Edge Elements Research Articles

Thermo-mechanical design of the neutralizer for CRAFT negative ion-based neutral beam injection system

The Comprehensive Research fAcility for Fusion Technology (CRAFT) has been launched in China and a negative ion-based neutral beam injection system (NNBI) is an important component of CRAFT. The primary target of the CRAFT NNBI is to realize a neutral hydrogen beam of >2 MW at the beam energy of 400 keV for the pulse duration of 100 s. In the CRAFT NNBI, the neutralization of the negative ion beam will be accomplished in a gas neutralizer mainly consisting of two vertical channels. Each channel has a rectangular cross-section of 0.145 m × 1.7 m and a length of 3 m, which is formed by several copper panels. A key issue of the neutralizer is to remove the heat load from the incident ion beam. This paper presents the thermo-mechanical design process of the neutralizer of the CRAFT NNBI. Because the heat load densities on the lateral walls of the panels are relatively low, their surface temperature can be well controlled under the safe values of copper by deep drilling of the cooling channels. The largest problem is the leading edge of the panels, where the heat load density is extremely high. Thus, the leading edge element (LEE) is carefully designed to avoid damage to these panels. The LEE is made of CuCrZr alloy and the twisted tape is inserted into the cooling channel to promote the turbulence and consequently the heat transfer capability. Finally, the thermo-mechanical properties of the heat load components of the neutralizer can be controlled under the required values in terms of the surface temperature, water temperature, stress, and deformation.

The Role of Vertebral Porosity and Implant Loading Mode on Bone-Tissue Stress in the Human Vertebral Body Following Lumbar Total Disc Arthroplasty.

Micro-computed tomography- (micro-CT-) based finite element analysis of cadaveric human lumbar vertebrae virtually implanted with total disc arthroplasty (TDA) implants. (1) Assess the relationship between vertebral porosity and maximum levels of bone-tissue stress following TDA; (2) determine whether the implant's loading mode (axial compression vs. sagittal bending) alters the relationship between vertebral porosity and bone-tissue stress. Implant subsidence may be related to the bone biomechanics in the underlying vertebral body, which are poorly understood. For example, it remains unclear how the stresses that develop in the supporting bone tissue depend on the implant's loading mode or on typical inter-individual variations in vertebral morphology. Data from micro-CT scans from 12 human lumbar vertebrae (8 males, 4 females; 51-89 years of age; bone volume fraction [BV/TV] = 0.060-0.145) were used to construct high-resolution finite element models (37 μm element edge length) comprising disc-vertebra-implant motion segments. Implants were loaded to 800 N of force in axial compression, flexion-, and extension-induced impingement. For comparison, the same net loads were applied via an intact disc without an implant. Linear regression was used to assess the relationship between BV/TV, loading mode, and the specimen-specific change in stress caused by implantation. The increase in maximum bone-tissue stress caused by implantation depended on loading mode (P < 0.001), increasing more in bending-induced impingement than axial compression (for the same applied force). The change in maximum stress was significantly associated with BV/TV (P = 0.002): higher porosity vertebrae experienced a disproportionate increase in stress compared with lower porosity vertebrae. There was a significant interaction between loading mode and BV/TV (P = 0.002), indicating that loading mode altered the relationship between BV/TV and the change in maximum bone-tissue stress. Typically-sized TDA implants disproportionately increase the bone-tissue stress in more porous vertebrae; this affect is accentuated when the implant impinges in sagittal bending.Level of Evidence: N/A.

3-D FEM–BEM Coupling for the Magnetic Field Computation in Thin Shells: Application to the Evaluation of Ship Magnetic Signature

In this article, a model based on finite element-boundary element methods (FEM-BEM) coupling is developed for the magnetic field computation in thin magnetic shells submitted to external magnetic fields. The model is formulated in terms of the reduced magnetic vector potential. Surface fictitious currents are used for the FEM-BEM coupling. Only the active arts are discretized by using edge elements. The model is validated by comparing with analytical results for a magnetic hollow sphere in a homogeneous magnetic field. An application to the evaluation of ship magnetization is then considered.

