Computer-Aided Design最新文献

Conditioned Numerical Shape Functions on Unfitted Reduced Coarse Elements for Robust Analysis of Complex Solid Structures 复杂实体结构鲁棒分析中非拟合简化粗单元的条件数值形状函数

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer-Aided Design

Pub Date : 2026-01-16 DOI: 10.1016/j.cad.2026.104038

Wei Chen, Ming Li

The unfitted finite element (FE) methods offer significant advantages in engineering analysis by embedding the structure within a simple background mesh and eliminating the need for complex and labor-intensive mesh generation. A high solution accuracy can still be achieved via constructing, on each coarse element, standard polynomial shape functions, or numerical (piecewise) shape functions. However, the strategy incurs significant technical challenges due to the unavoidable occurrence of cut elements of arbitrarily small size that may greatly deteriorate the condition number of the stiffness matrix. To address the issue, we propose the concept of reduced coarse elements. By formulating high-order numerical shape functions as the product of a boundary interpolator and a boundary–interior mapping, a detailed condition number analysis reveals the dependence of the numerical shape function conditioning on the boundary interpolator. Based on these findings, we develop a new type of reduced coarse elements and their associated numerical shape functions to address the conditioning challenges. The stability, accuracy, convergence rate, and efficiency of the approach are tested through various numerical examples in comparison with other cutting-edge approaches. Its performance on a multi-material printed circuit board (PCB) example of 183 million fine mesh nodes is also tested.

非拟合有限元（FE）方法通过将结构嵌入简单的背景网格中，消除了复杂和劳动密集型网格生成的需要，在工程分析中具有显著的优势。通过在每个粗元上构造标准多项式形状函数或数值（分段）形状函数，仍然可以获得较高的解精度。然而，由于不可避免地会出现任意小尺寸的切削元件，这可能会大大降低刚度矩阵的条件数，因此该策略面临着重大的技术挑战。为了解决这个问题，我们提出了简化粗元素的概念。通过将高阶数值形状函数表述为边界插值器与边界-内映射的乘积，详细分析了数值形状函数条件对边界插值器的依赖性。基于这些发现，我们开发了一种新型的简化粗元及其相关的数值形状函数来解决条件的挑战。通过各种数值算例与其他前沿方法进行比较，验证了该方法的稳定性、准确性、收敛速度和效率。在多材料印刷电路板（PCB）的1.83亿个细网格节点上进行了性能测试。

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引用次数: 0

CAD model reconstruction of spherical-jointed lattice structures from point clouds with discrete planar convex hulls 基于离散平面凸壳点云的球节点阵结构CAD模型重建

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer-Aided Design

Pub Date : 2025-12-22 DOI: 10.1016/j.cad.2025.104030

Bohan Zhang , Xiao Xiao , Mulin Yu , Chunjiang Wang , Zhiyuan Tang , Xiangdong Sun

Lattice structures consist of spatially discrete bars interconnected by joints. The complex geometric configurations of these lightweight structures present a challenge for point cloud segmentation, which is essential for CAD model reconstruction. We propose an efficient and robust pipeline to reconstruct CAD models of lattice structures from point clouds. The point cloud is first fitted by a set of planar convex hulls, which are optimized by local geometric operators guided by an energy function. The edges of discrete convex hulls are stored in an AABB tree for efficient hull adjacency queries. The convex hulls are then segmented based on their consistently oriented normals. Structural primitives are classified using principal component analysis of these oriented normals, and their dimensions are determined with least squares fitting of the associated points. The final CAD model is assembled from the detected primitives. The method has been validated using point clouds of various scales and complexities including real-scanned data. It shows robustness in the presence of uniform noise, outliers and data loss. Furthermore, its advantages in terms of reconstruction accuracy and efficiency are further highlighted in comparison to conventional and deep learning approaches.

