Wavelet Multi-Resolution Interpolation Galerkin Method for Linear Singularly Perturbed Boundary Value Problems

In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.

Monolithic Convex Limiting for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral-Element Methods

We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations of nonlinear hyperbolic problems with properties that greatly simplify the design of invariant domain-preserving high-resolution schemes.Compared to many other continuous and discontinuous Galerkin method variants,a particular advantage of the LGL spectral operator is the availability of a natural decomposition into a compatible subcellflux discretization.Representing a highorder spatial semi-discretization in terms of intermediate states,we performflux limiting in a manner that keeps these states and the results of Runge-Kutta stages in convex invariant domains.In addition,local bounds may be imposed on scalar quantities of interest.In contrast to limiting approaches based on predictor-corrector algorithms,our MCL procedure for LGL-DGSEM yields nonlinearflux approximations that are independent of the time-step size and can be further modified to enforce entropy stability.To demonstrate the robustness of MCL/DGSEM schemes for the compressible Euler equations,we run simulations for challenging setups featuring strong shocks,steep density gradients,and vortex dominatedflows.

ANALYSIS OF 2-D THIN STRUCTURES BY THE MESHLESS REGULAR HYBRID BOUNDARY NODE METHOD

Thin structures are generally solved by the Finite Element Method(FEM), using plate or shell finite elements which have manylimitations in applications, such as numerical locking, edge effects,length scaling and the cnvergence problem. Recently, by proposing anew approach to tranting the nearly- singular integrals, Liu et al.developed a BEM to successfully solve thin structures with thethickness-to- length ratios in the micro-or nano-scales. On the otherhand, the meshless Regular Hybrid Boundary Node Method (RHBNM), whichis proposed by the current authors and based on a modified functionaland the Moving Least-Square (MLS) approximation, has very promisingapplications for engineering problems owing To its meshless natureand dimension-reduction advantage, and not involving any singular ornearly-singular Integrals. Test examples show that the RHBNM can alsobe applied readily to thin structures with high accu- Racy withoutany modification.

A moving Kriging interpolation-based boundary node method for two-dimensional potential problems

In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This study combines the DIE method with the moving Kriging interpolation to present a boundary-type meshfree method, and the corresponding formulae of the MKIBNM are derived. In the present method, the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker＇s delta property, then the boundary conditions can be imposed directly and easily. To verify the accuracy and stability of the present formulation, three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically.

Shift control method for the local time at descendi ngnode based on sun-synchronous orbit satellite

This article analyzes the shift factors of the descending node local time for sun-synchronous satellites and proposes a shift control method to keep the local time shift within an allowance range. It is found that the satellite orbit design and the orbit injection deviation are the causes for the initial shift velocity, whereas the atmospheric drag and the sun gravitational perturbation produce the shift acceleration. To deal with these shift factors, a shift control method is put forward, through such methods as orbit variation design, orbit altitude, and inclination keeping control. The simulation experiment and practical application have proved the effectiveness of this control method.

PREDICTION OF TEXTILE FABRIC REINFORCED COMPOSITE PROPERTIES BASED ON NODE INTERPOLATION CELL METHOD

Node interpolation cell method（NICM）is a micromechanics method employing the virtual displacement principle and the representative volume element（RVE）scheme to obtain the relationship between the global and the local strain.Mechanical properties of 2-D textile fabric reinforced ceramic matrix composites are predicted by NICM.Microstructures of 2-D woven and braided fabric reinforced composite are modeled by two kinds of RVE scheme.NICM is used to predict the macroscopic mechanical properties.The fill and warp yarns are simulated with cubic B-spline and their undulating forms are approximated by sinusoid.The effect of porosity on the fiber and matrix are considered as a reduction of elastic module.The connection of microstructure parameters and fiber volume fraction is modeled to investigate the reflection on the mechanical properties.The results predicted by NICM are compared with that by the finite element method（FEM）.The comparison shows that NICM is a valid and feasible method for predicting the mechanics properties of 2-D woven and braided fabric reinforced ceramic matrix composites.

DUAL RECIPROCITY HYBRID BOUNDARY NODE METHOD FOR THREE-DIMENSIONAL ELASTICITY WITH BODY FORCE

Combining Dual Reciprocity Method （DRM） with Hybrid Boundary Node Method （HBNM）, the Dual Reciprocity Hybrid Boundary Node Method （DRHBNM） is developed for three-dimensional linear elasticity problems with body force. This method can be used to solve the elasticity problems with body force without domain integral, which is inevitable by HBNM. To demonstrate the versatility and the fast convergence of this method, some numerical examples of 3-D elasticity problems with body forces are examined. The computational results show that the present method is effective and can be widely applied in solving practical engineering problems.