NURBS-based geometries: A mapping approach for virtual serendipity elements

A NURBS-based serendipity virtual element method for general (arbitrary) element shapes is outlined in this work. The low-order VEM ansatz function is now extended towards higher-order formulation. In comparison with the already existing serendipity VEM, a general mapping scheme is developed within this contribution allowing to deviate from the assumption of straight edges of virtual elements. A number of numerical examples illustrates the robustness and accuracy of the new mapping methodology. The results are very promising and underline the advantages of the formulations for dealing with arbitrary geometries.

Using IoTCloudSamples as a software framework for simulations of edge computing scenarios

Realizing the potential of edge computing and networks connecting the edge and the cloud, researchers from academia and industries have increasingly developed techniques and tools for edge infrastructures and applications. This paper focuses on supporting complex edge application interactions, which span different layers and subsystems in edge-cloud environments. This paper addresses (i) diverse types of software components for emulating realistic functionality and configurations, like data transformation and service API interoperability, and (ii) techniques for connecting emulated scenarios to real edge software development and operations, and to IoT and cloud counterparts. We present IoTCloudSamples as a software framework with (i) modeling and implementation of diverse types of IoT, edge and cloud elements for complex edge scenarios, (ii) methods for constructing and steering emulations to study the interoperability across layers among different edge platforms and protocols, and (iii) extensive emulated scenarios and experiments integrated with real-world IoT and cloud services. IoTCloudSamples supports the approach of edge-simulation-as-code to allow the reuse and runtime steering of realistic emulation operations. We will present examples from our real-world projects concentrating on edge analytics applications.

A Hierarchical Error Estimator for the MSFEM for the Eddy Current Problem in 3-D

The aim of this article is to develop an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> hierarchical error estimator for the multiscale finite element method (MSFEM). The MSFEM is used to solve the linear eddy current problem in a stack of iron sheets. It allows for a calculation of the solution without having to resolve each sheet in the finite element mesh. A hierarchical local error estimator for nodal elements and edge elements is adapted to the multiscale setting. The estimator allows for adaptive p-refinement on the coarse multiscale mesh. Numerical examples show an increased order of convergence compared to uniform refinement. The proposed error estimator increases the efficiency of the MSFEM, requiring even fewer degrees of freedom. It is the first error estimator presented for the 3-D MSFEM for the eddy current problem.

Sliding Non-Conforming Interfaces for Edge Elements in Eddy Current Problems

In this work, a flexible discretization technique for the approximate solution of electromagnetic field problems with rotating parts, based on non-conforming (NC) interfaces of Nitsche-type, is investigated. This approach enables the use of edge elements of the first and second kind for the discretization of the magnetic vector potential without posing severe restrictions on gaps and overlaps of elements on both sides of the rotating interface. It improves the computational efficiency, compared to other NC interface formulations because no additional unknowns are introduced, and edge elements of different polynomial order can be coupled with this approach. The applicability is shown in two numerical examples, involving a cylindrical NC interface between a stationary and a rotating domain.

Vibration suppression of a rotating functionally graded beam with enhanced active constrained layer damping treatment in temperature field

This paper investigates the vibration control of a rotating functionally gradient material (FGM) beam under thermal environment by using an enhanced active constrained layer damping (EACLD) treatment. The present model is extended from a newly developed dynamic model for composite EACLD beams. The difference is that the base beam is composed of temperature-dependent FGM that was widely used in the aerospace industry as advanced heat-resisting composite and the temperature dependence of viscoelastic material in the constrained layer is also considered. The active piezoelectric layer has edge elements at both ends, which are modeled as equivalent springs and mass points. The Lagrange’s equation is used to derive the dynamic equations of the system and the deformation of the beam is described by the assumed-mode method. Based on the rigid-flexible coupling dynamic theory, the dynamic responses of the rotating FGM beam with various temperature differences are investigated. Simulation results show that the vibration suppression performance of the EACLD beam is better than the ACLD beam. The equivalent springs have more significant influences on the structural vibration suppression effect than the mass points. The larger the temperature difference is, the larger the thermal induced flutter of the structure is. The influences of VEM damping layer thickness, rotating speed, and control gain on the vibration of the structure with EACLD treatment are also discussed.

