Engineering Analysis with Boundary Elements最新文献

英文中文

An efficient computational method for solving the fractional form of the European option price PDE with transaction cost under the fractional Heston model 在分式赫斯顿模型下求解带交易成本的欧式期权价格 PDE 分式形式的高效计算方法

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-10-03 DOI: 10.1016/j.enganabound.2024.105972

Panumart Sawangtong , Mehran Taghipour , Alireza Najafi

This paper introduces a new method for precise option pricing analysis by utilizing the fractional form of the option price partial differential equation (PDE) and implementing a collocation technique based on the first Fermat polynomial sequence. The key innovation of this study is the exploration of the fractional formulation of European option pricing within the context of the fractional Heston model, which employs a collocation scheme utilizing Fermat polynomials to generate operational matrices characterized by numerous zeros, thereby enhancing computational efficiency. To achieve this, we first derive the option price PDE and convert it to its fractional form in the Caputo sense. We then solve the fractional PDE using fractional Fermat functions, expressing the solution as a series of multivariate Fermat functions with unknown coefficients. Following this, we compute the operational matrices for the Caputo fractional derivative and related partial derivatives, demonstrating how this computational framework transforms the primary problem into a nonlinear system of equations. Additionally, we conduct a convergence analysis of the collocation method. We conclude by presenting several numerical examples that illustrate the applicability and effectiveness of the proposed method, with its robust theoretical foundations and successful numerical tests indicating significant potential for practical applications in finance.

本文通过利用期权价格偏微分方程（PDE）的分式形式和基于第一费马多项式序列的配位技术，介绍了一种精确期权定价分析的新方法。本研究的主要创新点是在分式赫斯顿模型的背景下探索欧式期权定价的分式表述，利用费马多项式的配位方案生成以众多零为特征的运算矩阵，从而提高计算效率。为此，我们首先推导出期权价格 PDE，并将其转换为 Caputo 意义上的分数形式。然后，我们使用分数费马函数求解分数 PDE，将解法表示为一系列具有未知系数的多元费马函数。随后，我们计算了卡普托分数导数和相关偏导数的运算矩阵，展示了这一计算框架如何将主要问题转化为非线性方程组。此外，我们还对配位法进行了收敛分析。最后，我们列举了几个数值示例，说明了所提方法的适用性和有效性，其坚实的理论基础和成功的数值测试表明了该方法在金融领域的实际应用潜力巨大。

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引用次数: 0

Three-dimensional mesoscale analysis of the dynamic tensile behavior of concrete with heterogeneous mesostructure 具有异质中观结构的混凝土动态拉伸行为的三维中观分析

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-10-01 DOI: 10.1016/j.enganabound.2024.105982

Wenjun Cui , Zhijun Wu , Yang Liu , Penglin Zhang , Lei Weng

This paper investigates the dynamic tensile behavior of concrete under high strain rates. An optimized random concrete mesostructure generation procedure is established using the 3D entrance block (3D E(A, B)) algorithm to account for the intrinsic material heterogeneity. This approach avoids repetitive and complicated polyhedral aggregate overlapping checks in traditional methods, resulting in a highly efficient aggregate packing process. The nucleation, propagation, and coalescence of cracks are captured by a properly developed rate-dependent cohesive constitutive law. The mesoscale model is validated through comparison with experimental results. The crack evolution in the concrete under dynamic direct tensile loading conditions is explicitly presented, and the effects of the aggregate volume fraction and ITZ properties on the dynamic tensile strength enhancements are studied. The results indicate that material heterogeneity significantly influences the fracturing process and damage distribution. The dynamic tensile strength of concrete exhibits a two-strain rate regime dependence on the aggregate volume fraction concerning the strain rate. The influence of the mechanical properties of the ITZ on the dynamic tensile strength of concrete increases with the increasing strain rate.

