Hierarchical Mesh Research Articles

Dimensions and bases of hierarchical tensor-product splines

We prove that the dimension of trivariate tensor-product spline space of tri-degree (m,m,m) with maximal order of smoothness over a three-dimensional domain coincides with the number of tensor-product B-spline basis functions acting effectively on the domain considered. A domain is required to belong to a certain class. This enables us to show that, for a certain assumption about the configuration of a hierarchical mesh, hierarchical B-splines span the spline space.This paper presents an extension to three-dimensional hierarchical meshes of results proposed recently by Giannelli and Jüttler for two-dimensional hierarchical meshes.

Incremental Generation of Hierarchical Meshes for the Thermomechanical Simulation of NC-milling Processes

For the production of large structural components, the NC-milling process is often run with minimum quantity lubrication only. Additionally, most of the raw material will be removed by using process parameters that lead to a significant generation of heat. To guarantee error-free products, the thermally induced deformation has to be taken into account. Thus, a simulation of the milling process, which calculates the thermal expansion, can be used to predict deviations and to optimize milling strategies.In this paper a new approach for the simulation of the NC-milling process is presented. It combines a pure geometrical simulation with new techniques of adaptive finite element methods. The key for a fast simulation of linear thermo elasticity is a hierar chical mesh, based on hexahedra with additional geometric primitives on the lowest level of refinement. Using hexahedra permits the application of tensor-product approaches to achieve faster computations, whereas the use of constrained-approximation allows for multi-level hanging nodes in the mesh. In turn, hp-adaptive finite element methods can be applied.The investigation focuses on the basic coupling of the simulation components and the incremental generation of suitable meshes for the finite element analysis and thereby completely avoids any remeshing action. It is based on a hierarchical octree that is extended by an adaptive sub-mesh for each cell that is partially removed during the simulated cutting process. Thus, the mesh is incrementally refined and adapted during the simulation. Based on previous experimental and analytic investigations, a complete simulation cycle will be presented. For the prediction of the heat input, an empirical model has been developed in order to ensure a fast simulation. After the remote finite element analysis, local displacements are applied to the position of the milling tool instantly. In this way very accurate results can be achieved that serve as a basis for further process optimization operations.

On the Fully Implicit Solution of a Phase-Field Model for Binary Alloy Solidification in Three Dimensions

AbstractA fully implicit numerical method, based upon a combination of adaptively refined hierarchical meshes and geometric multigrid, is presented for the simulation of binary alloy solidification in three space dimensions. The computational techniques are presented for a particular mathematical model, based upon the phase-field approach, however their applicability is of greater generality than for the specific phase-field model used here. In particular, an implicit second order time discretization is combined with the use of second order spatial differences to yield a large nonlinear system of algebraic equations as each time step. It is demonstrated that these equations may be solved reliably and efficiently through the use of a nonlinear multigrid scheme for locally refined grids. In effect this paper presents an extension of earlier research in two space dimensions (J. Comput. Phys., 225 (2007), pp. 1271-1287) to fully three-dimensional problems. This extension is validated against earlier two-dimensional results and against some of the limited results available in three dimensions, obtained using an explicit scheme. The efficiency of the implicit approach and the multigrid solver are then demonstrated and some sample computational results for the simulation of the growth of dendrite structures are presented.