An accurate edge‐based FEM for electromagnetic analysis with its applications to multiscale structures

AbstractThis paper introduces an accurate edge‐based smoothed finite element method (ES‐FEM) for electromagnetic analysis for both two‐dimensional cylindrical and three‐dimensional Cartesian systems, which shows much better performance in terms of accuracy and numerical stability for mesh distortion compared with the traditional FEM. Unlike the traditional FEM, the computational domain in ES‐FEM is divided into non‐overlapping smoothing domains associated with each edge of elements, triangles in two‐dimensional domain and tetrahedrons in three‐dimensional domain. Then, the gradient smoothing technique is used to smooth the gradient components in the stiff matrix of the FEM. Several numerical experiments are carried out to validate its accuracy and numerical stability. Results show that the ES‐FEM can obtain much more accurate results compared with the traditional FEM and is almost independent of mesh distortion.

Creating Edge Element from Four Node Quadrilateral Element

When nodal based FEM is applied to vector field problems, some spurious eigen values appears. This can be avoided by adopting edge based FEM in the formulation. A separate conversion algorithm is used which takes the nodal information of quadrilateral element as input. Edge element is created from four node quadrilateral element to solve the 2D eigen value problem.

Dynamic shear band evolution by the numerical manifold method and the Drucker Prager model

To simulate the dynamic evolution of shear band in soil, the numerical manifold method (NMM) and the Drucker Prager model (DP) are used. Considering that the soil does not bear tension, the tensile part of DP is cut off. Then the constitutive integration could be reduced to mix complementarity problem, which is solved by the Gauss Seidel projection contraction method (GSPC). The discretization sequence is altered to resolve the transfer issue of degrees of freedom when dealing with dynamic discontinuities evolving. Different with the traditional discretization approach, the discretization of temporal variable is set prior to that of spatial variable so that all the degrees of freedom are valid only in a current step without the necessity to be transferred to the next time step. In this way, the shear band tip could stop anywhere naturally, without being improperly forced to stay on the element edge. For simplicity, the shear band is treated as a strong discontinuity with zero width. The interface contact is described by the NMM contact approach where open-close iteration is involved. Finally, a soil dam is studied to check the capability of the proposed method to capture the dynamic evolution of shear band.

A novel stabilization method for high-order shock fitting with finite element methods

A moving-grid, shock-fitting, finite element method has been implemented that can achieve high-order accuracy for flow simulations with shocks. In this approach, element edges in the computational mesh are fitted to the shock front and moved with the shock throughout the simulation. The Euler or Navier-Stokes equations are solved on the moving mesh in an arbitrary Lagrangian-Eulerian framework. The method is implemented in two-dimensions in the context of a streamwise upwind Petrov-Galerkin finite element discretization with unstructured triangular meshes and mesh adaptation. It is shown that the shock interface motion equation has a wave nature, and disturbances can propagate along the shock interface. A SUPG stabilization term is introduced to the interface motion equation that is critical for ensuring that interface disturbances do not lead to non-convergent solution behavior. The formal order of accuracy of the scheme is verified, and the performance of the proposed scheme is assessed for both inviscid and viscous problems. It was found that the present scheme predicts smooth and noise-free surface heating for hypersonic flow over a cylinder with purely irregular triangular elements.

Pattern synthesis of timed antenna array with the exploitation and suppression of harmonic radiation