本文研究了混凝土在高应变速率下的动态拉伸行为。利用三维入口块（三维 E(A,B)）算法建立了优化的随机混凝土中间结构生成程序，以考虑材料的内在异质性。这种方法避免了传统方法中重复而复杂的多面体骨料重叠检查，从而实现了高效的骨料堆积过程。裂缝的成核、扩展和凝聚由一个适当开发的速率依赖性内聚构成法则来捕捉。中尺度模型通过与实验结果的对比得到了验证。明确提出了混凝土在动态直接拉伸加载条件下的裂缝演变，并研究了骨料体积分数和 ITZ 特性对动态拉伸强度增强的影响。结果表明，材料的异质性对断裂过程和损伤分布有显著影响。混凝土的动态抗拉强度表现出与骨料体积分数和应变速率相关的双应变速率机制。随着应变速率的增加，ITZ 的力学性能对混凝土动态抗拉强度的影响也在增加。

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引用次数: 0

Shape optimization with level set-based method using a reaction diffusion equation for 2D sound barrier 利用反应扩散方程，采用基于水平集的方法优化二维声屏障的形状

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-10-01 DOI: 10.1016/j.enganabound.2024.105978

Qiuzi Yu , Fang Zhang , Toshiro Matsumoto , Haibo Chen

A level set-based method using a reaction diffusion equation is applied for optimization problems of two dimensional (2D) sound barriers. The level set method is employed to implicitly represent the sound barrier structure, which distinguishes the material and void domains by the value of the level set function. The boundary element method is employed to solve acoustic problems governed by Helmholtz equation. Topological derivatives are computed by the boundary integral equation combined with the adjoint variable method. The distribution of level set function is iteratively updated based on the reaction diffusion equation to find the optimal structure. For the existent floating scatterers in the optimization process and the sharp and narrow parts on the surface of the sound barrier, we propose a filtering algorithm to remove floating scatterers and develop a method to achieve a smooth surface of the sound barrier. The shape optimization of sound barriers is achieved using these techniques, integrating the level set-based topology optimization method. Numerical tests are provided to demonstrate the validity and effectiveness of the proposed methods.

基于反应扩散方程的水平集方法适用于二维（2D）声屏障的优化问题。采用水平集方法隐式表示声屏障结构，通过水平集函数值区分材料域和空域。边界元法用于解决受亥姆霍兹方程控制的声学问题。拓扑导数是通过边界积分方程结合邻接变量法计算得出的。根据反应扩散方程对水平集函数的分布进行迭代更新，以找到最佳结构。针对优化过程中存在的浮动散射体以及声屏障表面的尖锐和狭窄部分，提出了去除浮动散射体的滤波算法，并开发了实现声屏障表面光滑的方法。利用这些技术，结合基于水平集的拓扑优化方法，实现了声屏障的形状优化。数值测试证明了所提方法的有效性。

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引用次数: 0

A coupled FDEM-CFD method for modelling heat exchange effectiveness in enhanced geothermal systems-excavation 模拟强化地热系统热交换效果的 FDEM-CFD 耦合方法--开挖

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-09-30 DOI: 10.1016/j.enganabound.2024.105980

Taihua Yang , Linjie Gao , Quansheng Liu , Bin Liu , Yuan Zhou , Peng Li

Accurately assessing the impact of hydraulic fracturing technology on the heat exchange efficiency of Enhanced Geothermal Systems (EGS-E) is crucial. This paper proposes a coupled FDEM-CFD method to predict the heat exchange efficiency of EGS-E systems. Firstly, the FDEM method was adopted to establish a numerical model for EGS-E horizontal roadways. The physical process of fracture initiation, propagation, and the eventual formation of a coherent fracture network within intact rock mass were numerically studied. Subsequently, combined with CFD method, the flow and heat exchange processes between cold water and rock in horizontal roadway were investigated. The effects of hydraulic fracturing technology on the heat exchange efficiency of EGS-E project were comprehensively studied by comparing the water-rock heat exchange efficiency before and after fracturing. The results show that, hydraulic fracturing can increase the water-rock heat exchange area by 1385.5710 %, and the temperature difference between inlet and outlet increases by 8.3365 %. It shows that hydraulic fracturing improves the heat exchange efficiency of EGS-E.

准确评估水力压裂技术对强化地热系统（EGS-E）热交换效率的影响至关重要。本文提出了一种 FDEM-CFD 耦合方法来预测 EGS-E 系统的热交换效率。首先，采用 FDEM 方法建立了 EGS-E 水平巷道的数值模型。数值研究了完整岩体中断裂萌生、传播以及最终形成连贯断裂网络的物理过程。随后，结合 CFD 方法，研究了水平巷道中冷水与岩石之间的流动和热交换过程。通过对比压裂前后的水岩热交换效率，全面研究了水力压裂技术对 EGS-E 工程热交换效率的影响。结果表明，水力压裂可使水岩热交换面积增加 1385.5710%，进出口温差增加 8.3365%。这表明水力压裂提高了 EGS-E 的热交换效率。