A scaled boundary node method applied to two-dimensional crack problems

A boundary-type meshless method called the scaled boundary node method （SBNM） is developed to directly evaluate mixed mode stress intensity factors （SIFs） without extra post-processing. The SBNM combines the scaled boundary equations with the moving Kriging （MK） interpolation to retain the dimensionality advantage of the former and the meshless attribute of the latter. As a result, the SBNM requires only a set of scattered nodes on the boundary, and the displacement field is approximated by using the MK interpolation technique, which possesses the 5 function property. This makes the developed method efficient and straightforward in imposing the essential boundary conditions, and no special treatment techniques are required. Besides, the SBNM works by weakening the governing differential equations in the circumferential direction and then solving the weakened equations analytically in the radial direction. Therefore, the SBNM permits an accurate representation of the singularities in the radial direction when the scaling center is located at the crack tip. Numerical examples using the SBNM for computing the SIFs are presented. Good agreements with available results in the literature are obtained.

Analysis of identification methods of key nodes in transportation network

The identification of key nodes plays an important role in improving the robustness of the transportation network.For different types of transportation networks,the effect of the same identification method may be different.It is of practical significance to study the key nodes identification methods corresponding to various types of transportation networks.Based on the knowledge of complex networks,the metro networks and the bus networks are selected as the objects,and the key nodes are identified by the node degree identification method,the neighbor node degree identification method,the weighted k-shell degree neighborhood identification method(KSD),the degree k-shell identification method(DKS),and the degree k-shell neighborhood identification method(DKSN).Take the network efficiency and the largest connected subgraph as the effective indicators.The results show that the KSD identification method that comprehensively considers the elements has the best recognition effect and has certain practical significance.

MESHLESS ANALYSIS FOR THREE-DIMENSIONAL ELASTICITY WITH SINGULAR HYBRID BOUNDARY NODE METHOD

The singular hybrid boundary node method （SHBNM） is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares （MLS） approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The ＇boundary layer effect＇, which is the main drawback of the original Hybrid BNM, was overcome by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method （RHBNM） can be avoided. Numerical examples for some 3D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.

A novel virtual node method for polygonal elements

A novel polygonal finite element method （PFEM） based on partition of unity is proposed, termed the virtual node method （VNM）. To test the performance of the present method, numerical examples are given for solid mechanics problems. With a polynomial form, the VNM achieves better results than those of traditional PFEMs, including the Wachspress method and the mean value method in standard patch tests. Compared with the standard triangular FEM, the VNM can achieve better accuracy. With the ability to construct shape functions on polygonal elements, the VNM provides greater flexibility in mesh generation. Therefore, several fracture problems are studied to demonstrate the potential implementation. With the advantage of the VNM, the convenient refinement and remeshing strategy are applied.

Interpolating Isogeometric Boundary Node Method and Isogeometric Boundary Element Method Based on Parameter Space

In this paper,general interpolating isogeometric boundary node method(IIBNM)and isogeometric boundary element method(IBEM)based on parameter space are proposed for 2D elasticity problems.In both methods,the integral cells and elements are defined in parameter space,which can reproduce the geometry exactly at all the stages.In IIBNM,the improved interpolating moving leastsquare method(IIMLS)is applied for field approximation and the shape functions have the delta function property.The Lagrangian basis functions are used for field approximation in IBEM.Thus,the boundary conditions can be imposed directly in both methods.The shape functions are defined in 1D parameter space and no curve length needs to be computed.Besides,most methods for the treatment of the singular integrals in the boundary element method can be applied in IIBNM and IBEM directly.Numerical examples have demonstrated the accuracy of the proposed methods.

Implementing the Node Based Smoothed Finite Element Method as User Element in Abaqus for Linear and Nonlinear Elasticity

In this paper,the node based smoothed-strain Abaqus user element(UEL)in the framework of finite element method is introduced.The basic idea behind of the node based smoothed finite element(NSFEM)is that finite element cells are divided into subcells and subcells construct the smoothing domain associated with each node of a finite element cell[Liu,Dai and Nguyen-Thoi(2007)].Therefore,the numerical integration is globally performed over smoothing domains.It is demonstrated that the proposed UEL retains all the advantages of the NSFEM,i.e.,upper bound solution,overly soft stiffness and free from locking in compressible and nearly-incompressible media.In this work,the constant strain triangular(CST)elements are used to construct node based smoothing domains,since any complex two dimensional domains can be discretized using CST elements.This additional challenge is successfully addressed in this paper.The efficacy and robustness of the proposed work is obtained by several benchmark problems in both linear and nonlinear elasticity.The developed UEL and the associated files can be downloaded from https://github.com/nsundar/NSFEM.

Local differential quadrature method using irregularly distributed nodes for solving partial differential equations

In the conventional differential quadrature （DQ） method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local differential quadrature （LDQ） method was developed by using irregular distributed nodes, where any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of nodes in the local physical domain. The weighting coefficients in the new approach are determined by the quadrature rule with the aid of nodal interpolation. Since the proposed method directly approximates the derivative, it can be consistently well applied to linear and nonlinear problems and the mesh-free feature is still kept. Numerical examples are provided to validate the LDQ method.

