Computer Methods in Applied Mechanics and Engineering最新文献_第2页

Estimation based simulation on nodal networks: A novel interpolation-free approach for solution of structural mechanics problems 基于节点网络估计的模拟：一种解决结构力学问题的无插值新方法

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-24 DOI: 10.1016/j.cma.2025.118684

Suhas A. Kowshik , Arun R. Srinivasa , Saikat Sarkar , J.N. Reddy

We introduce a new numerical method for solving mechanics problems, called Estimation-Based Direct Simulation on Nodal Networks (EDISONN), which can be applied to any weak form, variational, or virtual work-based formulation of the underlying differential equation. The approach can utilize either traditional unstructured meshes or point clouds, but eschews the interpolation of field variables. Instead, the variational or weak form problem is first subject to a nodal quadrature; Then, based on ideas from stochastic estimation of gradients, a nodal gradient operator (Matrix) is defined for estimating the gradients of the field variables at nodes using adjacent nodal values. We show that the method has comparable accuracy to a quadrilateral mesh with one-point integration or a constant strain triangular (CST) mesh. We also show that the approach can be used without any modification for nearly incompressible solids (no volumetric locking) or nonlinear deformations of thick or thin plates (no shear or membrane locking). Even simple unstructured triangular grid generators can be used for first-order shear deformation models for plates (FSDT), and they do not have locking issues, even with thickness ratios of 1/100 or 1/1000. Furthermore, Since the approach eliminates the need for Gauss points and directly utilizes nodal quadrature, the total number of gradient calculations required is equal to the number of nodes, thereby reducing computations.

我们介绍了一种新的数值方法来解决力学问题，称为基于估计的节点网络直接模拟（edionn），它可以应用于任何弱形式、变分形式或基于虚功的底层微分方程公式。该方法既可以利用传统的非结构化网格，也可以利用点云，但避免了场变量的插值。相反，变分或弱形式问题首先受制于节点正交；然后，基于梯度随机估计的思想，定义了一个节点梯度算子（矩阵），用于利用相邻节点值估计节点处场变量的梯度。我们表明，该方法具有相当的精度四边形网格与一点积分或恒应变三角形（CST）网格。我们还表明，该方法可以在没有任何修改的情况下用于几乎不可压缩的固体（没有体积锁定）或厚板或薄板的非线性变形（没有剪切或膜锁定）。即使是简单的非结构化三角形网格发生器也可以用于板的一阶剪切变形模型（FSDT），并且它们没有锁定问题，即使厚度比为1/100或1/1000。此外，由于该方法不需要高斯点，直接利用节点正交，因此所需的梯度计算总数等于节点数，从而减少了计算量。

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引用次数: 0

Embedding structures in continua: Linear models and finite element discretizations 连续体中的嵌入结构：线性模型和有限元离散化

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-24 DOI: 10.1016/j.cma.2025.118683

David Portillo , Ignacio Romero

This work describes models and numerical approximations that describe the mechanical behavior of deformable continua with embedded structural members, such as rigid bodies, beams, shells, etc. The continuum formulation extends an idea first presented in the context of the Arlequin method and constrains the kinematics of the two types of bodies to be compatible in the energy sense. In the article, we exploit the shared similarities of all structural theories to introduce a general framework for energetically coupling the latter with continua. In addition, we show that the problems, as well as their finite element approximations, are well-posed. Numerical examples of bodies with inclusions, fibers, and embedded surfaces are provided to illustrate the generality and robustness of the approach.