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引用次数: 0

Optimisation of open pit slope design considering groundwater effects using particle swarm optimisation and scaled boundary finite element method 利用粒子群优化和比例边界有限元法优化考虑地下水影响的露天矿边坡设计

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-09-27 DOI: 10.1016/j.enganabound.2024.105976

Dakshith Ruvin Wijesinghe , Ethmadalage Perera , Ean Hin Ooi , Sundararajan Natarajan , Taghi Sherizadeh , Ean Tat Ooi

Slopes are a crucial structures in open pit mines. Their design has implications on the economic, safety and environmental operation of the mining industry. Designing stable slopes can be challenging due to the complexities introduced by the stratigraphy and hydrology of the strata. With rising commodity costs and inflation rates, mining operating costs are increasing. Reducing operational costs is necessary for mining industries to remain competitive. While steepening the pit slope can decrease stripping materials and save money, it also increases the risk associated with slope surges. Therefore, optimising slopes is crucial for both financial and safety reasons. Numerical models such as the finite element method experience challenges in mesh generation of heterogeneous systems characterised by varying material properties and stratigraphies. Moreover, the need for repetitive geometry update necessitates recursive mesh regeneration that increases the computational burden. Moreover, previous slope optimisation studies focus solely on dry conditions. To consider the complex condition of hydrology along with heterogeneity in the soil stratigraphy, this study develops an optimisation procedure by combining the particle swarm optimisation algorithm and the scaled boundary finite element with an image-based meshing technique to optimise slopes with groundwater and achieve the desired factor of safety (FoS). The method changes the slope design parameters and the phreatic surface of groundwater simultaneously, considering user-defined parameters while iteratively re-meshing the optimisation processes. Several cases are presented, demonstrating the optimisation of bench width, bench angle, backfill parameters, and groundwater pumping levels.

边坡是露天矿的重要结构。它们的设计对采矿业的经济、安全和环境运行都有影响。由于地层和水文条件的复杂性，设计稳定的边坡具有很大的挑战性。随着商品成本和通货膨胀率的上升，采矿业的运营成本也在不断增加。降低运营成本是采矿业保持竞争力的必要条件。虽然陡化矿坑边坡可以减少剥离材料并节约成本，但同时也会增加与边坡涌水相关的风险。因此，出于经济和安全考虑，优化边坡至关重要。有限元法等数值模型在生成具有不同材料特性和地层特征的异质系统的网格时遇到了挑战。此外，由于需要重复更新几何形状，因此必须进行递归网格再生，从而增加了计算负担。此外，以往的边坡优化研究仅关注干旱条件。为了考虑复杂的水文条件和土壤地层的异质性，本研究开发了一种优化程序，将粒子群优化算法和缩放边界有限元与基于图像的网格技术相结合，以优化有地下水的边坡，并达到所需的安全系数（FoS）。该方法在迭代重新网格化优化过程中，考虑用户定义的参数，同时改变边坡设计参数和地下水的喷涌面。文中介绍了几个案例，展示了对台阶宽度、台阶角度、回填参数和地下水抽水水平的优化。

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引用次数: 0

A novel meshless numerical simulation of oil-water two-phase flow with gravity and capillary forces in three-dimensional porous media 三维多孔介质中带有重力和毛细力的油水两相流的新型无网格数值模拟

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-09-26 DOI: 10.1016/j.enganabound.2024.105975

Wentao Zhan , Hui Zhao , Yuyang Liu , Zhijie Wei , Xiang Rao

This paper presents a novel fully implicit scheme for simulating three-dimensional (3D) oil-water two-phase flow with gravity and capillary forces using the meshless generalized finite difference method (GFDM). The approach combines an implicit Eulerian scheme in time with a GFDM discretization method in space to compute implicit solutions for the pressure and saturation in the flow control equations. The research introduces an L² norm error formula and conducts a sensitivity analysis on the impact of varying influence domain radii on computational accuracy within the Cartesian node collocation scheme. Findings suggest that larger influence domain radii correspond to reduced computational accuracy, providing a preliminary guideline for selecting the domain radius in 3D GFDM applications. Overall, this paper presents an effective and precise meshless method for addressing two-phase flow challenges in 3D porous media, highlighting the promising prospects of GFDM in numerical simulations.

