Local Refinement Algorithm Research Articles

Local refinement for analysis-suitable++ T-splines

We develop an optimized local refinement algorithm for analysis-suitable++ T-splines (AS++ T-splines) which produces less propagation of control points. We then demonstrate its use as an adaptive framework for isogeometric analysis. AS++ T-splines are a class of T-splines which include analysis-suitable T-spline as a special case, are linearly independent, form a weighted partition of unity and are optimal convergent. These properties, coupled with the local refinement algorithm, make the AS++ T-spline appealing as a better basis both for design and analysis.

Large-eddy simulation of a jet in crossflow using local mesh refinement

A numerical simulation of a turbulent round jet issuing into a laminar crossflow is performed using the method of large-eddy simulation (LES). In order to employ LES efficiently for such multi-scale problems, the code utilises a local mesh refinement (LMR) algorithm and employs a multigrid method to solve the incompressible Navier-Stokes equations. The accuracy of several LMR implementations is assessed for the Taylor-Green vortex problem. Second order accuracy of the LES-LMR code is achieved when ghost cell pressures are computed through an approximate projection method and velocities are computed using quadratic interpolation. Three different LMR strategies for a jet in crossflow are then setup in order to assess the predictive capabilities of the method. The simulations are validated against similar LES and experimental data and excellent agreement with experimental data is found for medium and fine LMR grids, while the coarse LMR grid suffers from over-prediction of the jet centreline speed.

Geometry-Based Global Alignment for GSMS Remote Sensing Images

Alignment of latitude and longitude for all pixels is important for geo-stationary meteorological satellite (GSMS) images. To align landmarks and non-landmarks in the GSMS images, we propose a geometry-based global alignment method. Firstly, the Global Self-consistent, Hierarchical, High-resolution Geography (GSHHG) database and GSMS images are expressed as feature maps by geometric coding. According to the geometric and gradient similarity of feature maps, initial feature matching is obtained. Then, neighborhood spatial consistency based local geometric refinement algorithm is utilized to remove outliers. Since the earth is not a standard sphere, polynomial fitting models are used to describe the global relationship between latitude, longitude and coordinates for all pixels in the GSMS images. Finally, with registered landmarks and polynomial fitting models, the latitude and longitude of each pixel in the GSMS images can be calculated. Experimental results show that the proposed method globally align the GSMS images with high accuracy, recall and significantly low computation complexity.

Numerical Simulation of cracked orthotropic materials using extended isogeometric analysis

In the present study, extended isogeometric analysis (XIGA) is used to analyse cracks in orthotropic media. NURBS and T-splines geometric technologies are used to define the geometry and the solution. Knot insertion and order elevation are used in NURBS models, while a new local refinement algorithm is applied to T-spline models. In XIGA, the basic idea of the extended finite element method (X-FEM) is used along with isogeometric analysis for modelling discontinuities by including enrichment functions. Special orthotropic crack tip enrichments are used to reproduce the singular fields near a crack tip, and fracture properties of the models are defined by the mixed mode stress intensity factors (SIFs), which are obtained by means of the interaction integral (M-integral). Results of the proposed method are compared with other available results.

A PCI planning algorithm for jointly reducing reference signal collisions in LTE uplink and downlink

In this paper, a novel automatic planning method is proposed for allocating Physical Cell Identifiers (PCI) to cells in a Long Term Evolution (LTE) system based on handover and cell load measurements. The method aims at avoiding PCI collision and confusion problems, while reducing Reference Signal (RS) collisions between neighbor cells. For this purpose, the problem is formulated to consider RS collisions both in DownLink (DL) and UpLink (UL). Then, a classical graph partitioning algorithm is adapted to solve the graph coloring problem behind PCI planning. The considered algorithm is the multi-level version of the Fiduccia and Mattheyses local refinement algorithm. Performance assessment is carried out on graphs constructed from data collected in live LTE network. Results show that the proposed algorithms can avoid PCI collision and confusion problems, while reducing DL RS collisions and almost eliminating UL RS collisions compared to a random plan.

