Engineering Analysis with Boundary Elements最新文献

Optimally shaped nanotubes for field concentration 用于场强集中的最佳形状纳米管

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-11-16 DOI: 10.1016/j.enganabound.2024.106022

Konstantinos V. Kostas , Constantinos Valagiannopoulos

The problem of concentrating electromagnetic fields into a nanotube from an ambient source of light, is considered. An isogeometric analysis approach, in a boundary element method setting, is employed to evaluate the local electric field, which is represented with the exact same basis functions used in the geometric representation of the nanotube. Subsequently, shape optimization of the nanotubes is performed with the aim of maximizing the field concentration in their interior. The optimization framework comprises: (i) one global optimizer implemented as the combination of a derivative-free guided random search approach and a gradient-based algorithm for accurately determining the shape at the final stages, (ii) one parametric modeler generating valid non-self-intersecting nanotube shapes with a relatively small number of parameters, and (iii) one isogeometric-enabled boundary element method solver approximating the value of the electric field on the nanotube with high accuracy. The optimal shapes for a wide range of optical sizes are determined, resulting in a collected energy enhancement of more than two orders of magnitude, compared to the respective circular designs. Importantly, the frequency and angular responses of selected optimal shapes tend to maintain their superior performance over extensive wavelength and directional bands. Therefore, the presented results may assist substantially the photonic inverse design in nanotube-based setups with applications spanning from field localization and power accumulation to wave steering and energy harvesting.

研究考虑了从环境光源向纳米管集中电磁场的问题。在边界元方法设置中，采用等几何分析方法来评估局部电场，该方法使用与纳米管几何表示法完全相同的基函数来表示局部电场。随后，对纳米管的形状进行优化，目的是使其内部的电场浓度最大化。优化框架包括：(i) 结合无导数引导随机搜索方法和基于梯度的算法实现的全局优化器，用于在最后阶段精确确定形状；(ii) 参数建模器，以相对较少的参数生成有效的非自相交纳米管形状；(iii) 支持等几何的边界元素法求解器，高精度地近似纳米管上的电场值。确定了适用于各种光学尺寸的最佳形状，与相应的圆形设计相比，收集的能量提高了两个数量级以上。重要的是，所选最佳形状的频率和角度响应往往能在广泛的波长和方向频段内保持其卓越性能。因此，本文介绍的结果可能对基于纳米管的光子反向设计有很大帮助，其应用范围包括场定位、功率积累、波转向和能量收集。

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引用次数: 0

Special inclusion elements for thermal analysis of composite materials 用于复合材料热分析的特殊包含元素

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-11-16 DOI: 10.1016/j.enganabound.2024.106017

Keyong Wang , Renyu Zeng , Peichao Li , Hao Cen

A novel fundamental solution based finite element method (HFS-FEM) is proposed to analyze heat conduction problem of two-dimensional composite materials. In the proposed method, a linear combination of fundamental solutions at source points is taken as intra-element trial functions to construct the interior temperature field. The required fundamental solution is established by the charge simulation method, which makes it possible to establish arbitrarily shaped inclusion elements. The frame temperature field is independently approximated by the conventional finite element interpolation function to enforce the continuity between neighboring elements. The domain integral is eliminated by applying the divergence theorem to the modified variational functional, which gives HFS-FEM great flexibility in mesh generation. To assess the performance of the proposed elements, numerical examples are conducted and comparisons are made between HFS-FEM and ABAQUS. Numerical results show that HFS-FEM can capture the discontinuity of inclusion and exhibits high efficiency.

本文提出了一种基于基本解的新型有限元方法（HFS-FEM），用于分析二维复合材料的热传导问题。在所提出的方法中，源点处的基本解的线性组合作为元素内试算函数来构建内部温度场。所需的基本解是通过电荷模拟方法建立的，因此可以建立任意形状的包含元素。框架温度场由传统的有限元插值函数独立逼近，以确保相邻元素之间的连续性。通过对修改后的变分函数应用发散定理来消除域积分，这使得 HFS-FEM 在网格生成方面具有极大的灵活性。为了评估所建议的元素的性能，我们进行了数值示例，并在 HFS-FEM 和 ABAQUS 之间进行了比较。数值结果表明，HFS-FEM 可以捕捉包含的不连续性，并表现出很高的效率。