本文提出了一种新颖的全隐式方案，利用无网格广义有限差分法（GFDM）模拟具有重力和毛细力的三维（3D）油水两相流。该方法结合了时间上的隐式欧拉方案和空间上的 GFDM 离散方法，以计算流量控制方程中压力和饱和度的隐式解。研究引入了 L2 准则误差公式，并对笛卡尔节点配置方案中不同影响域半径对计算精度的影响进行了敏感性分析。研究结果表明，影响域半径越大，计算精度越低，这为在三维 GFDM 应用中选择影响域半径提供了初步指导。总之，本文提出了一种有效而精确的无网格方法来解决三维多孔介质中的两相流难题，凸显了 GFDM 在数值模拟中的广阔前景。

{"title":"A novel meshless numerical simulation of oil-water two-phase flow with gravity and capillary forces in three-dimensional porous media","authors":"Wentao Zhan , Hui Zhao , Yuyang Liu , Zhijie Wei , Xiang Rao","doi":"10.1016/j.enganabound.2024.105975","DOIUrl":"10.1016/j.enganabound.2024.105975","url":null,"abstract":"<div><div>This paper presents a novel fully implicit scheme for simulating three-dimensional (3D) oil-water two-phase flow with gravity and capillary forces using the meshless generalized finite difference method (GFDM). The approach combines an implicit Eulerian scheme in time with a GFDM discretization method in space to compute implicit solutions for the pressure and saturation in the flow control equations. The research introduces an <em>L</em><sup>2</sup> norm error formula and conducts a sensitivity analysis on the impact of varying influence domain radii on computational accuracy within the Cartesian node collocation scheme. Findings suggest that larger influence domain radii correspond to reduced computational accuracy, providing a preliminary guideline for selecting the domain radius in 3D GFDM applications. Overall, this paper presents an effective and precise meshless method for addressing two-phase flow challenges in 3D porous media, highlighting the promising prospects of GFDM in numerical simulations.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"169 ","pages":"Article 105975"},"PeriodicalIF":4.2,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Multi-dimensional modeling of solitary wave–structure interaction problems by using a δ-LES-SPH model 利用 δ-LES-SPH 模型对孤波-结构相互作用问题进行多维建模

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-09-25 DOI: 10.1016/j.enganabound.2024.105965

Tihan Fu , Dianlei Feng , Jifu Yin , Can Yi , Jianyu Chen

The interaction mechanisms between waves and marine structures are a popular research topic. This paper applies the weakly compressible smoothed particle hydrodynamics (WCSPH) method to study the dynamics of green water overtopping. To enhance the accuracy of the simulations, the SPH method coupled with the large eddy simulation (LES) model is employed for numerical investigations. Initially, we validate the effectiveness of the model by simulating the generation of solitary waves and irregular waves, as well as numerically reproducing the water surface morphology during the interaction between solitary waves and the deck. Subsequently, the validated model is used to study the dynamic characteristics of different types of waves overtopping, revealing significant variations in their motion. Furthermore, we investigate the effect of deck roughness during the entire green water overtopping process in terms of both protrusions extent and distribution, confirming that a reasonable setting of the protrusions can greatly reduce the wave impact loads on the deck, thereby protecting the structure. Additionally, a three-dimensional model is developed to study the green water problem, and we find that the turbulence phenomenon is more pronounced in the three-dimensional scenario.

波浪与海洋结构之间的相互作用机制是一个热门研究课题。本文采用弱可压缩平滑粒子流体力学（WCSPH）方法研究绿水倾覆动力学。为了提高模拟的准确性，采用了 SPH 方法与大涡流模拟（LES）模型相结合进行数值研究。首先，我们通过模拟孤波和不规则波的产生来验证模型的有效性，并在数值上再现了孤波与甲板相互作用时的水面形态。随后，我们利用经过验证的模型研究了不同类型波浪倾覆时的动态特征，发现了其运动的显著变化。此外，我们还从突起物的范围和分布两方面研究了整个绿水倾覆过程中甲板粗糙度的影响，证实合理设置突起物可大大降低波浪对甲板的冲击载荷，从而保护结构。此外，我们还建立了一个三维模型来研究绿水问题，我们发现在三维场景下湍流现象更加明显。

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引用次数: 0

A mesh-free method using Pascal polynomials for analyzing space-fractional PDEs in irregular biological geometries 利用帕斯卡多项式的无网格方法分析不规则生物几何中的空间分式 PDEs

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-09-25 DOI: 10.1016/j.enganabound.2024.105932