The ageing ovary and uterus: new biological insights

BACKGROUND Advanced maternal age is associated with reduced fertility and adverse pregnancy outcomes. This review details recent developments in our understanding of the biology and mechanisms underlying reproductive ageing in women and the implications for fertility and pregnancy. METHODS Sociological online libraries (IBSS, SocINDEX), PubMed and Google Scholar were searched for relevant demographic, epidemiological, clinical and biological studies, using key words and hierarchical MeSH terms. From this, we identified and focused on key topics where it was judged that there had been clinically relevant advances in the understanding of ovarian and uterine ageing with implications for improved diagnostics and novel interventions. RESULTS Mapping of the ovarian reserve, follicular dynamics and associated biomarkers, across the reproductive lifespan has recently been performed. This now allows an assessment of the effects of environmental, lifestyle and prenatal exposures on follicular dynamics and the identification of their impact during periods of germ cell vulnerability and may also facilitate early identification of individuals with shorter reproductive lifespans. If women choose to time their family based on their ovarian reserve this would redefine the meaning of family planning. Despite recent reports of the potential existence of stem cells which may be used to restore the primordial follicle and thereby the oocyte pool, therapeutic interventions in female reproductive ageing at present remain limited. Maternal ageing has detrimental effects on decidual and placental development, which may be related to repeated exposure to sex steroids and underlie the association of ageing with adverse perinatal outcomes. CONCLUSIONS Ageing has incontrovertible detrimental effects on the ovary and the uterus. Our enhanced understanding of ovarian ageing will facilitate early identification of individuals at greatest risk, and novel therapeutic interventions. Changes in both ovary and uterus are in addition to age-related co-morbidities, which together have synergistic effects on reducing the probability of a successful pregnancy outcome.

Adaptive finite elements using hierarchical mesh and its application to crack propagation analysis

In the present paper, a high-speed adaptive meshing using a hierarchical mesh is studied. We use the level-of-detail approximations of the mesh data structure used often in the computer graphics field. To achieve the correct level of detail, we employ the hierarchical regional partitions. Meshes using this data structure can be realized in a very quick manner. Finally, we apply the level of detail approximation to the adaptive analyses of crack propagation, demonstrating the efficiency of the present method.

A load-balanced routing method for large-scale mesh multiprocessors

Research on message routing in large-scale mesh multiprocessors usually focuses on routing in light traffic. Studies employ simple routing methods that are not load-balanced but do not need route initiation before message transmission. In non-light and/or non-uniform input traffic situations, maximum bandwidth utilization and average latency of such routing methods can be poor due to congestion caused by unbalanced load in global mesh regions. Existing load-balanced routing methods applied in mobile ad hoc mesh networks require route initiation before message transmission, which is not acceptable in mesh multiprocessors. In this research, we designed a load-balanced hierarchical mesh-routing method without route initiation. We organize a large-scale mesh into a virtually structured hierarchical mesh structure. Global mesh routing can thus be transformed into a number of load-balanced routing subtasks at levels of hierarchical submesh regions. In such a structure, we designed periodical hierarchical traffic state polling and distribution with very low overhead. We developed two congestion-avoidance routing methods for load-balanced routing at levels of submesh regions with polled traffic states. Experimental results show that maximum bandwidth utilization and average latency in non-light and/or non-uniform input traffic situations can be improved significantly in comparison with ordinary mesh multiprocessor routing methods.

Performance analysis and comparison of 2 × 4 network on chip topology

The performance analysis and comparison of 2×4 network on chip (NoC) topology are mainly presented in this paper. Firstly, three common 2×4 topologies, 2D Mesh topology, 2D Torus topology and hierarchical Mesh topology are designed. Secondly, the performances of three topologies are analyzed and compared in detail by using NoC performance evaluation standard. Finally, the occupying resources of three topologies are also compared. The result shows that 2D Torus topology can achieve higher throughput and lower average network latency in occupying fewer resources.

On the linear finite element analysis of fully coupled point contact elastohydrodynamic lubrication problems

The fully coupled approach for the solution of elastohydrodynamic lubrication point contact problems requires the numerical solution of the elasticity problem on a large 3D domain. A sufficiently fine computational mesh is required to obtain the elastic deformation solution to the necessary accuracy, and hence, a sufficiently accurate elastohydrodynamic lubrication point contact solution. This article discusses the accuracy of an elastohydrodynamic lubrication point contact solution over different finite element meshes. We present a family of efficient 3D meshes which can be used to calculate accurate elastohydrodynamic lubrication point contact solutions at a minimal computational cost. This article also illustrates the fact that the unstructured hierarchical meshes can lead to a poor quality elastohydrodynamic lubrication solution unless an appropriate post-processing, smoothing technique is applied.