点阵结构由空间上离散的由节点连接的杆组成。这些轻量化结构的复杂几何构型给点云分割带来了挑战，而点云分割是CAD模型重建的关键。我们提出了一种有效的、鲁棒的管道来从点云重建点阵结构的CAD模型。首先用一组平面凸包对点云进行拟合，然后用能量函数指导下的局部几何算子对凸包进行优化。为了实现高效的凸壳邻接查询，离散凸壳的边缘存储在AABB树中。然后根据它们一致的定向法线对凸包进行分割。结构基元的分类使用这些定向法线的主成分分析，并确定其尺寸与最小二乘拟合的相关点。最终的CAD模型由检测到的原语组装而成。该方法已在不同尺度和复杂程度的点云（包括实际扫描数据）上进行了验证。该方法在均匀噪声、异常值和数据丢失的情况下均表现出鲁棒性。此外，与传统和深度学习方法相比，该方法在重建精度和效率方面的优势进一步突出。

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引用次数: 0

Part orientation fused shape optimization for minimisation of print time and material waste in extrusion-based 3D printing 零件方向融合形状优化，以最大限度地减少基于挤压的3D打印的打印时间和材料浪费

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer-Aided Design

Pub Date : 2025-12-17 DOI: 10.1016/j.cad.2025.104029

Don Pubudu Vishwana Joseph Jayakody , Bailin Deng , Ravindra S. Goonetilleke , Lauren E.J. Thomas-Seale , Hyunyoung Kim

Support structure generation is a critical requirement in additive manufacturing (AM) to prevent material collapse in overhanging regions. However, it increases print time, material waste, and overall production cost, especially in extrusion-based AM. To mitigate these problems, design engineers often resort to manually finetuning or even redesigning prototype geometry to minimise support structures, which is time-consuming and inefficient. A direct geometric optimisation that preserves locality of shape changes whilst corresponding to the part orientation remains an underdetermined problem.

In this paper, we present a novel alternating optimisation framework that finds the corresponding part geometry and orientation to minimise support structures under minimal geometric deviation. Whilst global-level support structure reduction is realised by the part orientation change, we introduce an efficient energy minimisation-based geometric optimisation framework, which is governed by saliency-aware elementwise projections and a set of manufacturing constraints. The proposed framework is validated through extensive computational and physical printing experiments employing multiple 3D printers and support structure types, on a diverse set of complex models including topologically non-trivial parts such as gyroid structures. Our results show an average reduction of 50 % in support structure print time, 27 % in material usage and 25 % in total print time, demonstrating the effectiveness of the proposed framework and its potential as a paradigm shift in manufacturing-oriented design.

支撑结构生成是增材制造（AM）中防止悬垂区域材料坍塌的关键要求。然而，它增加了打印时间，材料浪费和整体生产成本，特别是在基于挤出的AM中。为了缓解这些问题，设计工程师经常求助于手动微调甚至重新设计原型几何形状，以最大限度地减少支撑结构，这既耗时又低效。一个直接的几何优化，保持局部性的形状变化，同时对应的部分方向仍然是一个未确定的问题。在本文中，我们提出了一种新的交替优化框架，该框架可以在最小的几何偏差下找到相应的零件几何和方向，以最小化支撑结构。虽然全球水平的支撑结构减少是通过改变零件方向来实现的，但我们引入了一个高效的基于能量最小化的几何优化框架，该框架由显著性感知元素投影和一组制造约束控制。所提出的框架通过广泛的计算和物理打印实验进行了验证，该实验采用了多种3D打印机和支撑结构类型，在各种复杂模型上进行了验证，包括拓扑上非琐碎的部件，如陀螺结构。我们的研究结果显示，支撑结构打印时间平均减少了50%，材料使用量减少了27%，总打印时间减少了25%，这表明了所提出框架的有效性及其作为面向制造的设计范式转变的潜力。

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引用次数: 0

RLCAD: Reinforcement learning training gym for revolution involved CAD command sequence generation RLCAD：革命强化学习训练馆，涉及CAD命令序列生成

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer-Aided Design

Pub Date : 2025-12-17 DOI: 10.1016/j.cad.2025.104027

Xiaolong Yin , Xingyu Lu , Jiahang Shen , Jingzhe Ni , Hailong Li , Ruofeng Tong , Min Tang , Peng Du

A CAD command sequence is a typical parametric design paradigm in 3D CAD systems where a model is constructed by overlaying 2D sketches with operations such as extrusion, revolution, and Boolean operations. Although there is growing academic interest in the automatic generation of command sequences, existing methods and datasets only support operations such as 2D sketching, extrusion, and Boolean operations. This limitation makes it challenging to represent more complex geometries.