引用次数: 0

Fluid topology optimization using quadtree-based scaled boundary finite element method 利用基于四叉树的缩放边界有限元法优化流体拓扑结构

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-11-15 DOI: 10.1016/j.enganabound.2024.106019

Guifeng Gao, Jianghong Yang, Xinqing Li, Jinyu Gu, Yingjun Wang

This paper presents a fluid topology optimization method utilizing a quadtree scaled boundary finite element method (SBFEM). The method aims to minimize energy dissipation during fluid flow by employing quadtree mesh refinement in the design domain, integrating both velocity and pressure fields. Finer meshes are used near the fluid-structure interface and coarser meshes elsewhere. By leveraging the Stokes control equations for incompressible viscous fluids, the scaled boundary finite element transformation addresses hanging node issues between different elements and simplifies numerical computations by eliminating the need to solve fundamental solutions within the domain. The density-based topology optimization method is then used to determine optimal channel layouts. This proposed method reduces the number of elements and degrees of freedom (DOFs) of design variables while enhancing numerical analysis accuracy. By testing a series of numerical examples, the proposed method can obtain consistent results as those of finite-element-method (FEM)-based topology optimization with shortened time, which demonstrates the accuracy and efficiency of the proposed method.

本文介绍了一种利用四叉树缩放边界有限元法（SBFEM）进行流体拓扑优化的方法。该方法旨在通过在设计域中采用四叉树网格细化，整合速度场和压力场，最大限度地减少流体流动过程中的能量耗散。在流体-结构界面附近使用较细的网格，其他地方则使用较粗的网格。通过利用不可压缩粘性流体的斯托克斯控制方程，缩放边界有限元变换解决了不同元素之间的悬挂节点问题，并通过消除在域内求解基本解的需要简化了数值计算。然后使用基于密度的拓扑优化方法来确定最佳通道布局。这种拟议的方法减少了元素数量和设计变量的自由度 (DOF)，同时提高了数值分析的准确性。通过对一系列数值实例的测试，所提出的方法可以在更短的时间内获得与基于有限元法（FEM）的拓扑优化方法一致的结果，这证明了所提出方法的准确性和高效性。

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引用次数: 0

Efficient exact quadrature of regular solid harmonics times polynomials over simplices in R3 R3 中简约上正则实体谐波乘多项式的高效精确正交

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-11-15 DOI: 10.1016/j.enganabound.2024.106023

Shoken Kaneko , Ramani Duraiswami

A generalization of a recently introduced recursive numerical method (Gumerov et al., 2023) for the exact evaluation of integrals of regular solid harmonics and their normal derivatives over simplex elements in

R^{3}

is presented. The original Quadrature to Expansion (Q2X) method (Gumerov et al., 2023) achieves optimal per-element asymptotic complexity for computing

O (p_{s}^{2})

integrals of all regular solid harmonics bases with truncation degree

p_{s}

by exploiting recurrence relations of the regular solid harmonics as well as the flatness and straightness of the faces and edges, respectively, of simplex elements. However, it considered only constant density functions over the elements. Here, we generalize this method to support arbitrary degree polynomial density functions, which is achieved in an extended recursive framework while maintaining the optimality of the per-element complexity for evaluating all regular solid harmonics and monomial density functions. The method is derived for 1- and 2- simplex elements in

R^{3}

and can be used for the boundary element method and vortex methods coupled with the fast multipole method.

本文介绍了对最近引入的递归数值方法（Gumerov 等人，2023 年）的推广，该方法用于精确计算 R3 中单元上的正则实体谐波积分及其正导数。最初的正交展开（Q2X）方法（Gumerov 等人，2023 年）通过利用正交实体谐波的递推关系以及简元的面和边分别具有的平面度和直线度，在计算截断度为 ps 的所有正交实体谐波基的 O(ps2)积分时实现了最优的每元素渐近复杂度。但是，它只考虑了元素上的恒密度函数。在这里，我们将这种方法推广到支持任意度多项式密度函数，这是在一个扩展递归框架中实现的，同时保持了评估所有正则实体谐波和单项式密度函数的每元素复杂性的最优性。该方法适用于 R3 中的 1- 和 2- 单纯形元素，可用于边界元素法和与快速多极法相结合的涡流法。

