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CHARACTERISTIC GALERKIN METHOD FOR CONVECTION-DIFFUSION EQUATIONS AND IMPLICIT ALGORITHM USING PRECISE INTEGRATION 认领 引用 被引量：3
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作者 李锡夔 武文华 《Acta Mechanica Sinica》 SCIE EI CAS 1999年第4期371-382,共12页
This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using prec... This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability. 展开更多
关键词 convection-diffusion equation characteristic Galerkin method finite element procedure precise integration implicit algorithm
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PREDICTOR-CORRECTOR ALGORITHMS FOR SOLVING GENERALIZED MIXED IMPLICIT QUASI-EQUILIBRIUM PROBLEMS 认领 引用
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作者 丁协平 林炎诚 姚任之 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第9期1157-1164,共8页
A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems... A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings 展开更多
关键词 generalized mixed implicit quasi-equilibrium problem auxiliary variational inequality predictor-corrector iterative algorithms partially relaxed implicit strong monotonicity
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AN IMPLICIT ALGORITHM OF THIN LAYER EQUATIONS IN VISCOUS,TRANSONIC,TWO-PHASE NOZZLE FLOW 认领 引用
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作者 何洪庆 侯晓 +1 位作者 蔡体敏 吴心平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第4期323-334,共12页
Omitting viscosity along flow direction, we have simplified the dimensionless N-Sequations in arbitrary curved coordinate system as the thin layer equations. Using theimplicit approximate-factorization algorithm to so... Omitting viscosity along flow direction, we have simplified the dimensionless N-Sequations in arbitrary curved coordinate system as the thin layer equations. Using theimplicit approximate-factorization algorithm to solve the gas-phase governing equ-ations and the characteristic method to follow the tracks of particles, we then obtainedthe full coupled numerical method of two-phase.transonic, turbulent flow. Here, par- ticle size may be grouped, the subsonic boundary condition at entry of nozzle is ireatedby quasi-characteristic method in reference plane and the algebraic model is used forturbulent flow. These methods are applied in viscous two-phase flow. calculation of ro-cket nozzle and in the prediciton of thrust and specific impulse for solid propellant ro-cket motor. The calculation results are in good agreement with the measurerment va-lues. Moreover, the influences of different particle radius, different particle mass frac-tion and particle size grouped on flow field have been discussed, and the influences of particle two-dimensional radial velosity component and viscosity on specific impulse ofrocket motor have been analysed.The method of this paper possesses the advantage of saving computer time. More important, the effect is more obvious for the calculation of particle size being grouped. 展开更多
关键词 thin layer equations two-phase viscous transonic nozzle flow,implicit algorithm
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EXISTENCE AND ALGORITHM OF SOLUTIONS FOR GENERAL MULTIVALUED MIXED IMPLICIT QUASI-VARIATIONAL INEQUALITIES 认领 引用
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作者 曾六川 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第11期1324-1333,共10页