Mostafa Abbaszadeh , Mohammad Ivan Azis , Mehdi Dehghan

In recent years, various numerical methods, including finite difference method (FDM), finite volume method (FVM), and finite element method (FEM), have been devised to solve time-fractional PDEs, on different computational geometries. However, owing to the presence of integrals in the definition of space-fractional PDEs (SFPDEs), only a few numerical procedures have been developed for solving SFPDEs on irregular regions. This limitation arises because a Gauss–Legendre quadrature must be employed to approximate certain integrals in the calculation of fractional derivatives. The present paper introduces a novel numerical solution based upon Pascal polynomials and a multiple-scale idea. The strength of this technique lies in the construction of Pascal polynomials from monomials. The Pascal polynomials will be employed for estimating the spatial derivatives of SFPDEs on different non-rectangular physical areas.

近年来，人们设计了各种数值方法，包括有限差分法（FDM）、有限体积法（FVM）和有限元法（FEM），用于求解不同计算几何条件下的时间分式 PDE。然而，由于空间分式 PDEs（SFPDEs）的定义中存在积分，目前仅开发了少数数值程序用于求解不规则区域上的 SFPDEs。造成这种限制的原因是，在计算分数导数时，必须使用高斯-勒格正交来近似某些积分。本文介绍了一种基于帕斯卡多项式和多尺度思想的新型数值解法。这种技术的优势在于从单项式构造帕斯卡多项式。帕斯卡多项式将用于估算不同非矩形物理区域的 SFPDE 空间导数。

引用次数: 0

Nonlinear NMM analysis for large deformation and contact problems: Using full strain-rotation decomposition algorithm and augmented Lagrangian method enhanced open-closed iteration 大变形和接触问题的非线性 NMM 分析：使用全应变旋转分解算法和增强型拉格朗日法增强开闭迭代法

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-09-25 DOI: 10.1016/j.enganabound.2024.105971

Wenshuai Han , Shuhong Wang , Wenfang Liu , Wenpan Sun , Qinkuan Hou

Nonlinear analysis deals with problems that involve large displacements, strains, rotations, and contact problems. Accurate results can be obtained by choosing a reasonable method for decomposing strain and rotation to avoid errors and ensure the correct contact force. A novel full strain-rotation (S-R) decomposition and an augmented Lagrangian enhanced contact model are established within the numerical manifold method (NMM) framework. Limitations in simplified S-R NMM are overcome using our redesigned resolution procedure. A new method has been applied to analyse beams with large deflections, block columns under compression, block sliding, rock falling, and semi-ring contact with block problems. Promising results from the analysis indicate that proposed method is more accurate and effective in theory and numerically than prior approaches when resolving contact problems and large deformations.

非线性分析处理的问题涉及大位移、大应变、大旋转和大接触问题。选择合理的应变和旋转分解方法可以避免误差并确保正确的接触力，从而获得精确的结果。在数值流形法（NMM）框架内，建立了新颖的全应变-旋转（S-R）分解和增强拉格朗日增强接触模型。利用我们重新设计的解析程序，克服了简化 S-R NMM 的局限性。新方法已被用于分析大挠度梁、受压块柱、块体滑动、落石以及块体半环接触问题。分析结果表明，在解决接触问题和大变形问题时，所提出的方法在理论上和数值上都比以前的方法更加精确和有效。

引用次数: 0

Kernel-based learning methods for stochastic partial differential equations 基于核的随机偏微分方程学习方法

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2024-09-24 DOI: 10.1016/j.enganabound.2024.105960

Qi Ye

This article delves into the study of kernel-based learning methods for stochastic partial differential equations. The theory of generalized data and kernel-based probability measures is introduced to construct kernel-based learning estimators, kernel-based learning functions, and discrete kernel-based learning solutions for addressing stochastic differentials, elliptic stochastic partial differential equations, and parabolic stochastic partial differential equations, respectively. The convergence theorems of kernel-based learning algorithms are demonstrated by combining meshfree approximation and kriging interpolation. Moreover, the numerical examples show the efficiency and robustness of kernel-based learning algorithms using various positive definite kernels.

本文深入研究了基于核的随机偏微分方程学习方法。文章介绍了广义数据和基于核的概率度量理论，分别针对随机微分方程、椭圆随机偏微分方程和抛物线随机偏微分方程构建了基于核的学习估计器、基于核的学习函数和基于核的离散学习解。通过结合无网格逼近和克里格插值，证明了基于内核学习算法的收敛定理。此外，数值示例显示了使用各种正定核的基于核的学习算法的效率和鲁棒性。

引用次数: 0

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