这项工作描述了模型和数值近似，描述了具有嵌入结构构件（如刚体，梁，壳等）的可变形连续体的力学行为。连续体公式扩展了最初在Arlequin方法中提出的思想，并约束了两类物体的运动学在能量意义上是相容的。在本文中，我们利用所有结构理论的共同相似性来引入后者与连续体能量耦合的一般框架。此外，我们还证明了这些问题及其有限元近似是适定的。给出了带有夹杂物、纤维和嵌入表面的物体的数值例子，以说明该方法的通用性和鲁棒性。

引用次数: 0

Extended discrete material optimization: A generalized framework for multi-material topology optimization of nonlinear material constitutive models 扩展离散材料优化：非线性材料本构模型多材料拓扑优化的广义框架

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-23 DOI: 10.1016/j.cma.2025.118682

Jike Han , Kazuhiro Izui , Shinji Nishiwaki

Multi-material topology optimization (MMTO) has been widely studied for designing structures composed of multiple materials to achieve optimal performance. However, conventional MMTOs, typically based on parameter interpolation, are limited to materials governed by the same material constitutive model. In particular, they require the energy density function, evolution laws for inelastic strains, and material parameters to share a common form across all base materials, which fundamentally restricts their applicability to nonlinear materials with distinct behaviors. To overcome this limitation, we propose an extended discrete material optimization (XDMO) framework that generalizes MMTO based on the original concept of DMO. The key idea of XDMO is to interpolate the governing equations and evolution laws (or, conceptually, the potential energy) that define the mechanical response of each base material. This formulation enables the unified treatment of a broad range of nonlinear and irreversible materials, such as those exhibiting plasticity or damage, within a single optimization problem. For generality, the primal, adjoint, and sensitivity equations are derived in an abstract form without assuming specific material models, and the formulation is independent of temporal or spatial discretization schemes. Numerical examples demonstrate the versatility of XDMO in stiffness maximization and plastic dissipation-based design problems. The proposed framework thus represents a significant step toward generalizing MMTO and provides a new pathway for topology optimization involving nonlinear and irreversible material behaviors.

多材料拓扑优化（MMTO）被广泛研究，用于设计由多种材料组成的结构以达到最佳性能。然而，通常基于参数插值的传统mmto仅限于由相同材料本构模型控制的材料。特别是，它们要求能量密度函数、非弹性应变演化规律和材料参数在所有基材中具有共同的形式，这从根本上限制了它们对具有不同行为的非线性材料的适用性。为了克服这一限制，我们提出了一个扩展的离散材料优化（XDMO）框架，该框架基于DMO的原始概念对MMTO进行了推广。XDMO的关键思想是插入定义每种基材的机械响应的控制方程和演化定律（或者，从概念上讲，势能）。该配方能够在单个优化问题中统一处理广泛的非线性和不可逆材料，例如那些表现出可塑性或损伤的材料。为了通用性，原始方程、伴随方程和灵敏度方程以抽象形式推导，不假设特定的材料模型，并且公式独立于时间或空间离散化方案。数值算例证明了XDMO在刚度最大化和基于塑性耗散的设计问题中的通用性。因此，所提出的框架代表了向MMTO推广迈出的重要一步，并为涉及非线性和不可逆材料行为的拓扑优化提供了新的途径。

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引用次数: 0

I-FENN with DeepONets: Accelerating simulations in coupled multiphysics problems I-FENN与DeepONets：耦合多物理场问题的加速模拟

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-23 DOI: 10.1016/j.cma.2025.118645

Fouad M. Amin , Diab W. Abueidda , Panos Pantidis , Mostafa E. Mobasher

Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the Finite Element Method (FEM) to address coupled thermoelasticity and poroelasticity problems. This integration occurs within the context of the I-FENN framework, where a neural network (NN) is coupled with FEM in a hybrid staggered solver. In this approach, FEM computes the mechanical field while the NN predicts the coupled field, effectively reducing the number of FEM unknowns and lowering the overall computational cost. The proposed work introduces a new I-FENN architecture with extended generalizability due to the DeepONets’ ability to efficiently address several combinations of natural boundary conditions and body loads. A modified DeepONet architecture is introduced to accommodate multiple inputs, along with a streamlined strategy for enforcing boundary conditions on distinct boundaries. We showcase the applicability and merits of the proposed work through numerical examples covering thermoelasticity and poroelasticity problems, demonstrating computational efficiency, accuracy, and generalization capabilities. In all examples, the test cases involve unseen loading conditions. The computational savings scale with the model complexity while preserving an accuracy of more than 95 % in the non-trivial regions of the domain.

