the new method is about 30 times faster than that of the traditional method, which employs the Gauss–Legendre quadrature rule and a 2-D adaptive subdivision approach, while keeping almost the same computational accuracy. When applying the new method to an ice shell with unequal thicknesses, the results reveal that the relative errors of calculating V, Vz and Vzz are smaller than 10−8, 10−6 and 10−4, respectively if the Taylor series expansion is truncated at order 4, while the computational time consumed by the new method is about 7 times less than that of the traditional method. Finally, the influence of the truncation order on the computational accuracy and the strategies for dividing the latitude band into several parts to further improve the accuracy are discussed.

Analytical model of flow velocity in gravel-bed streams under the effect of gravel array with different densities

The standard exponential and logarithmic laws for flow velocity evaluation cannot be applied for gravel-bed streams due to the effect of large-scale roughness. An analytical model based on a two-layer subdivision approach was developed to predict flow velocity over a gravel array with different densities. The velocity distribution in the gravel layer was derived by solving the Darcy-Forchheimer-Brinkman (DFB) differential equation based on the concept of porous medium flows. The velocity in the surface layer was modeled by the mixing length theory with the length scale modified by taking into account the porous effect of the gravel (ball) arrays. To assess the model, flow velocities over gravel beds simulated by Ping-Pong ball arrays with different densities (or porosities) were measured in a laboratory flume. The results show that the predicted velocities by this subdivision model agree well with experimental data, reflecting that the porosity of the gravel array essentially impacts the flows both in the gravel layer and surface layer. In comparison with the existing models not considering the porous effect of the gravel bed, this model can effectively predict vertical velocity distributions and thereby flow resistances in gravel streams. The permeable interface velocity atop the gravel layer, as the boundary condition for the two-layer model, is sensitive to the bed context effect rather than the hydraulic effect, suggesting that the inflection point of the full velocity profile might be vital in determining the accuracy of the model. Moreover, with other data sources over dense gravel-bed, our model is suitable for data pre-dealt with the spatially averaging, where the spatial non-uniformity effect is great.

An hp-version adaptive finite element algorithm for eigensolutions of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation

PurposeThis study presents a novel hp-version adaptive finite element method (FEM) to investigate the high-precision eigensolutions of the free vibration of moderately thick circular cylindrical shells, involving the issues of variable geometrical factors, such as the thickness, circumferential wave number, radius and length.Design/methodology/approachAn hp-version adaptive finite element (FE) algorithm is proposed for determining the eigensolutions of the free vibration of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation. This algorithm first develops the established h-version mesh refinement method for detecting the non-uniform distributed optimised meshes, where the error estimation and element subdivision approaches based on the superconvergent patch recovery displacement method are introduced to obtain high-precision solutions. The errors in the vibration mode solutions in the global space domain are homogenised and approximately the same. Subsequently, on the refined meshes, the algorithm uses higher-order shape functions for the interpolation of trial displacement functions to reduce the errors quickly, until the solution meets a pre-specified error tolerance condition. In this algorithm, the non-uniform mesh generation and higher-order interpolation of shape functions are suitable for addressing the problem of complex frequencies and modes caused by variable structural geometries.FindingsNumerical results are presented for moderately thick circular cylindrical shells with different geometrical factors (circumferential wave number, thickness-to-radius ratio, thickness-to-length ratio) to demonstrate the effectiveness, accuracy and reliability of the proposed method. The hp-version refinement uses fewer optimised meshes than h-version mesh refinement, and only one-step interpolation of the higher-order shape function yields the eigensolutions satisfying the accuracy requirement.Originality/valueThe proposed combination of methodologies provides a complete hp-version adaptive FEM for analysing the free vibration of moderately thick circular cylindrical shells. This algorithm can be extended to general eigenproblems and geometric forms of structures to solve for the frequency and mode quickly and efficiently.

ESTABLISHING INDOOR SUBSPACING REQUIREMENTS OF AN LOD (LEVEL OF DETAIL) MODEL FOR GENERATING NETWORK-BASED TOPOLOGICAL DATA

Abstract. Nowadays, the complexity of structures in urban environments and the interest in location-based applications increase simultaneously. Along with this is the rise in demand for the firm establishment of data models representing these spaces. Establishing network models that portray topological relationships of space have strengthened support for navigation applications. However, researchers have revisited the limitations of existing standards. As analogous standards have specifications for expressing space at various scales, most have focused on outdoor space or the geometric aspect. Hence, this paper proposes subspacing requirements for a Level of Detail (LOD) model for network-based topological data. We examine various constraints that influence space partition and align these with various application cases for indoor navigation. Through these, we investigate appropriate space subdivision approaches for each level according to applicable constraints and recommended applications. This study poses as an initial study towards establishing a general framework for implementing a 3D hierarchical network-based topological data model.