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引用次数: 0

Modified space-time radial basis function collocation method for solving three-dimensional transient elastodynamic problems 用于求解三维瞬态弹性力学问题的修正时空径向基函数搭配法

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-11-15 DOI: 10.1016/j.enganabound.2024.106027

Xiaohan Jing , Lin Qiu , Fajie Wang , Yan Gu

In this paper, we improve the traditional space-time radial basis function (RBF) collocation method for solving three-dimensional elastodynamic problems. The proposed approach arranges source points outside the entire space-time domain by introducing space and time amplification factors, rather than locating them within the computational domain. Additionally, a multiple-scale technique is developed to address the ill-conditioning issue in the resulting matrix system. The coefficient matrix produced by the modified RBF collocation method depends solely on the space-time distances between the collocation points and the source points, making it simple in structure and easy to compute. Numerical examples involving complex geometries and mixed boundary conditions are simulated to verify the performance of the presented approach. In cases where exact solutions are unavailable, the results achieved by the proposed method closely match those obtained by the finite element method (FEM), validating the effectiveness of the developed approach. In addition, the proposed approach has faster convergence rate than the FEM. Comparison results among the modified method, the FEM, and the traditional space-time RBF collocation method demonstrate the superior accuracy of the proposed approach, positioning it as a promising tool for handling transient elastodynamic problems.

本文改进了用于解决三维弹性力学问题的传统时空径向基函数（RBF）配准法。所提出的方法通过引入空间和时间放大系数，将源点布置在整个时空域之外，而不是将其布置在计算域之内。此外，还开发了一种多尺度技术，以解决由此产生的矩阵系统中的条件不良问题。修正的 RBF 配准法产生的系数矩阵仅取决于配准点与源点之间的时空距离，因此结构简单，易于计算。我们模拟了涉及复杂几何形状和混合边界条件的数值示例，以验证所提出方法的性能。在无法获得精确解的情况下，所提方法得出的结果与有限元法（FEM）得出的结果非常接近，验证了所开发方法的有效性。此外，与有限元法相比，拟议方法的收敛速度更快。修改后的方法、有限元法和传统的时空 RBF 搭配法之间的比较结果表明，所提出的方法具有更高的精确度，是处理瞬态弹性力学问题的一种有前途的工具。

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引用次数: 0

Convergence properties of the radial basis function-finite difference method on specific stencils with applications in solving partial differential equations 特定模版上径向基函数-有限差分法的收敛特性及其在求解偏微分方程中的应用

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-11-13 DOI: 10.1016/j.enganabound.2024.106026

Fazlollah Soleymani , Shengfeng Zhu

We consider the problem of approximating a linear differential operator on several specific stencils using the radial basis function method in the finite difference scheme. We prove a linear convergence order on a non-equispaced five-point stencil. Then, we discuss how the convergence rate can be boosted up to the second-order on an equispaced stencil. Moreover, we show that including additional nearby nodes (six to twelve) in the stencil does not improve the convergence rate, thus increasing the computational load without enhancing convergence. To overcome this limitation, we propose a stencil that accelerates the convergence up to four using a nine-point stencil, unlike existing approaches which are based on thirteen-point equispaced stencils to achieve such an order of convergence. To support our findings, we conduct numerical experiments by solving Poisson equations and a parabolic problem.

我们考虑了在有限差分方案中使用径向基函数法在几个特定模版上逼近线性微分算子的问题。我们证明了在非匀速五点模版上的线性收敛阶次。然后，我们讨论了如何在等间距模版上将收敛率提高到二阶。此外，我们还表明，在模版中加入额外的邻近节点（6 到 12 个）并不能提高收敛速度，因此会增加计算负荷，却不会提高收敛速度。为了克服这一局限，我们提出了一种模版，使用九点模版将收敛速度提高到四倍，这与现有方法不同，现有方法是基于十三点等距模版来达到这样的收敛速度。为了支持我们的发现，我们通过求解泊松方程和抛物线问题进行了数值实验。

引用次数: 0

A local radial basis function-compact finite difference method for Sobolev equation arising from fluid dynamics 流体动力学索波列方程的局部径向基函数-紧凑有限差分法

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-11-13 DOI: 10.1016/j.enganabound.2024.106020