对于高维、大规模问题的耦合多物理场模拟由于其计算需求可能会非常昂贵。本文提出了一种将深度算子网络（DeepONet）与有限元方法（FEM）相结合的新框架来解决热弹性和孔隙弹性耦合问题。这种集成发生在I-FENN框架的背景下，其中神经网络（NN）在混合交错求解器中与FEM耦合。该方法采用有限元法计算力学场，神经网络预测耦合场，有效地减少了有限元法的未知量，降低了整体计算成本。由于DeepONets能够有效地处理自然边界条件和身体负载的几种组合，因此提出了一种具有扩展泛化能力的新I-FENN架构。引入改进的DeepONet架构以适应多个输入，以及在不同边界上执行边界条件的精简策略。我们通过涵盖热弹性和孔隙弹性问题的数值示例展示了所提出工作的适用性和优点，展示了计算效率，准确性和泛化能力。在所有的例子中，测试用例都包含了看不见的加载条件。计算节省与模型复杂度成正比，同时在域的非平凡区域保持95%以上的精度。

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引用次数: 0

Geometry-informed neural operator transformer for partial differential equations on arbitrary geometries 任意几何上偏微分方程的几何信息神经算子变换

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-23 DOI: 10.1016/j.cma.2025.118668

Qibang Liu , Weiheng Zhong , Hadi Meidani , Diab Abueidda , Seid Koric , Philippe Geubelle

Machine-learning-based surrogate models offer significant computational efficiency and faster simulations compared to traditional numerical methods, especially for problems requiring repeated evaluations of partial differential equations. This work introduces the Geometry-Informed Neural Operator Transformer (GINOT), which integrates the transformer architecture with the neural operator framework to enable forward predictions on arbitrary geometries. GINOT employs a sampling and grouping strategy together with an attention mechanism to encode surface point clouds that are unordered, exhibit non-uniform point densities, and contain varying numbers of points for different geometries. The geometry information is seamlessly integrated with query points in the solution decoder through the attention mechanism. The performance of GINOT is validated on multiple challenging datasets, showcasing its accuracy and generalization capabilities for complex and arbitrary 2D and 3D geometries.

与传统数值方法相比，基于机器学习的代理模型提供了显著的计算效率和更快的模拟速度，特别是对于需要反复评估偏微分方程的问题。这项工作介绍了几何信息神经算子变压器（GINOT），它将变压器架构与神经算子框架集成在一起，可以对任意几何进行前向预测。GINOT采用采样和分组策略以及注意机制来编码无序的表面点云，表现出不均匀的点密度，并且包含不同几何形状的不同数量的点。几何信息通过注意机制与解解码器中的查询点无缝集成。GINOT的性能在多个具有挑战性的数据集上进行了验证，展示了其对复杂和任意2D和3D几何形状的准确性和泛化能力。

引用次数: 0

Surface lattice structure design via computational conformal mapping and structural optimization 通过计算保角映射和结构优化设计表面点阵结构

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-23 DOI: 10.1016/j.cma.2025.118680

Chang Liu , Wu Xu , Wendong Huo , Yilin Guo , Xu Guo

This paper presents a novel approach for optimizing graded lattice structures embedded in curved shell surfaces, combining computational conformal mapping (CCM) with structural optimization. Using the moving morphable components framework, we define the topological configuration of lattice structures with few geometry-related design variables, which reduces computational complexity. Partitioned coordinate mapping, constructed with the B-spline basis functions, enables the non-uniform lattice structures generation with smooth transitions between neighboring unit cells. Furthermore, CCM-based mesh parameterization maps general triangulated surfaces to a planar domain with low distortion, on which we define the MMC-based topology description function (TDF) for the graded lattice with closed-form, adjoint-consistent derivatives and seam-safe continuity. This integrated approach simultaneously optimizes the shape and size of lattice structures on curved surfaces, preserving structural boundary clarity without filtering operators while balancing aesthetic appearance with structural performance. The proposed method provides an efficient pathway for the optimization of complex graded lattice structures embedded in curved surfaces.