In this paper, we present a reinforcement learning (RL) training gym specifically designed for CAD model generation, along with an RL-based algorithm that generates command sequences from boundary representation (B-Rep) geometry within this training gym. Given an input B-Rep, the policy network of the RL algorithm first outputs an action. This action, together with previously generated actions, is processed within the gym to produce the corresponding CAD geometry, which is then fed back into the policy network. Rewards, computed by the difference between the generated and target geometries within the gym, are used to update the RL network. Our method supports operations beyond sketches, Boolean, and extrusion, including revolution operations. With this training gym, we achieve state-of-the-art (SOTA) quality in generating command sequences from B-Rep geometries.

CAD命令序列是3D CAD系统中典型的参数化设计范例，其中通过将2D草图与挤压、旋转和布尔运算等操作叠加来构建模型。尽管学术界对命令序列的自动生成越来越感兴趣，但现有的方法和数据集只支持2D草图绘制、挤压和布尔运算等操作。这一限制使得表示更复杂的几何形状具有挑战性。在本文中，我们提出了一个专门为CAD模型生成设计的强化学习（RL）训练馆，以及一个基于RL的算法，该算法从该训练馆内的边界表示（B-Rep）几何生成命令序列。给定输入B-Rep， RL算法的策略网络首先输出一个动作。此动作与先前生成的动作一起在体育馆内进行处理，生成相应的CAD几何图形，然后将其反馈到策略网络中。根据生成的几何形状和目标几何形状之间的差异计算奖励，用于更新RL网络。我们的方法支持绘图、布尔和挤压以外的操作，包括旋转操作。有了这个训练健身房，我们在生成B-Rep几何图形的命令序列方面达到了最先进的（SOTA）质量。

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引用次数: 0

Collocation and mass matrix in least-squares isogeometric analysis 最小二乘等几何分析中的配置与质量矩阵

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer-Aided Design

Pub Date : 2025-12-16 DOI: 10.1016/j.cad.2025.104026

Gengchen Li, Hongwei Lin

In this paper, we conduct a systematic numerical analysis of the spectral properties of the collocation and mass matrices in the isogeometric least-squares collocation method (IGA-L), for the approximation of the Poisson problem with homogeneous Dirichlet boundary conditions. This study primarily focuses on the spectral properties of the IGA-L collocation and mass matrices in relation to the isogeometric discretization parameters, such as the mesh size, degree, regularity, spatial dimension, and the number and distribution of the collocation points. Through a comprehensive numerical investigation, we provide estimations for the condition number, as well as the maximum and minimum singular values, in relation to the mesh size, degree and regularity. Moreover, in this paper we also study the effects of the number and distribution of the collocation points on the spectral properties of the collocation matrix, providing insights into the optimization of the collocation points for achieving better-conditioned linear systems.

本文针对齐次Dirichlet边界条件下泊松问题的近似问题，对等几何最小二乘配点法（IGA-L）中配点法和质量矩阵的谱性质进行了系统的数值分析。本研究主要关注IGA-L配置矩阵和质量矩阵的光谱特性与等几何离散化参数的关系，如网格大小、度、规则性、空间维度以及配置点的数量和分布。通过全面的数值研究，我们提供了条件数的估计，以及最大和最小的奇异值，与网格尺寸，程度和规则有关。此外，本文还研究了搭配点的数量和分布对搭配矩阵谱性质的影响，为实现更好条件线性系统的搭配点优化提供了见解。

引用次数: 0

Multi-axis rough milling tool path generation based on 3D Hodge decomposition of vector fields 基于矢量场三维Hodge分解的多轴粗铣刀轨迹生成