Mohammad Ilati

In this article, a new high-order, local meshless technique is presented for numerically solving multi-dimensional Sobolev equation arising from fluid dynamics. In the proposed method, Hermite radial basis function (RBF) interpolation technique is applied to approximate the operators of the model over local stencils. This leads to compact RBF generated finite difference (RBF-FD) formula, which provides a significant improvement in the accuracy and computational efficiency. In the first stage of the proposed method, the time discretization is performed by Crank–Nicolson finite difference scheme along with temporal Richardson extrapolation technique. In the second stage, the space dimension is discretized by applying the local radial basis function-compact finite difference (RBF-CFD) method. By performing some numerical simulations and comparing the results with existing methods, the high accuracy and computational efficiency of the proposed method are clearly demonstrated. The numerical results show that the presented method has fourth-order accuracy in both space and time dimensions. Finally, it can be concluded that the proposed method is a suitable alternative to the existing numerical techniques for the Sobolev model.

本文提出了一种新的高阶局部无网格技术，用于数值求解流体力学中产生的多维 Sobolev 方程。在所提出的方法中，应用了 Hermite 径向基函数（RBF）插值技术来逼近局部模板上的模型算子。这就产生了紧凑的 RBF 生成有限差分（RBF-FD）公式，显著提高了精度和计算效率。在拟议方法的第一阶段，时间离散化是通过 Crank-Nicolson 有限差分方案和时间理查德森外推技术来实现的。在第二阶段，应用局部径向基函数-紧凑有限差分（RBF-CFD）方法对空间维度进行离散化。通过进行一些数值模拟并将结果与现有方法进行比较，清楚地表明了所提出方法的高精度和计算效率。数值结果表明，所提出的方法在空间和时间维度上都具有四阶精度。最后，可以得出结论，所提出的方法是现有 Sobolev 模型数值技术的合适替代方法。

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引用次数: 0

A merging approach for hole identification with the NMM and WOA-BP cooperative neural network in heat conduction problem 热传导问题中使用 NMM 和 WOA-BP 协同神经网络进行孔识别的合并方法

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-11-13 DOI: 10.1016/j.enganabound.2024.106042

X.L. Ji, H.H. Zhang, S.Y. Han

Defect identification is an important issue in structural health monitoring. Herein, originated from inverse techniques, a merging approach is established by the numerical manifold method (NMM) and whale optimization algorithm-back propagation (WOA-BP) cooperative neural network to identify hole defects in heat conduction problems. On the one hand, the NMM can simulate varying hole configurations on a fixed mathematical cover, which eases the generation of “big data” for the training of neural network to a large extent. On the other hand, the WOA, a global optimization algorithm, is adopted to optimize the initial weights and thresholds of the BP neural network to alleviate its frequently encountered local optimum phenomenon. The boundary temperatures of sampling points by the NMM and the associated hole geometries are used for the learning of WOA-BP neural network, which is then applied to predict the hole defects. Numerical examples concerning the detection of circular/ elliptical holes demonstrate that the proposed method possesses higher accuracy and satisfying robustness in holes prediction compared with standard BP network under the same condition. The present work provides a convenient pathway and great potential in application of structural health monitoring.

缺陷识别是结构健康监测中的一个重要问题。本文从反演技术出发，建立了数值流形法（NMM）与鲸鱼优化算法-反向传播（WOA-BP）合作神经网络的融合方法，以识别热传导问题中的孔洞缺陷。一方面，数值流形法可以在固定的数学覆盖面上模拟不同的孔构造，这在很大程度上简化了神经网络训练所需的 "大数据 "的生成。另一方面，采用全局优化算法 WOA 来优化 BP 神经网络的初始权值和阈值，以缓解其经常出现的局部最优现象。利用 NMM 采样点的边界温度和相关的孔几何形状来学习 WOA-BP 神经网络，然后将其用于预测孔缺陷。有关圆形/椭圆形孔洞检测的数值实例表明，在相同条件下，与标准 BP 网络相比，所提出的方法在孔洞预测方面具有更高的准确性和令人满意的鲁棒性。本研究为结构健康监测的应用提供了便捷的途径和巨大的潜力。

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引用次数: 0

Fluid flow simulation with an H2-accelerated Boundary-Domain Integral Method 用 H2- 加速边界域积分法模拟流体流动

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-11-13 DOI: 10.1016/j.enganabound.2024.106015

J. Tibaut , J. Ravnik , M. Schanz

The development of new numerical methods for fluid flow simulations is challenging but such tools may help to understand flow problems better. Here, the Boundary-Domain Integral Method is applied to simulate laminar fluid flow governed by a dimensionless velocity–vorticity formulation of the Navier–Stokes equation. The Reynolds number is chosen in all examples small enough to ensure laminar flow conditions. The false transient approach is utilized to improve stability.