将计算保角映射（CCM）与结构优化相结合，提出了一种优化嵌入在弯曲壳体表面的梯度点阵结构的新方法。采用移动可变形构件框架，定义了晶格结构的拓扑构型，减少了几何相关的设计变量，降低了计算复杂度。利用b样条基函数构造的分块坐标映射，实现了相邻单元胞间平滑过渡的非均匀点阵结构生成。此外，基于ccm的网格参数化将一般三角曲面映射到具有低畸变的平面域，并在此基础上定义了具有封闭形式、伴随一致导数和接缝安全连续性的梯度晶格的基于mmc的拓扑描述函数（TDF）。这种集成的方法同时优化了曲面上晶格结构的形状和大小，在不过滤算子的情况下保持结构边界的清晰度，同时平衡了美学外观和结构性能。该方法为嵌入曲面的复杂梯度点阵结构的优化提供了一条有效途径。

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引用次数: 0

A stabilized finite element formulation for simulating ordered arrays of immersed flexible fibers with applications in cellular mechanics 一种用于模拟浸入式柔性纤维有序排列的稳定有限元公式及其在细胞力学中的应用

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-23 DOI: 10.1016/j.cma.2025.118659

Stylianos Varchanis, David B. Stein

We present a new computational tool for the simulation of aligned assemblies of thin, bendable, but inextensible fibers immersed in a linear Stokes fluid. Such systems are of great importance in cellular mechanics because they arise in many intracellular (e.g., cytoskeleton-cytoplasm interactions) and extracellular (e.g., ciliary locomotion) microscale biological processes. The fiber bed is represented as an anisotropic poroelastic medium that obeys the Euler-Bernoulli beam theory and is hydrodynamically coupled to the viscous fluid through local-slender body theory. We develop two methodologies to solve the resulting fluid-structure interaction problem: (1) a classical approach where the solid is solved in the Lagrangian frame, and the fluid is solved using an Arbitrary-Lagrangian-Eulerian (ALE) method, and (2) a novel approach where the solid equations are expressed in the Eulerian frame and the fiber-fluid system is solved together using an ALE method. In both cases, the resulting set of equations is approximated using a Petrov-Galerkin stabilized finite element method specifically designed for the fiber-fluid interaction problem. Equal-order continuous finite elements are used for the spatial discretization of the deforming physical domain, and finite differences are used for temporal discretization. Both approaches are shown to be numerically stable and convergent at the expected order; and additionally, the pure ALE method can resolve extreme fiber deformations without the need for mesh reconstruction. Finally, our methods are validated by direct comparisons to discrete fiber simulations in two benchmark tests: (a) the shearing of an anchored fiber bed and (b) the emergence and evolution of cell-spanning vortices in cellular geometries.