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer-Aided Design

Pub Date : 2025-12-14 DOI: 10.1016/j.cad.2025.104028

XuLin Cai, Wen-An Yang, XueFeng Yang, YouPeng You

This study develops a novel framework for generating multi-axis rough milling tool path by leveraging a full 3D Hodge decomposition of the volume-vector field (VFD). First, the stock material is tetrahedralized to form a computational mesh, on which a discrete five-term Hodge decomposition is performed. This process yields two orthogonal harmonic fields: a normal field that delineates the “near-net” rough-machining layers conforming precisely to the target geometry, and a tangential field that generates smooth, raster cutter-contact (CC) curves on each layer. Moreover, by taking the cross-product of these two fields, one can derive continuous, smooth circumferential CC curves. By enforcing mixed boundary conditions and incorporating a scallop-height-constrained scalar field, the method achieves graded layer thickness for material removal while precisely controlling residual heights. A tool-orientation planning module assigns collision-free, smoothly varying orientations along each CC curve, and CC-curve sequencing is optimized to minimize tool repositioning and idle motion. Comparative experiments on complex parts demonstrate that the VFD-based method not only guarantees complete, collision-free rough machining but also reduces total toolpath length and machining time while achieving effective residual-height control—outperforming both 3D area-clearance and blisk area-clearance strategies. Relative to an advanced geodesic-distance–based method, the VFD-based method shows markedly lower sensitivity to mesh resolution and therefore greater robustness. This work constitutes the first rigorous application of 3D Hodge theory to CNC rough machining and provides a flexible, efficient solution for five-axis volumetric machining.

本研究通过利用体积矢量场（VFD）的完整3D Hodge分解，开发了一种新的框架，用于生成多轴粗铣刀轨迹。首先，将原始材料四面体化，形成计算网格，在计算网格上进行离散五项霍奇分解。这一过程产生了两个正交谐波场：一个法向场描绘了精确符合目标几何形状的“近净”粗加工层，一个切向场在每一层上产生光滑的栅格刀具接触（CC）曲线。此外，通过取这两个场的外积，可以得到连续的、光滑的周向CC曲线。通过执行混合边界条件并结合扇贝高度约束标量场，该方法在精确控制残余高度的同时实现了材料去除的渐变层厚度。刀具方向规划模块沿着每条CC曲线分配无碰撞、平滑变化的方向，并优化CC曲线排序，以最大限度地减少刀具重新定位和空闲运动。在复杂零件上的对比实验表明，基于vfd的方法不仅保证了完整的、无碰撞的粗加工，而且减少了总刀路长度和加工时间，实现了有效的剩余高度控制，优于三维面积间隙和叶片面积间隙策略。相对于先进的基于测地线距离的方法，基于vfd的方法对网格分辨率的灵敏度明显较低，因此具有更强的鲁棒性。这项工作构成了3D Hodge理论在CNC粗加工中的首次严格应用，并为五轴体积加工提供了灵活，高效的解决方案。

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引用次数: 0

Self-intersection detection algorithm of sweep surfaces based on geometric features of spine curves 基于脊柱曲线几何特征的扫描曲面自交检测算法

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer-Aided Design

Pub Date : 2025-12-09 DOI: 10.1016/j.cad.2025.104024

Chuan He , Aizeng Wang , Gang Zhao

In modern CAD/CAM workflows, sweep surfaces play a pivotal role in aerospace and automotive design, yet robust self‐intersection analysis remains an open challenge. This paper presents an approach for detecting self‐intersections in parametric sweep surfaces generated by a planar profile along a planar spine. We first classify self‐intersections into local and global categories and further distinguish those arising from individual offset‐curve interactions versus offset‐strip interactions. For local self‐intersections, we develop an efficient algorithm based on curvature extrema and offset‐distance extrema. For global self‐intersections caused by single offset curve, we address spine‐curve minimal‐distance pairs by decomposing the NURBS spine into curvature‐monotonic and globally convex Bézier segments; and introduce a critical offset distance concept for detecting endpoint‐induced self-intersections. For global self‐intersections caused by offset‐strip self‐intersections, we reduce detection to curve–curve intersection and curve–surface intersection subproblems. Numerical experiments demonstrate the proposed methods’ completeness, numerical stability, and applicability to high‐precision sweep surface modeling and downstream process verification.