A new class of general multivalued mixed implicit quasi-variational inequalities in a real Hilbert space was introduced, which includes the known class of generalized mixed implicit quasi-variational inequalities as a... A new class of general multivalued mixed implicit quasi-variational inequalities in a real Hilbert space was introduced, which includes the known class of generalized mixed implicit quasi-variational inequalities as a special case , introduced and studied by Ding Xie-ping . The auxiliary variational principle technique was applied to solve this class of general multivalued mixed implicit quasi-variational inequalities. Firstly, a new auxiliary variational inequality with a proper convex , lower semicontinuous , binary functional was defined and a suitable functional was chosen so that its unique minimum point is equivalent to the solution of such an auxiliary variational inequality . Secondly , this auxiliary variational inequality was utilized to construct a new iterative algorithm for computing approximate solutions to general multivalued mixed implicit quasi-variational inequalities . Here , the equivalence guarantees that the algorithm can generate a sequence of approximate solutions. Finally, the existence of solutions and convergence of approximate solutions for general multivalued mixed implicit quasi-variational inequalities are proved. Moreover, the new convergerce criteria for the algorithm were provided. Therefore, the results give an affirmative answer to the open question raised by M. A . Noor, and extend and improve the earlier and recent results for various variational inequalities and complementarity problems including the corresponding results for mixed variational inequalities, mixed quasi-variational inequalities and quasi-complementarity problems involving the single-valued and set- valued mappings in the recent literature . 展开更多
关键词 general multivalued mixed implicit quasi-variational inequality auxiliary variational principle technique existence algorithm
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Existence and algorithm of solutions for a system of generalized mixed implicit equilibrium problems in Banach spaces 认领 引用
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作者 丁协平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第9期1049-1062,共14页
A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is intro... A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is introduced. By using the notion, a system of generalized equation problems is considered, and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved. Next, by applying the system of generalized equation problems, we suggest and analyze an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicit equilibrium problems. The strong convergence of the iterative sequences generated by the algorithm is proved under quite mild conditions. The results are new and unify and generalize some recent results in this field. 展开更多
关键词 generalized mixed implicit equilibrium problem Yosida proximal mapping,generalized equation problem iterative algorithm Banach space
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Iterative algorithm for solutions to new system of generalized mixed implicit equilibrium 认领 引用
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作者 丁协平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2013年第1期113-126,共14页