我们提出了一种新的计算工具，用于模拟在线性斯托克斯流体中浸入的可弯曲但不可扩展的薄纤维的排列组件。这些系统在细胞力学中非常重要，因为它们出现在许多细胞内（如细胞骨架-细胞质相互作用）和细胞外（如纤毛运动）的微尺度生物过程中。纤维床层按照欧拉-伯努利梁理论表示为各向异性孔隙弹性介质，并通过局部细长体理论与粘性流体进行流体动力耦合。我们开发了两种方法来解决由此产生的流固耦合问题：(1)在拉格朗日框架中求解固体，并使用任意拉格朗日-欧拉（ALE）方法求解流体的经典方法；(2)在欧拉框架中表示固体方程，并使用ALE方法求解纤维-流体系统。在这两种情况下，所得到的方程组都是使用专门为纤维-流体相互作用问题设计的Petrov-Galerkin稳定有限元法进行近似的。等阶连续有限元用于变形物理域的空间离散化，有限差分用于时间离散化。这两种方法在数值上都是稳定的，并且在期望阶上收敛；此外，纯ALE方法可以在不需要网格重建的情况下解决极端纤维变形。最后，我们的方法通过两个基准测试（a)锚定纤维床的剪切和(b)细胞几何中细胞跨越漩涡的出现和演变）与离散纤维模拟的直接比较得到验证。

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引用次数: 0

A higher-order time-domain boundary element formulation based on isogeometric analysis and the convolution quadrature method 基于等几何分析和卷积求积法的高阶时域边界元公式

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-22 DOI: 10.1016/j.cma.2025.118609

T. Kramer, B. Marussig, M. Schanz

An isogeometric boundary element method (BEM) is presented to solve scattering problems in an isotropic, homogeneous medium. We consider wave propagation problems governed by the scalar wave equation as in acoustics and the Lamé-Navier equations for elastodynamics considering the theory of linear elasticity. The underlying boundary integral equations imply time-dependent convolution integrals and allow us to determine the sought quantities in the bounded interior or the unbounded exterior after solving for the unknown Cauchy data. In the present work, the time-dependent convolution integrals are approximated by multi-stage Runge-Kutta (RK)-based convolution quadratures that involve steady-state solutions in the Laplace domain. The proposed method discretizes the spatial variable in the framework of isogeometric analysis (IGA), entailing a patchwise smooth spline basis. While previous studies have struggled to develop higher-order discretization methods for evolutionary boundary value problems, the present work introduces a novel combination of multi-stage RK-based convolution quadratures and isogeometric spatial approximation, yielding a fully higher-order method with high convergence rates in both space and time. The implementation scheme follows an element structure defined by the non-empty knot spans in the knot vectors and local, uniform Bernstein polynomials as basis functions. The algorithms to localize the basis functions on the elements are outlined and explained. The solutions of the mixed problems are approximated by the BEM based on a symmetric Galerkin variational formulation and a collocation method. We investigate convergence rates of the approximate solutions in a mixed space-and-time error norm.

提出了一种求解各向同性均匀介质散射问题的等几何边界元法。我们考虑由声学中的标量波动方程和考虑线弹性理论的弹性动力学中的lam - navier方程控制的波传播问题。潜在的边界积分方程意味着时间相关的卷积积分，并允许我们在求解未知的柯西数据后确定有界内部或无界外部的求量。在目前的工作中，时间相关的卷积积分是由多阶段龙格-库塔（RK）为基础的卷积正交近似，涉及稳态解在拉普拉斯域。该方法在等几何分析（IGA）框架中离散化空间变量，得到一个拼接光滑样条基。虽然以前的研究一直在努力开发用于进化边值问题的高阶离散化方法，但本研究引入了一种基于rq的多阶段卷积正交和等几何空间近似的新组合，从而产生了一种在空间和时间上都具有高收敛率的全高阶方法。实现方案遵循由结向量中的非空结跨度和局部一致Bernstein多项式作为基函数定义的单元结构。对基函数在元素上的定位算法进行了概述和说明。基于对称伽辽金变分公式和配点法，用边界元逼近了混合问题的解。研究了混合时空误差范数下近似解的收敛速率。

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引用次数: 0

Neural network-enriched RKPM for dynamics based on action minimization 基于动作最小化的基于神经网络的动态RKPM

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-22 DOI: 10.1016/j.cma.2025.118662