SummaryThe pattern synthesis of timed antenna array with the exploitation and suppression of harmonic radiation is proposed in this paper. Timed arrays are the time‐domain alternatives of conventional antenna arrays, where an additional control parameter “time” is used to generate the desired time‐averaged radiation pattern. This additional control also comes with the inherent hindrance of harmonic radiation, generally considered as an undesired effect of time modulation. In this work, this hindrance is overcome with different objectives considering the exploitation and suppression of harmonic radiation of timed arrays. To demonstrate the exploitation of harmonic radiation, a simultaneous sum and difference pattern with reduced sidelobe suitable for monopulse tracking radar systems is obtained at the fundamental and the first harmonic frequency by an optimal subarrayed pulse splitting and shifting approach. Two separate cases, considering uniform and optimized static excitations along with the proposed subarrayed pulse sequence, are presented for the exhaustive analysis of the simultaneous multibeam pattern. To address the suppression of harmonic radiation, the sidelobe level (SLL) at the fundamental frequency and the sideband levels (SBLs) of higher‐order harmonic frequencies are simultaneously reduced. In this regard, a unique pulse shifting approach for the edge elements of the array, along with an optimal set of static excitations, is proposed to enhance the efficiency of the antenna system by reducing SLL and SBLs at the same time. Two uniquely defined cost functions are chosen to address the above‐mentioned objectives by exploiting and suppressing the harmonic radiation of timed arrays, which further increases the adaptability and reconfigurability of the array. A set of 16‐element “time‐modulated” linear array (TMLA) is considered for optimization, and a wavelet mutation‐based differential evolution (DEWM) algorithm is employed to obtain the optimal solutions. Obtained numerical results are reported and also compared with previously published works to show the proposed approach's potentialities.

Superconvergence recovery of cubic edge elements for Maxwell’s equations

In this article, a new recovery method is designed and analyzed for curl conforming elements on cuboid mesh. The proposed recovery method fully exploits the potential of symmetry to obtain the superconvergence of recovered edge finite element solution in discrete ℓ2 norm. The idea is to identify a symmetry sub-domain such that a polynomial of the same degree is recovered by local L2 projection, based on which the recovered values follow. Combined with extrapolation and the least square fitting for the linear edge elements and quadratic edge elements, respectively, we obtain global superconvergence for recovered quantities in L2 norm. Numerical experiments are provided to validate our theoretical findings.

Synaptonemal complex formation produces a particular arrangement of the lateral element-associated DNA

During meiosis, homologous chromosomes exchange genetic material. This exchange or meiotic recombination is mediated by a proteinaceous scaffold known as the Synaptonemal complex (SC). Any defects in its formation produce failures in meiotic recombination, chromosome segregation and meiosis completion. It has been proposed that DNA repair events that will be resolved by crossover between homologous chromosomes are predetermined by the SC. Hence, structural analysis of the organization of the DNA in the SC could shed light on the process of crossover interference. In this work, we employed an ultrastructural DNA staining technique on mouse testis and followed nuclei of pachytene cells. We observed structures organized similarly to the SCs stained with conventional techniques. These structures, presumably the DNA in the SCs, are delineating the edges of both lateral elements and no staining was observed between them. DNA in the LEs resembles two parallel tracks. However, a bubble-like staining pattern in certain regions of the SC was observed. Furthermore, this staining pattern is found in SCs formed between non-homologous chromosomes, in SCs formed between sister chromatids and in SCs without lateral elements, suggesting that this particular organization of the DNA is determined by the synapsis of the chromosomes despite their lack of homology or the presence of partially formed SCs.

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An alternative approach to the processing of elements of linear discriminant functions for the classification of objects is proposed in the paper. This approach is based on the method of processing a vector array of data by differential slices which is distributed in the column of matrix representation of elements of discriminant functions. In its turn, it indicates the spatially distributed nature of the processing of matrix elements with dimension m ? n, where m is the number of classes, n is the dimension of the input data vector. The linearity of the representation of each discriminant function in a set of discriminant functions allows not only to represent their terms in the form of matrix elements, but also apply to their processing some rules concerning such properties as associativity and commutativity of components (terms) of the sum. As a result, such complex procedures as multi-operand summation in the formation of each discriminant function are replaced. Moreover, it is followed by their comparison with each other with the aim of identifying the one with the maximum value. In each processing cycle of the proposed method, the basic operation is a simultaneous reduction in the magnitude of the elements similarity of the same name in the columns of the matrix, which allows determining the maximum value of the discriminant function. The operation of transposition (advancement) to the edge of all current zero elements in each row of the matrix is also involved. This approach is applied to linear discriminant functions as an apparatus of the statistical method of object classification. Consequently, according to the known decision rule, the maximum discriminant function determines the corresponding class to which the input object, represented as an n-dimensional feature vector, belongs. One of the options for the hardware application of such classifier is the decision support subsystem for medical diagnosis.