Volumetric Method of Moments and Conceptual Multilevel Building Blocks for Nanotopologies

On the basis of the relationship between charge dimensionality and singular field behavior, it is proven that in a volumetric description of a volume current carrying topology, half rooftops of different binary hierarchical level are allowed without introducing numerical difficulties. This opens the possibility to use a very efficient multilevel hierarchical meshing scheme in a volumetric method-of-moments (V-MoM) algorithm. The new meshing scheme is validated by numerical calculations and experiments. It paves the way toward a much more efficient use of MoM in the description of arbitrarily shaped nanostructures at infrared and optical frequencies.

Fully implicit adaptive method using discontinuous Galerkin finite elements for high speed flows

In this paper, we present automatic and effective mesh refinement techniques for discontinuous Galerkin finite elements methods (DGFEMs) applied to high speed inviscid flows, and based on the CONCHA finite element Library. CONCHA is a C++ software designed for the simulation of complex flow problems. The structure of its finite element library is described in this publication. It also provides different implicit methods for numerical resolution, a posteriori error estimation, and local mesh refinement. The refinement techniques presented are built on hierarchical non-conforming meshes. Then, two test cases of supersonic flows are studied in order to emphasise CONCHA’s efficiency, robustness and flexibility. Perspectives as well as limitations of such refinement techniques are finally discussed.

A virtual hierarchical optical mesh based data center network

Reducing the routing table size to obtain better scalability of network is more and more important for data center networks in cloud computing era. In this paper, virtual hierarchical mesh networks with different agent selection methods of different subnets are proposed to solve the network scaling embarrassment problem. Theoretical analysis and simulation results show the multi-agent selection methods outperform the single one in terms of end-to-end latency and load balance.

A hierarchical mesh film with superhydrophobic and superoleophilic properties for oil and water separation

AbstractBACKGROUND: Solid surfaces possessing both superhydrophobic and superoleophilic properties have attracted great interest for fundamental research and potential application. However, fabrication of the reported surfaces is usually time‐consuming and the wetability of the surfaces could not be achieved to the desired level in rugged environments.RESULTS: A hierarchical stainless steel mesh film comprising structures with three scales of roughness was synthesized by a simple chemical bath deposition method. After being modified with a low surface energy material e.g. Teflon, these films exhibit superhydrophobic and superoleophilic properties. In this study it was demonstrated that the unique properties of the as‐prepared films match well with the requirements for the effective separation of oil and water mixtures.CONCLUSION: It was confirmed that the unique surface wetability of the surface is due to the cooperative effect of the hierarchical structures of the stainless steel mesh films and the natural low surface tension of Teflon. Furthermore, fabrication is simple and economic, and the surface exhibited robust durability even in a rugged environment. Copyright © 2011 Society of Chemical Industry

Channel Assignment Strategy for Multi-radio Virtual Hierarchical Wireless Mesh Networks

A virtual hierarchical wireless mesh network architecture is studied in this paper, which gains fine user diversity and routing stability. As each node inside a cell is equipped with multiple radios and multiple channels are available, an efficient channel assignment algorithm based on this multi-radio multi-channel virtual hierarchical wireless mesh network is proposed, which combines the channel pre-allocation algorithm with the time-slot multi-graph decomposition algorithm, so as to increase channel resource utilization and ensure the fairness of channel allocation. In the channel preallocation algorithm, a generalized set T-coloring model based on graph theory is utilized. Then, the time-slot multi-graph decomposition algorithm is conducted according to the channel pre-assignment, which exploits spatial reuse features of a multi-channel multi-radio system to optimize the network performance. The algorithm analysis and simulation results show that the proposed channel assignment strategy can improve the network performance effectively with lower complexity and achieve higher channel utilization.

Simulation of Ultrasonic Flaw Responses by Using a Hierarchical Triangular Meshing Method

Simulation of Ultrasonic Flaw Responses by Using a Hierarchical Triangular Meshing Method

A Hybrid Mesh Routing protocol for ubiquitous internet connectivity in hierarchical Wireless Mesh Networks

We propose a cross-layer-aware Hybrid Mesh Routing (HMR) protocol for the ubiquitous Internet connectivity in hierarchical Wireless Mesh Networks (WMNs) that can provide the Internet access for users by mesh routers. The HMR protocol applies two independent routing metrics to obtain high performance. The HMR is able to take advantage of each of those protocols strengths depending on the situation, and more suitable than other protocols in hierarchical hybrid WMNs by providing the benefits of both hop count and link quality metrics. Through simulations, we show that our schemes perform better than existing mechanisms in terms of various performance measures.