Modeling life‐cycle inventory for multi‐product biorefinery: tracking environmental burdens and evaluation of uncertainty caused by allocation procedure

AbstractLife‐cycle inventory (LCI) is a fundamental phase in the quantification of the environmental performance of products. However, when it comes to the LCI of a multi‐product system, discussions about the choice of the appropriate methodology to allocate environmental impacts still continue. A further system subdivision and the implementation of a mechanism allowing environmental burdens to be tracked would help to improve model accuracy. This study focuses on the LCI modeling of a lignocellulosic biorefinery producing ethanol, lignin oligomers, and electricity, and demonstrates the application of the matrix‐based approach for detailed system subdivision and environmental burden tracking. Forty scenarios utilizing process‐specific allocation methods were tested to account for the global warming potential of outputs. The main findings of the paper are: (i) the importance of specific allocation methods applied to combined heat and power plants that stress the key role of internal energy supply in carrying environmental burdens; (ii) a negligible effect of allocation methods applied to wastewater treatment facilities; (iii) the inconsistency of results obtained via two allocation methods, one based on the total mass and the second based on the dry mass allocation, which raises questions about the validity of water accounting in the allocation procedure of related products; (iv) the role of upstream greenhouse gas (GHG) emissions in lignin‐derived outputs, which emphasizes the importance of a proper allocation methodology to be applied to this residue; and (v) an important role of the biomass pretreatment and lignin solvolysis processes in the accumulation of emissions, which highlights the importance of decreasing the amount of solids and methanol content in the processes discussed here. © 2021 The Authors. Biofuels, Bioproducts and Biorefining published by Society of Industrial Chemistry and John Wiley & Sons Ltd.

Genetic algorithm based adaptive histogram equalization (GAAHE) technique for medical image enhancement

In Magnetic Resonance Imaging (MRI), the poor quality images may not provide the sufficient information for the visual interpretation of the affected locations of human body. So, to improve the image visions and to provide computational support, a novel adaptive image enhancement technique has been proposed in this paper, named as genetic algorithm based adaptive histogram equalization (GAAHE) technique. The proposed framework includes genetic algorithm, histogram sub-division and modified probability density function (PDF). A novel approach of subdivision is applied to the histogram using the exposure threshold and optimal threshold for preserving the brightness and reducing the information loss. To make the proposed technique more adaptive, the threshold parameters are optimized by utilizing the concept of genetic algorithm, guided by the proposed multi-objective fitness function. Then, the PDF of each sub-histogram is modified to enhance the image quality. The experimental results show that, the proposed GAAHE technique performs superior over other existing enhancement techniques.

Interpolatory Catmull-Clark volumetric subdivision over unstructured hexahedral meshes for modeling and simulation applications

Volumetric modeling is an important topic for material modeling and isogeometric simulation. In this paper, two kinds of interpolatory Catmull-Clark volumetric subdivision approaches over unstructured hexahedral meshes are proposed based on the limit point formula of Catmull-Clark subdivision volume. The basic idea of the first method is to construct a new control lattice, whose limit volume by the Catmull–Clark subdivision scheme interpolates vertices of the original hexahedral mesh. The new control lattice is derived by the local push-back operation from one Catmull–Clark subdivision step with modified geometric rules. This interpolating method is simple and efficient, and several shape parameters are involved in adjusting the shape of the limit volume. The second method is based on progressive-iterative approximation using limit point formula. At each iteration step, we progressively modify vertices of an original hexahedral mesh to generate a new control lattice whose limit volume interpolates all vertices in the original hexahedral mesh. The convergence proof of the iterative process is also given. The interpolatory subdivision volume has C2-smoothness at the regular region except around extraordinary vertices and edges. Furthermore, the proposed interpolatory volumetric subdivision methods can be used not only for geometry interpolation, but also for material attribute interpolation in the field of volumetric material modeling. The application of the proposed volumetric subdivision approaches on isogeometric analysis is also given with several examples.

Landslide susceptibility hazard map in southwest Sweden using artificial neural network

Landslides as major geo-hazards in Sweden adversely impact on nearby environments and socio-economics. In this paper, a landslide susceptibility map using a proposed subdivision approach for a large area in southwest Sweden has been produced. The map has been generated by means of an artificial neural network (ANN) model developed using fourteen causative factors extracted from topographic and geomorphologic, geological, land use, hydrology and hydrogeology characteristics. The landslide inventory map includes 242 events identified from different validated resources and interpreted aerial photographs. The weights of the causative factors employed were analyzed and verified using accepted mathematical criteria, sensitivity analysis, previous studies, and actual landslides. The high accuracy achieved using the ANN model demonstrates a consistent criterion for future landslide susceptibility zonation. Comparisons with earlier susceptibility assessments in the area show the model to be a cost-effective and potentially vital tool for urban planners in developing cities and municipalities.

Isogeometric analysis for surface PDEs with extended Loop subdivision

We investigate the isogeometric analysis for surface PDEs based on the extended Loop subdivision approach. The basis functions consisting of quartic box-splines corresponding to each subdivided control mesh are utilized to represent the geometry exactly, and construct the solution space for dependent variables as well, which is consistent with the concept of isogeometric analysis. The subdivision process is equivalent to the h-refinement of NURBS-based isogeometric analysis. The performance of the proposed method is evaluated by solving various surface PDEs, such as surface Laplace-Beltrami harmonic/biharmonic/triharmonic equations, which are defined on the limit surfaces of extended Loop subdivision for different initial control meshes. Numerical experiments show that the proposed method has desirable performance in terms of the accuracy, convergence and computational cost for solving the above surface PDEs defined on both open and closed surfaces. The proposed approach is proved to be second-order accuracy in the sense of L2-norm with theoretical and/or numerical results, which is also outperformed over the standard linear finite element by several numerical comparisons.