Aerothermodynamics Response of Hypersonic Flow over a Blunt Cone under Distributed Rough Element

A direct numerical simulation method is used to simulate the hypersonic blunt cone flow field under the condition of smooth wall and distributed rough element. The effects of smooth wall and distributed rough element on hypersonic flow field and wall are compared and analyzed, and the aerothermodynamic response characteristics of hypersonic flow field to distributed rough element are studied. The results show that the effect of the distributed rough element on the hypersonic flow field and boundary layer is significantly higher than that of the smooth wall. The friction coefficient of the wall is directly proportional to the velocity gradient of the flow direction in the boundary layer, while the velocity gradient of the flow direction is inversely proportional to the thickness of the boundary layer. The heat flux density of the wall increases at the front edge of the rough element to promote the heating, and decreases at the second half of the rough element to inhibit the heating.

On total coloring the direct product of complete graphs

A k-total coloring of a graph G is an assignment of k colors to the elements (vertices and edges) of G so that adjacent or incident elements have different colors. The total chromatic number is the smallest integer k for which G has a k-total coloring. The well known Total Coloring Conjecture states that the total chromatic number of a graph is either ∆(G) + 1 or ∆(G) + 2, where ∆(G) is the maximum degree of G. We consider the direct product of complete graphs Km × Kn. It is known that if at least one of the numbers m or n is even, then Km × Kn has total chromatic number equal to ∆(Km × Kn) + 1, except when m = n = 2. We prove that the graph Km × Kn has total chromatic number equal to ∆(Km × Kn) + 1 when both m and n are odd numbers, ensuring in this way that all graphs Km × Kn have total chromatic number equal to ∆ (Km × Kn) + 1, except when m = n = 2.

Shape Optimization for Superconductors Governed by H(curl)-Elliptic Variational Inequalities

This paper is devoted to the theoretical and numerical study of an optimal design problem in high-temperature superconductivity (HTS). The shape optimization problem is to find an optimal superconductor shape minimizes a certain cost functional under a given target on the electric field over a specific domain of interest. For the governing PDE-model, we consider an elliptic curl-curl variational inequality (VI) of the second kind with an L1-type nonlinearity. In particular, the nonsmooth VI character and the involved H(curl)-structure make the corresponding shape sensitivity analysis challenging. To tackle the nonsmoothness, a penalized dual VI formulation is proposed, leading to the Gateaux differentiability of the corresponding dual variable mapping. This property allows us to derive the distributed shape derivative of the cost functional through rigorous shape calculus on the basis of the averaged adjoint method. The developed shape derivative turns out to be uniformly stable with respect to the penalization parameter, and strong convergence of the penalized problem is guaranteed. Based on the achieved theoretical findings, we propose three-dimensional numerical solutions, realized using a level set algorithm and a Newton method with the Nédélec edge element discretization. Numerical results indicate a favorable and efficient performance of the proposed approach for a specific HTS application in superconducting shielding.

Space-Time-Parallel 3-D Finite Element Transformer Model With Adaptive TLM and Parareal Techniques for Electromagnetic Transient Analysis

In this paper, a novel massively space-time parallel finite element (FE) transformer model is proposed for power system electromagnetic transient simulations. The method utilizes the reduced magnetic vector potential (RMVP) formulation to solve the electromagnetic field in the transformer, and the 3-D tetrahedral edge element is applied to discretize the RMVP formulation. The discretized nonlinear system is solved by adaptive transmission line modeling (TLM) and matrix-free conjugate gradient iterator, which allows parallelism at the elemental-level and eliminates the need for Newton-Raphson (NR) iterations over the large-scale global matrix. The paper also integrates the parallel-in-time method with the finite element solver to further parallelize the model at space-time level, and the GPU implementation of the model realized a speedup of over 55 and high accuracy, compared with a commercial FE software.