Singular Hybrid Boundary Node Method for Solving Poisson Equation

As a boundary-type meshless method, the singular hybrid boundary node method（SHBNM） is based on the modified variational principle and the moving least square（MLS） approximation, so it has the advantages of both boundary element method（BEM） and meshless method. In this paper, the dual reciprocity method（DRM） is combined with SHBNM to solve Poisson equation in which the solution is divided into particular solution and general solution. The general solution is achieved by means of SHBNM, and the particular solution is approximated by using the radial basis function（RBF）. Only randomly distributed nodes on the bounding surface of the domain are required and it doesn＇t need extra equations to compute internal parameters in the domain. The postprocess is very simple. Numerical examples for the solution of Poisson equation show that high convergence rates and high accuracy with a small node number are achievable.

THREE-DIMENSIONAL FINITE ELEMENT DELAUNAY MESH GENERATION BY A PERFECTED NODE CONNECTION METHOD

How to automatically generate three-dimensional finite element Delaunay mesh by a peifected node connection method is introduced, where nodes are generated based on existing elements, instead of independence of node creation and elements generation in traditional node connection method. Therefore, Ihe the difficulty about how to automatically create nodes in the traditional method is overcome.

An Approximation Algorithm for the solution of astrophysics equations using rational scaled generalized Laguerre function collocation method based on transformed Hermite-Gauss nodes

In this paper we propose a collocation method for solving Lane-Emden type equation which is nonlinear or-dinary differential equation on the semi-infinite domain. This equation is categorized as singular initial value problems. We solve this equation by the generalized Laguerre polynomial collocation method based on Her-mite-Gauss nodes. This method solves the problem on the semi-infinite domain without truncating it to a fi-nite domain and transforming domain of the problem to a finite domain. In addition, this method reduces so-lution of the problem to solution of a system of algebraic equations.

超声造影体表定位联合纳米炭示踪行前哨淋巴结活检在cN0期浸润性乳腺癌病人中的应用分析

目的对比分析在cN0期浸润性乳腺癌(IBC)病人中应用超声造影(CEUS)体表定位联合纳米炭示踪行前哨淋巴结活检(SLNB)与单一染料法示踪行SLNB的手术耗时及其对前哨淋巴结(SLN)的检出率与检出数目,探讨CEUS体表定位联合纳米炭示踪行SLNB的可行性。方法收集2018年1月1日~2023年4月30日于北京市顺义区医院诊治的199例cN0期IBC病人临床病理学资料,根据SLN示踪方法不同将所有病人分为染料法组100例和联合法组99例,染料法组应用纳米炭示踪行SLNB,联合法组术前应用CEUS对SLN行体表标记定位,术中应用纳米炭示踪行SLNB。结果SLN检出率为96.48%(192/199),染料法组检出率为95.00%,平均检出SLN(2.79±1.228)枚,联合法检出率为97.98%,平均检出SLN(3.32±1.469)枚,两组SLN的检出率比较差异无统计学意义(P>0.05),联合法组SLN的平均检出数目多于染料法组(P<0.05),但两组SLN检出数目分布比较差异无统计学意义(P>0.05),联合法组的SLNB手术耗时明显短于染料法[(13.83±4.58)min比(19.85±3.20)min,P<0.05]。结论联合法行SLNB可降低手术耗时并提高SLN的检出率及检出数目。

物联网环境下复杂光纤通信传输网络节点调度

为了解决物联网环境下,光纤通信传输网络节点能耗高、调度效率低的问题,提出一种物联网环境下复杂光纤通信传输网络节点调度方法。在物联网环境下,分析光纤通信传输网络节点的分布情况,根据动态联盟理论,以最快调度速度和最小投资为目标,构建复杂光纤通信传输网络节点调度模型。通过蚁群和粒子群算法相结合的融合算法展开全部搜索,获取最佳调度方案,实现光纤通信传输网络节点调度。实验结果表明,所提方法的节点平均能耗在6.0 mJ以下,LBF值始终高于0.20,且节点调度耗时始终低于200 ms,具有良好的调度效果。

特深井钻柱动力学特性模拟与分析

随着钻井深度不断增加,钻柱运动所涉及的力学问题变得更加复杂,钻柱动力学特性模拟及分析可为安全优质高效钻井提供支撑。为了探求特深井钻柱的运动特性,将钻柱运动的控制方程采用Newmark法对时间离散后,运用SOR节点迭代法,对每一时间步的钻柱整体构形进行求解,实现了总长超9000 m的钻柱动力学特性模拟,不仅给出了钻柱4个典型位置的涡动轨迹、涡动速度和横向加速度,还分析了钻柱的粘滑特性。分析结果表明,上部钻柱的涡动及粘滑现象不明显;随着位置下移,出现不规则涡动及不充分粘滑现象;近钻头位置的钻柱会出现较剧烈涡动,也会出现粘滑振动;中性点位置处钻柱的涡动最为剧烈、碰摩严重,可能给钻柱带来安全隐患。研究结果为特深井安全钻井提供了理论依据。