Extended isogeometric analysis using analysis-suitable T-splines for plane crack problems

This study is dedicated to modeling cracks in plane problems by applying the recent technique analysis-suitable T-splines in the extended isogeometric analysis. A new local refinement algorithm is integrated for increasing the solution accuracy and reducing the excessive propagation of control points. However the singular fields near a crack tip are reproduced by the crack tip enrichment functions, and the Heaviside function is used to represent crack discontinuity. The results accuracy is tested by evaluation the mixed mode stress intensity factors which are computed by means of the interaction integral approach (M -integral). The obtained results are compared with the analytical methods.DOI: http://dx.doi.org/10.5755/j01.mech.23.1.13475

Finite Element Modeling and Experimental Verification of Nitriding Process in S30C Steel

A mathematical model has been developed to simulate the nitriding process of plain carbon steel, considering the simultaneous diffusion of nitrogen in different iron-nitrogen (Fe-N) phases and the precipitation dynamics of γ’e and iron-nitride. The model can predict the distribution of nitrogen concentration, volume fraction of Fe-N phases and hardness. Furthermore, a finite element method (FEM) post-process technology is presented to avoid the limit of FEM mesh improvement and time-saving. The uniform-sum-division algorithm is adopted as local refinement algorithm (LRA) of meshes. The modified inverse distance weighting (IDW) method is used to interpolate the FEM simulated results. Then, the nitriding model and post-process technology are incorporated within the framework of the developed FEM code COSMAP (COmputer Simulation of MAnufacturing Process) based on metallo-thermo-mechanical theory. In order to validate the nitriding model and FEM post-process technology, the nitriding process of S30C steel is modeled by COSMAP software. The simulated distributions of nitrogen content and hardness are consistent with the measured ones. In addition, the simulated results at different mesh size are compared for two-dimensional model. It is indicated that the interpolated results agree well with the simulated results of fine mesh model and the experimental ones.Keywords: finite element, nitriding, S30C, iron nitride, inverse distance weighting

Crack analysis in bimaterial interfaces using T-spline based XIGA

Analysis-suitable T-splines are used for the modeling and analyzing of cracks in bimaterial interfaces within the framework of an extended isogeometric analysis (XIGA). The crack tip enrichment functions of bimaterial interface cracks are implemented to reproduce singular fields, and the signed distance functions are used to treat the crack face and the interface in the models. A compatible local refinement algorithm is applied to refine location of the crack and the interface, which helps one to avoid produce excessive propagation of control points. The mixed mode stress intensity factors (SIFs) which are evaluated by the interaction integral (M-integral) are used as analysis parameters. Numerical simulations are performed to analyze the problem and to examine the efficiency of the proposed method. The obtained results are compared with other available results.

Refinable spaces and local approximation estimates for hierarchical splines

We study the local approximation properties in hierarchical spline spaces through multiscale quasi-interpolation operators. This construction suggests the analysis of a subspace of the classical hierarchical spline space (Vuong et al. (2011) A hierarchical approach to adaptive local refinement in isogeometric analysis. Comput. Methods Appl. Mech. Eng., 200, 3554–3567) which still satisfies the essential properties of the full space. The B-spline basis of such a subspace can be constructed using parent–children relations only, making it well adapted to local refinement algorithms.