A new system of generalized mixed implicit equilibrium problems （SGMIEP） involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium pro... A new system of generalized mixed implicit equilibrium problems （SGMIEP） involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium problem （AMEP） is introduced. The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions. Next, by using the solution mapping of the AMEP, a system of generalized equation problems （SGEP） is considered, and its equivalence with the SGMIEP is shown. By using the SGEP, a new iterative algorithm for solving the SGMIEP is proposed and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new, which unify and generalize some recent results in this field. 展开更多
关键词 system of generalized mixed implicit equilibrium problems （SGMIEP）,auxiliary mixed equilibrium problem （AMEP） system of generalized equation problems（SGEP） iterative algorithm reflexive Banach space
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A New Eighth Order Implicit Block Algorithms for the Direct Solution of Second Order Ordinary Differential Equations 认领 引用
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作者 Ademola M. Badmus 《American Journal of Computational Mathematics》 2014年第4期376-386,共11页
This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The... This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The continuous formulation and its first derivatives were evaluated at some selected grid and off grid points to obtain our proposed method. The superiority of the method over the existing methods is established numerically. 展开更多
关键词 Uniform Order Second Order Initial Value Problem Implicit Block Algorithms Zero Stable
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Existence and Algorithm of Solutions for Generalized Mixed Implicit Quasi-Variational-Like Inequalities 认领 引用
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作者 胡润雪 张勇 张红龄 《Journal of Southwest Jiaotong University(English Edition)》 2005年第1期87-91,共5页
By applying the auxiliary variational principle technique, the existence of solutions for a new class of generalized mixed implicit quasi-variational-like inequalities and the convergence criteria of a new iterative a... By applying the auxiliary variational principle technique, the existence of solutions for a new class of generalized mixed implicit quasi-variational-like inequalities and the convergence criteria of a new iterative algorithm to compute approximate solutions are proved in Hilbert spaces. The obtained result is a improvement over and generalization of the main theorem proposed by Ding. 展开更多
关键词 Generalized mixed implicit quasi-variational-like inequality Auxiliary principle technique Gap function Iterative algorithm
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适用于非结构混合网格的改进线隐式BLU-SGS迭代算法 认领 引用 被引量：2
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作者 张耀冰 李明 +2 位作者 张健 周乃春 龚小权 《航空学报》 EI CAS CSCD 北大核心 2026年第6期79-93,共15页
LU-SGS方法是当前计算流体力学(CFD)中主流的时间推进算法,其采用谱半径近似雅可比矩阵以降低计算开销,但会牺牲收敛效率。尤其在基于非结构混合网格的高雷诺数流动模拟中,附面层网格在壁面法向的加密会导致数值刚性显著增强,使得计算... LU-SGS方法是当前计算流体力学(CFD)中主流的时间推进算法,其采用谱半径近似雅可比矩阵以降低计算开销,但会牺牲收敛效率。尤其在基于非结构混合网格的高雷诺数流动模拟中,附面层网格在壁面法向的加密会导致数值刚性显著增强,使得计算的收敛速度与稳定性进一步下降。鉴于此,提出一种改进的线隐式BLU-SGS算法。该算法基于局部网格几何特征与流场物理特性并行构造隐式线,通过对隐式线内控制体进行联立求解,有效缓解附面层法向小网格尺度对时间步长的限制,并提升远场区域上下游流场信息的交互效率,从而显著提升计算收敛速度。同时,沿隐式线推导出与离散方程右端项相协调的雅可比矩阵,在前向与后向扫描过程中充分考虑非对角线块的隐式贡献,通过保持隐式时间推进的部分非线性特性进一步提高收敛效率。采用二维平板、三维M6机翼及CHN-T1飞机典型算例进行数值验证,结果表明,相较于传统LU-SGS方法,新算法收敛速度可提升5~10倍。 展开更多
关键词 计算流体力学 非结构混合网格 LU-SGS 线隐式算法 收敛效率