As all boundary element methods, the Boundary-Domain Integral Method has a quadratic complexity. Here, the

H^{2}

-methodology is applied to obtain an almost linear complexity. This acceleration technique is not only applied to the boundary only part but more important to the domain related part of the formulation. The application of the

H^{2}

-methodology does not allow to use the rigid body method to determine the singular integrals and the integral free term as done until now. It is shown how to apply the technique of Guigiani and Gigante to handle the strongly singular integrals in this application. Further, a parametric study shows the influence of the introduced approximation parameters. For this purpose the example of a lid driven cavity is utilized. The second example demonstrates the performance of the proposed method by simulating the Hagen–Poiseuille flow in a pipe. The third example considers the flow around a rigid cylinder to show the behavior of the method for an unstructured grid. All examples show that the proposed method results in an almost linear complexity as the mathematical analysis promisses.

为流体流动模拟开发新的数值方法极具挑战性，但这些工具有助于更好地理解流动问题。在此，我们采用边界域积分法模拟纳维-斯托克斯方程的无量纲速度-涡度公式控制的层流流体流动。在所有示例中，雷诺数都选得足够小，以确保层流条件。与所有边界元方法一样，边界域积分法具有二次复杂性。与所有边界元方法一样，边界域积分法的复杂度为二次方，而这里采用的 H2 方法的复杂度几乎为线性。这种加速技术不仅适用于边界部分，更重要的是适用于公式中与域相关的部分。H2 方法的应用不允许使用刚体方法来确定奇异积分和自由积分项。本文展示了如何在此应用中应用 Guigiani 和 Gigante 的技术来处理强奇异积分。此外，参数研究显示了引入的近似参数的影响。为此，我们使用了一个盖子驱动空腔的例子。第二个例子通过模拟管道中的哈根-普绪耶流，展示了所提方法的性能。第三个例子考虑了刚性圆柱体周围的流动，以显示该方法在非结构网格中的行为。所有示例都表明，正如数学分析所预测的那样，所提出的方法几乎具有线性复杂性。

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引用次数: 0

Underwater acoustic scattering of multiple elastic obstacles using T-matrix method 利用 T 矩阵法研究多重弹性障碍物的水下声散射

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-11-09 DOI: 10.1016/j.enganabound.2024.106028

Yuzheng Yang , Qiang Gui , Yingbin Chai , Wei Li

In this paper, the T-matrix method is applied to investigate the monostatic and bistatic far-field acoustic scattering patterns of underwater elastic multi-obstacles, which is a semi-analytical method and its results can be used to verify the accuracy of various numerical methods. The T-matrix formula for underwater multi-obstacle acoustic scattering is obtained by utilizing the addition theorem of the spherical harmonic function. Furthermore, an iterative algorithm is introduced to quickly solve the separation matrix in the addition theorem. The investigation into the far-field acoustic scattering characteristics of a pair of solid elastic spheres covers a full range of scattering angles, revealing that the resonance structure presented in the scattering spectra is attributed to the Rayleigh wave, specular reflections and Franz waves. Finally, experimental validation demonstrates good agreement between the numerical simulation results and experimental results.

本文应用 T 矩阵法研究了水下弹性多障碍物的单静态和双静态远场声散射模式，这是一种半解析方法，其结果可用于验证各种数值方法的准确性。利用球谐函数的加法定理得到了水下多障碍物声散射的 T 矩阵公式。此外，还引入了一种迭代算法来快速求解加法定理中的分离矩阵。对一对实心弹性球的远场声散射特性的研究涵盖了整个散射角范围，揭示了散射谱中呈现的共振结构归因于瑞利波、镜面反射和弗兰兹波。最后，实验验证证明了数值模拟结果与实验结果之间的良好一致性。

引用次数: 0