Automatic clustering algorithms for indoor site selection in LTE

Small cell systems are a cost-effective solution to provide adequate coverage inside buildings. Nonetheless, the addition of any indoor site requires evaluating the trade-off between the coverage and capacity gain provided by the new site and its monetary cost. In this paper, a new automatic indoor site selection algorithm based on clustering techniques is presented. The algorithm calculates the number of antennas, radio heads, and baseband units needed for the area under study. Then, a clustering algorithm groups several radio heads of different buildings in a single pooled baseband unit, reducing deployment costs. The proposed clustering algorithm is based on a local refinement algorithm, whose starting point considers a new baseband unit for every new site, and then, possible reallocation to existing units is checked. To assess the method, the proposed indoor site selection algorithm is included in a network planning tool. The algorithm is tested in a real heterogeneous network scenario, taking into account vendor specifications and operator constraints. Results show that the use of the proposed clustering algorithm can reduce the total network cost by up to 58 % in a real scenario.

Globally Structured Three-Dimensional Analysis-Suitable T-Splines: Definition, Linear Independence and $m$-graded local refinement

This paper addresses the linear independence of T-splines that correspond to refinements of three-dimensional tensor-product meshes. We give an abstract definition of analysis-suitability, and prove that it is equivalent to dual-compatibility, wich guarantees linear independence of the T-spline blending functions. In addition, we present a local refinement algorithm that generates analysis-suitable meshes and has linear computational complexity in terms of the number of marked and generated mesh elements.

A local anisotropic adaptive algorithm for the solution of low-Mach transient combustion problems

A novel numerical algorithm for the simulation of transient combustion problems at low Mach and moderately high Reynolds numbers is presented. These problems are often characterized by the existence of a large disparity of length and time scales, resulting in the development of directional flow features, such as slender jets, boundary layers, mixing layers, or flame fronts. This makes local anisotropic adaptive techniques quite advantageous computationally. In this work we propose a local anisotropic refinement algorithm using, for the spatial discretization, unstructured triangular elements in a finite element framework. For the time integration, the problem is formulated in the context of semi-Lagrangian schemes, introducing the semi-Lagrange-Galerkin (SLG) technique as a better alternative to the classical semi-Lagrangian (SL) interpolation. The good performance of the numerical algorithm is illustrated by solving a canonical laminar combustion problem: the flame/vortex interaction. First, a premixed methane-air flame/vortex interaction with simplified transport and chemistry description (Test I) is considered. Results are found to be in excellent agreement with those in the literature, proving the superior performance of the SLG scheme when compared with the classical SL technique, and the advantage of using anisotropic adaptation instead of uniform meshes or isotropic mesh refinement. As a more realistic example, we then conduct simulations of non-premixed hydrogen-air flame/vortex interactions (Test II) using a more complex combustion model which involves state-of-the-art transport and chemical kinetics. In addition to the analysis of the numerical features, this second example allows us to perform a satisfactory comparison with experimental visualizations taken from the literature.

NUAT T-splines of odd bi-degree and local refinement

This paper presents a new kind of spline surfaces, named non-uniform algebraic-trigonometric T-spline surfaces (NUAT T-splines for short) of odd bi-degree. The NUAT T-spline surfaces are defined by applying the T-spline framework to the non-uniform algebraic-trigonometric B-spline surfaces (NUAT B-spline surfaces). Based on the knot insertion algorithm of the NUAT B-splines, a local refinement algorithm for the NUAT T-splines is given. This algorithm guarantees that the resulting control grid is a T-mesh as the original one. Finally, we prove that, for any NUAT T-spline of odd bi-degree, the linear independence of its blending functions can be determined by computing the rank of the NUAT T-spline-to-NUAT B-spline transformation matrix.

Hierarchical T-splines: Analysis-suitability, Bézier extraction, and application as an adaptive basis for isogeometric analysis

In this paper hierarchical analysis-suitable T-splines (HASTS) are developed. The resulting spaces are a superset of both analysis-suitable T-splines and hierarchical B-splines. The additional flexibility provided by the hierarchy of T-spline spaces results in simple, highly localized refinement algorithms which can be utilized in a design or analysis context. A detailed theoretical formulation is presented. Bézier extraction is extended to HASTS simplifying the implementation of HASTS in existing finite element codes. The behavior of a simple HASTS refinement algorithm is compared to the local refinement algorithm for analysis-suitable T-splines demonstrating the superior efficiency and locality of the HASTS algorithm. Finally, HASTS are utilized as a basis for adaptive isogeometric analysis.