A level-set based adaptive-grid method for premixed combustion

A numerical method to simulate premixed combustion is analyzed. It consists of a Cartesian cut-cell flow solver for compressible viscous flows coupled with a level-set method which solves the G-equation to describe the kinematics of the premixed flame. The coupling of the two solvers is achieved via a dual hierarchical dynamic adaptive-mesh framework. Both solvers operate on different Cartesian hierarchical meshes sharing a common background grid level through which they are connected. For the flow solver, feature- and G-based adaptive mesh refinement is taken advantage of, while a uniform high-resolution grid is used for the level-set solver. The heat release due to combustion is described by a source-term formulation by which the reaction rate profile of the premixed flame can be attached to the flame front, the motion of which is governed by the G-equation. A flame–vortex interaction problem is discussed in detail to validate the proposed methodology and to demonstrate the benefits of solution-adaptive mesh refinement in the context of the level-set approach for premixed combustion. After a forced laminar Bunsen flame is considered as an example for attached flames, the coalescence of two spherical flame kernels is simulated to assess the performance of the method and the potential savings in terms of computational costs for three-dimensional problems. The results of the test problems show the artificial thickening of the flame and numerical errors in the level-set solution on coarser grids to possess a comparatively small impact on the overall accuracy. The best findings in the sense of efficiency and physical quality are achieved by the combined feature-/ G-based adaptation method.

Optimization for Cathodic Protection with Hierarchical Mesh Generation and Genetic Algorithm

This study presents an optimization technique with hierarchical mesh generation technique and genetic algorithm. The present technique is applied to optimize layout of electrodes on cathodic protection.

A Hierarchical Hybrid Routing Protocol for Wireless Mesh Network

Clustering route is an important routing way. Combined the characteristics of WMN with clustering route commonly used in wireless mobile networks, a cluster-based hierarchical wireless mesh network architecture was proposed. At the same time, this paper presented a corresponding routing protocol lHierarchical Hybrid Routing Protocol (HHRP), which combines the advantages of proactive routing and reactive routing, and its route maintenance uses local route discovery mechanism. Simulation results using OPNET show that this clustering scheme is more suitable for hybrid wireless mesh network, and the proposed routing has less end-to-end delay, less route cost ratio and more packet delivery ratio, compared with AODV.

Multigrid solver with automatic mesh refinement for transient elastoplastic dynamic problems

AbstractThis paper presents an adaptive refinement strategy based on a hierarchical element subdivision dedicated to modelling elastoplastic materials in transient dynamics. At each time step, the refinement is automatic and starts with the calculation of the solution on a coarse mesh. Then, an error indicator is used to control the accuracy of the solution and a finer localized mesh is created where the user‐prescribed accuracy is not reached. A new calculation is performed on this new mesh using the non‐linear ‘Full Approximation Scheme’ multigrid strategy. Applying the error indicator and the refinement strategy recursively, the optimal mesh is obtained. This mesh verifies the error indicator on the whole structure. The multigrid strategy is used for two purposes. First, it optimizes the computational cost of the solution on the finest localized mesh. Second, it ensures information transfer among the different hierarchical meshes. A standard time integration scheme is used and the mesh is reassessed at each time step. Copyright © 2010 John Wiley & Sons, Ltd.

An adaptive, multilevel scheme for the implicit solution of three‐dimensional phase‐field equations

AbstractPhase‐field models, consisting of a set of highly nonlinear coupled parabolic partial differential equations, are widely used for the simulation of a range of solidification phenomena. This article focuses on the numerical solution of one such model, representing anisotropic solidification in three space dimensions. The main contribution of the work is to propose a solution strategy that combines hierarchical mesh adaptivity with implicit time integration and the use of a nonlinear multigrid solver at each step. This strategy is implemented in a general software framework that permits parallel computation in a natural manner. Results are presented that provide both qualitative and quantitative justifications for these choices.© 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010