在现代CAD/CAM工作流程中，扫描曲面在航空航天和汽车设计中发挥着关键作用，但强大的自交分析仍然是一个开放的挑战。本文提出了一种检测由平面轮廓沿平面脊线生成的参数化扫描曲面的自交的方法。我们首先将自交分为局部和全局两类，并进一步区分由个别偏移曲线相互作用和偏移带相互作用产生的自交。对于局部自交，我们提出了一种基于曲率极值和偏移距离极值的有效算法。对于由单偏移曲线引起的全局自交，我们通过将NURBS脊柱分解为曲率单调段和全局凸段来解决脊柱-曲线最小距离对；并引入了检测端点诱导自交的临界偏移距离概念。对于偏置条自交引起的全局自交，我们将检测简化为曲线-曲线交和曲线-曲面交子问题。数值实验证明了该方法的完备性、数值稳定性以及对高精度扫描曲面建模和下游工艺验证的适用性。

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引用次数: 0

An efficient layer-based rough machining framework for subtractive manufacturing 一种高效的分层粗加工框架

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer-Aided Design

Pub Date : 2025-12-06 DOI: 10.1016/j.cad.2025.104025

Li-Yong Shen , Chang Liu , Hong-Yu Ma , Chun-Ming Yuan , Shuo-Peng Chen , Shi-Chu Li , Bo-Wen Zhang

Rough machining, which directly determines overall subtractive machining efficiency, aims to efficiently remove 70%–90% of the stock material to approximate the final workpiece geometry. Prior mainstream tool path generation algorithms for roughing primarily adopt the Contour Parallel method, which can ensure quality but generate curved paths with frequent acceleration/deceleration, limiting efficiency. To address this challenge, this paper presents a comprehensive high-efficiency rough machining framework that optimizes tool retraction count (idle paths) and path smoothness (encouraging linear trajectories in material-removal zones to enhance feedrates), is compatible with multiple tools and generates single start-end tool paths for simply connected regions. Experiments show an efficiency gain of

>

14% over the Contour Parallel method, effectively resolving the core trade-off of balancing quality and efficiency in the rough machining phase.

粗加工的目的是有效地去除70%-90%的库存材料，以接近最终工件的几何形状，直接决定整体减法加工效率。目前主流的粗加工刀具轨迹生成算法主要采用轮廓平行法，该方法能保证加工质量，但产生的曲线轨迹加减速频繁，限制了加工效率。为了解决这一挑战，本文提出了一个全面的高效粗加工框架，该框架优化了刀具回撤次数（空闲路径）和路径平滑度（鼓励材料去除区域的线性轨迹以提高进给速度），与多个刀具兼容，并为单连通区域生成单一的起止刀具路径。实验结果表明，该方法的效率提高了14%，有效地解决了粗加工阶段质量与效率之间的平衡问题。

引用次数: 0

Gen-Porous: An INR-based generative framework for multiscale TPMS-like porous structure design and optimization Gen-Porous：一个基于inr的多尺度tpms类多孔结构设计和优化生成框架

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer-Aided Design

Pub Date : 2025-12-02 DOI: 10.1016/j.cad.2025.104020

Shengfa Wang , Hao Zheng , Jiangbei Hu , Yu Jiang , Liang Du , Hao Du , Na Lei , Zhongxuan Luo

Porous structures originating from triply periodic minimal surfaces (TPMSs), referred to as TPMS-like porous structures, have been widely applied across various domains due to their advantageous structural properties. However, the limited morphological diversity and the simulation challenges posed by the complex features have impeded the further development and practical utilization of TPMS-like porous structures. Recent breakthroughs in artificial intelligence have demonstrated remarkable potential for creativity in industrial design. Capitalizing on these developments, we propose Gen-Porous - a novel framework employing implicit neural representations (INR) to design and optimize TPMS-like porous structures. The proposed methodology delineates a comprehensive paradigm for the acquisition and synthesis of various TPMS-like porous structures through Implicit Neural Representation (INR), facilitating simulation-driven optimization in a meshfree manner directly within the acquired latent space. Initially, we collect a dataset comprising multiscale TPMS-like porous structures, employing implicit functions to achieve this. Subsequently, we utilize an Auto-Decoder network architecture to encode these structures into a compact latent space via implicit neural representation learning, thereby permitting the generation of novel configurations with augmented morphological diversity. Moreover, we develop a differentiable computational framework using neural meshfree simulations. This integration not only makes optimization more efficient, but also simplifies sensitivity analysis through automatic differentiation, enabling diverse constraints and objectives to be more easily incorporated. We demonstrate the efficacy of the framework through a lightweight design case study, where optimized solutions are identified through latent space exploration. The core innovation lies in the neural unification of representation and simulation, achieving significant improvements in computational efficiency by circumventing traditional meshing bottlenecks and enabling full differentiability.