Automatic Segmentation of a Fetal Echocardiogram Using Modified Active Appearance Models and Sparse Representation

A novel approach is presented to automatically segment the left ventricle in fetal echocardiograms. The proposed approach strategically integrates sparse representation, global constraint, and local refinement algorithms into an active appearance model (AAM) framework. In the training stage, we construct an enhanced AAM texture model to deal with the speckle and texture ambiguities. In the segmentation stage, the initial pose is located by a sparse representation method. Globally constrained points and local features with high clinical relevance are effectively incorporated into the AAM framework to make the model converge toward a desired position. Our proposed approach has been compared with the traditional ASM, the traditional AAM, and the globally constrained AAM on the synthetic and clinical data. The results show that compared with experts drawn contours, the overall segmentation accuracy of overlapped area in the synthetic and clinical images are 84.12% and 84.39%, respectively, superior to those of the other three methods. The experiments demonstrate that sparse representative methods greatly facilitate the initializations and our approach is capable of detecting the fetal left ventricle effectively, offering a better segmentation results.

An influence-knot set based new local refinement algorithm for T-spline surfaces

Local refinement is widely applied in surface modeling. This paper proposes the concept of influence knot set, and uses it to establish a new algorithm for the local refinement of T-spline surfaces, whose effectiveness is demonstrated by several examples. Compared with existing algorithms, the present one may have two advantages: (a) it does not produce excessive propagation of control points because the number of additional control points is reduced; (b) it simplifies the process of judging whether an additional control point needs to be added or not, and so the final T-mesh topology can be obtained more easily.

Transformation optics based local mesh refinement for solving Maxwellʼs equations

In this paper, a novel local mesh refinement algorithm based on transformation optics (TO) has been developed for solving the Maxwellʼs equations of electrodynamics. The new algorithm applies transformation optics to enlarge a small region so that it can be resolved by larger grid cells. The transformed anisotropic Maxwellʼs equations can be stably solved by an anisotropic FDTD method, while other subgridding or adaptive mesh refinement FDTD methods require time–space field interpolations and often suffer from the late-time instability problem. To avoid small time steps introduced by the transformation optics approach, an additional application of the mapping of the material matrix to a dispersive material model is employed. Numerical examples on scattering problems of dielectric and dispersive objects illustrate the performance and the efficiency of the transformation optics based FDTD method.

Comparison of the meccano method with standard mesh generation techniques

The meccano method is a novel and promising mesh generation technique for simultaneously creating adaptive tetrahedral meshes and volume parameterizations of a complex solid. The method combines several former procedures: a mapping from the meccano boundary to the solid surface, a 3-D local refinement algorithm and a simultaneous mesh untangling and smoothing. In this paper we present the main advantages of our method against other standard mesh generation techniques. We show that our method constructs meshes that can be locally refined using the Kossaczky bisection rule and maintaining a high mesh quality. Finally, we generate volume T-mesh for isogeometric analysis, based on the volume parameterization obtained by the method.

Spectral Element Approximation for the Eigenvalue Problem of Hydrogen Atoms Electronic Structure

In this paper, the spectral element methods are adopted to solve the eigenvalue problem of hydrogen atoms electronic structure. A local refinement algorithm based on spectral element approximation is constructed to solve the problem on different domains. Numerical experiments indicate this algorithm is highly efficient.

Local refinement of analysis-suitable T-splines

We develop a local refinement algorithm for analysis-suitable T-splines which does not produce excessive propagation of control points. We then demonstrate its use as an adaptive framework for isogeometric analysis. Analysis-suitable T-splines are a class of T-splines which are linearly independent and form a partition of unity. These properties, coupled with local refinement, make this class of T-splines appealing as a basis for isogeometric analysis.