Yanran Wang , Jiun-Shyan Chen , Samuel E. Casebolt

Conventional numerical methods for dynamic problems can be computationally intensive when addressing localized features where local adaptive refinement is needed. Local adaptive refinement is tedious in meeting the regularity requirements, and the analytical enrichment functions to capture local features are often unavailable. These complexities become even more pronounced in transient problems. This work introduces a neural network-enriched Reproducing Kernel Particle Method (NN-RKPM) for solving dynamic problems based on action minimization under a symplectic space-time framework. In this approach, RKPM is employed in the background spatial discretization and approximation, and the background solution is adaptively enriched with neural network basis functions. With NN-RKPM, the dynamic problem is solved as an optimization problem, with the time domain interpolation constructed using

C^{0}

or

C^{1}

temporal polynomials. The neural network enrichment functions are pre-trained during the offline stage to learn specific local features through Ritz-type energy minimization. The evolution of the background RKPM and NN enriched time-dependent solution is driven by minimizing the action functional under a symplectic formulation of mechanics for a Newtonian four-space, applied to various elastodynamics problems. The proposed method offers a unified framework consistent with the classical field theory and has been shown to accurately capture the time-dependent response of mechanical systems.

传统的动态问题数值方法在处理需要局部自适应细化的局部特征时计算量很大。局部自适应细化在满足正则性要求时是繁琐的，并且通常无法获得捕获局部特征的分析富集函数。这些复杂性在暂态问题中变得更加明显。在辛时空框架下，提出了一种基于动作最小化的神经网络再生核粒子方法（NN-RKPM）。该方法将RKPM用于背景空间离散和逼近，并自适应地丰富了神经网络基函数。NN-RKPM将动态问题作为一个优化问题来解决，并使用C0或C1时间多项式构造时域插值。在离线阶段对神经网络富集函数进行预训练，通过Ritz-type能量最小化来学习特定的局部特征。背景RKPM和NN富时变解的演变是通过最小化牛顿四空间力学辛公式下的作用泛函来驱动的，并应用于各种弹性动力学问题。提出的方法提供了一个与经典场论一致的统一框架，并已被证明可以准确地捕获机械系统的时变响应。

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引用次数: 0

Mass-lumping technique for fully explicit time integration of the shifted-basis variant of the 3D extended finite element method 三维扩展有限元法移基变形的全显式时间积分质量集总技术

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-22 DOI: 10.1016/j.cma.2025.118636

Louis Scheidt , Jean-Philippe Crété , Patrice Longère

A diagonalization technique of the mass matrix in the context of the shifted-basis variant of the extended finite element method (SBXFEM) is proposed based on a mass scaling factor imposed on the enriched part of the mass matrix. The objective is to be able to perform 3D fully explicit analysis involving ductile damage and fracture process, within the framework of large deformation and high strain rates, including but not limited to, high-velocity impacts and shocks. Furthermore, the developed methodology is compatible with implementation in a commercial finite element software package, specifically Abaqus in the context of this work. At the element scale the mass-scaling factor helps to minimize the error in kinetic energy to ensure accurate results while, considering complex structures, the ill-conditioning of the diagonalized enriched mass matrix tends to vanish. The accuracy and efficiency of the technique are assessed through both analytical investigations and numerical validations using 1D and 3D benchmark examples.

提出了一种在扩展有限元法（SBXFEM）移基变型中，基于质量矩阵富集部分施加质量标度因子的质量矩阵对角化技术。目标是能够在大变形和高应变率的框架下，包括但不限于高速撞击和冲击，进行涉及延性损伤和断裂过程的3D完全明确分析。此外，所开发的方法与商业有限元软件包中的实现兼容，特别是在本工作的背景下的Abaqus。在单元尺度上，质量标度因子有助于最小化动能误差以保证结果的准确性，而在考虑复杂结构时，对角化富集质量矩阵的病态趋于消失。通过分析研究和使用1D和3D基准示例的数值验证，评估了该技术的准确性和效率。

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引用次数: 0