源自三周期极小表面（tpms）的多孔结构被称为类tpms多孔结构，由于其优越的结构特性而被广泛应用于各个领域。然而，有限的形态多样性和复杂特征带来的模拟挑战阻碍了tpms类多孔结构的进一步发展和实际应用。最近人工智能的突破显示了工业设计创造力的巨大潜力。利用这些发展，我们提出了Gen-Porous -一个采用隐式神经表征（INR）来设计和优化类似tpms的多孔结构的新框架。所提出的方法描述了通过隐式神经表征（INR）获取和合成各种类似tpms的多孔结构的综合范例，促进了在获取的潜在空间内直接以无网格方式进行模拟驱动的优化。首先，我们收集了一个包含多尺度tpms类多孔结构的数据集，采用隐式函数来实现这一目标。随后，我们利用Auto-Decoder网络架构通过隐式神经表征学习将这些结构编码到紧凑的潜在空间中，从而允许生成具有增强形态多样性的新配置。此外，我们开发了一个可微计算框架使用神经网格模拟。这种集成不仅提高了优化效率，而且通过自动区分简化了敏感性分析，使不同的约束和目标更容易合并。我们通过轻量级设计案例研究证明了该框架的有效性，其中通过潜在的空间探索确定了优化的解决方案。核心创新在于表征和模拟的神经统一，通过绕过传统网格瓶颈和实现完全可微性，显著提高了计算效率。

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引用次数: 0

An efficient multi-threaded partitioning parallel strategy for tetrahedral mesh improvement 面向四面体网格改进的高效多线程分区并行策略

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer-Aided Design

Pub Date : 2025-11-28 DOI: 10.1016/j.cad.2025.104021

Yunyun Du , Yingjian Fu , Junhe Xie , Guozhong Zhao , S.H. Lo , Leiping Xu , Zhenqun Guan

The improvement of large-scale meshes is a time-consuming process. In this study, a new coarse-grained multi-threaded parallel strategy is proposed to accelerate the improvement process. This strategy is characterized by the following features: (i) The improvement process is divided into two stages, which are parallelized independently. The first stage aims to improve the entire mesh, whereas the second stage targets low-quality elements; (ii) The background grid is utilized for partitioning. For the first stage, an adjacent-first search algorithm based on the uniform grid is proposed. This algorithm effectively addresses the demands of load balancing for task decomposition and demonstrates high efficiency on large meshes. For the second stage, the octree is employed given its enhanced adaptability to irregularly distributed low-quality elements; (iii) To ensure effective improvement, during parallel improvement, elements located near inter-partition boundaries that lack sufficient improvement space are collected and processed iteratively. A parallel partition expansion algorithm is proposed that predicts and occupies the space required for improving partitions, and employs atomic operations to avoid data races. This algorithm strives to maximize the available space for the partitions and accelerate the iterative process. Experimental results indicate that, without compromising improvement effectiveness, the parallel efficiency of the first stage can reach 73 % at 48 threads, whereas the second stage can achieve 77 % at 24 threads. The time required to improve one billion tetrahedra can be reduced from over 2.5 h to approximately 10 min.

大规模网格的改进是一个耗时的过程。在本研究中，提出了一种新的粗粒度多线程并行策略来加速改进过程。该策略具有以下特点：(i)改进过程分为两个阶段，每个阶段独立并行。第一阶段的目标是改善整个网格，第二阶段的目标是低质量的元素；利用背景网格进行分区。第一阶段，提出一种基于均匀网格的邻接优先搜索算法。该算法有效地解决了任务分解的负载均衡问题，在大网格下具有较高的效率。在第二阶段，由于八叉树对不规则分布的低质量元素具有较强的适应性，因此采用八叉树；（iii）为了确保有效改进，在并行改进时，收集位于分区间边界附近缺乏足够改进空间的元素，并对其进行迭代处理。提出了一种并行分区扩展算法，该算法预测和占用分区改进所需的空间，并采用原子操作避免数据竞争。该算法力求最大限度地利用分区的可用空间，加快迭代过程。实验结果表明，在不影响改进效果的前提下，第一级并行效率在48线程时可达73%，第二级并行效率在24线程时可达77%。改善10亿个四面体所需的时间可以从超过2.5小时减少到大约10分钟。

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引用次数: 0