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基于NSGA-Ⅲ算法的商用车驾驶室轻量化设计 认领 引用
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作者 彭雪梅 孙永厚 +1 位作者 刘夫云 刘凯扬 《机械设计与制造》 北大核心 2026年第4期6-10,共5页
为了提升商用车驾驶室轻量化优化效果,以企业某型号商用车驾驶室为研究对象,在SFE-Concept中建立驾驶室隐式参数化模型并生成有限元模型,通过试验分析验证了模型的准确性;以弹性模量为变量进行结构灵敏度分析,筛选出相关结构的厚度和截... 为了提升商用车驾驶室轻量化优化效果,以企业某型号商用车驾驶室为研究对象,在SFE-Concept中建立驾驶室隐式参数化模型并生成有限元模型,通过试验分析验证了模型的准确性;以弹性模量为变量进行结构灵敏度分析,筛选出相关结构的厚度和截面形状作为设计变量用于试验设计;根据模态置信因子自动追踪模态阵型并验证了近似模型的拟合精度;利用NSGA-Ⅲ算法进行驾驶室轻量化多目标优化研究,结合TOPSIS方法筛选出最优方案。结果表明:驾驶室质量降低22.5kg,降幅达7.3%,同时提升了刚度,满足驾驶室轻量化和性能要求。 展开更多
关键词 轻量化 隐式参数化 结构灵敏度 NSGA-Ⅲ算法 多目标优化
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结构动力学自启动单解隐式积分器的分析与优化 认领 引用
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作者 李金泽 刘耀坤 +1 位作者 崔乃刚 于开平 《振动工程学报》 EI CSCD 北大核心 2026年第7期1878-1896,共19页
时间积分算法是分析大型航天结构动态响应的一种常用且高效的数值求解技术。在众多算法中,具有竞争性的隐式时间积分法通常需满足一系列严苛要求,包括自启动性、单解性、无条件稳定性、二阶精度、数值高频耗散的可控性以及零阶超调。为... 时间积分算法是分析大型航天结构动态响应的一种常用且高效的数值求解技术。在众多算法中,具有竞争性的隐式时间积分法通常需满足一系列严苛要求,包括自启动性、单解性、无条件稳定性、二阶精度、数值高频耗散的可控性以及零阶超调。为了深入探讨自启动单解隐式积分法的局限性,本文构建了一个具有普遍适用性的自启动单解时间积分算法框架,并详细分析了实现一致精度阶数、超调阶数和可控数值高频耗散所需的代数条件。基于这一框架,证明了在没有额外技术的加持下,自启动单解隐式积分法无法同时满足位移和速度的二阶精度、零阶位移和至多一阶速度超调,以及可控的数值高频耗散。鉴于这一限制,本文进一步分析、设计和优化了三类具有不同超调阶数的隐式积分算法。提出的算法均具备自启动性、单解性、无条件稳定性、二阶精度和可控数值高频耗散(全历程变化),而不同之处在于加速度的精度阶数与超调的阶数。通过优化振幅与相位误差,提出的三类算法在性能上均优于已发表的自启动单解隐式积分法。性能比较和数值算例验证了理论分析,并充分体现了提出的三类算法在精度方面的显著优势。 展开更多
关键词 自启动隐式算法 单解 时间积分方法 振幅和相位误差 最优化设计
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基于隐式表示的全局-局部关系注意力三维重建方法研究 认领 引用
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作者 于然 王凯亮 +3 位作者 谢旭峰 闵照惠 张姣姣 佟昆睿 《电子器件》 CAS 2026年第1期165-170,共6页
隐式表示三维重建方法是一种在计算机视觉领域中面向高效重建复杂三维模型的创新技术,具有重要的实际应用价值。已有的三维重建技术面临几何失真、细节恢复差等问题,尤其在稀疏点云和复杂几何结构的重建中表现尤为明显。为此,提出了一... 隐式表示三维重建方法是一种在计算机视觉领域中面向高效重建复杂三维模型的创新技术,具有重要的实际应用价值。已有的三维重建技术面临几何失真、细节恢复差等问题,尤其在稀疏点云和复杂几何结构的重建中表现尤为明显。为此,提出了一种基于隐式表示的全局-局部关系注意力三维重建方法,首先利用点-网Transformer模块提取点和网格特征,接着通过全局-局部关系注意力模块来全面捕捉点特征与网格特征之间的复杂关系,在更新特征时,不仅考虑了局部的几何信息,还融入了全局的结构信息。同时,引入多头码本策略建立跨类别的先验知识,提高了模型重建不同类别物体的表现力。最后采用基于边缘的等值面提取算法进行重建,解决了现有方法在尖锐边缘和复杂结构中的边界模糊问题。通过实验证明,该方法在ShapeNet数据集上,其评估指标IoU、CD和F-Score均取得显著提升。 展开更多
关键词 隐式表示 三维重建 基于边缘的等值面提取算法 多头码本策略
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新型、隐性腐败的算法识别与法治应对 认领 引用
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作者 黄竹智 蔡宝刚 《常州大学学报（社会科学版）》 2026年第3期52-62,共11页
新型、隐性腐败呈现主体多元化、客体虚拟化、行为隐蔽化、危害持续化等特征,对传统反腐识别机制构成严峻挑战。利用图神经网络、自然语言处理等算法技术构建的腐败识别算法,通过对腐败行为的智能聚类与关系穿透分析,将其运行机制化,形... 新型、隐性腐败呈现主体多元化、客体虚拟化、行为隐蔽化、危害持续化等特征,对传统反腐识别机制构成严峻挑战。利用图神经网络、自然语言处理等算法技术构建的腐败识别算法,通过对腐败行为的智能聚类与关系穿透分析,将其运行机制化,形成非人格化识腐体系。该机制具有虚拟主体超然性、系统反腐协同性、多重错位破解性等优势,但其应用也带来了深刻的技术黑箱、责任认定模糊、程序正当性争议及个人权利保护等法治挑战。其法治应对须通过构建“数据输入-算法分析-线索输出”逻辑闭环,以标准化立法明确算法边界,通过模块化架构实现技术隔离与动态优化。最终形成“算法归算法,权力归制度”的协同治理范式,推动反腐败工作从经验驱动向数据驱动转型,实现技术理性与制度理性的深度融合。 展开更多
关键词 新型腐败 隐性腐败 非人格化 算法识别腐败机制
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基于无监督文本特征的隐含主题自动抽取方法 认领 引用
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作者 包永红 《现代电子技术》 北大核心 2026年第4期42-46,共5页
文本数据中蕴含着丰富的信息,但这些信息往往以隐含的方式存在,不易被直接观察或理解。目前传统的监督学习方法需要大量的人工标注数据来训练模型,易受标注者的主观性影响,为解决该问题,提出一种基于无监督文本特征的隐含主题自动抽取... 文本数据中蕴含着丰富的信息,但这些信息往往以隐含的方式存在,不易被直接观察或理解。目前传统的监督学习方法需要大量的人工标注数据来训练模型,易受标注者的主观性影响,为解决该问题,提出一种基于无监督文本特征的隐含主题自动抽取方法。利用双向最大匹配法对文本进行分词后,去除其中的停用词,完成文本预处理工作;采用无监督TF-IDF算法提取预处理后文本的特征,再将文本数据转换为数值型特征向量,构建词特征向量集;引入LDA模型自动抽取隐含主题,即构建词特征向量中词汇对应隐含主题的概率分布模型,并利用Gibbs快速抽样法获取模型超参数,得到隐含主题概率分布,进而依据该分布结果实现文本隐含主题的自动抽取。实验结果表明,所提方法在应用过程中的F1值高于0.93,困惑度低于0.6,能够精准地抽取文本中的隐含主题。 展开更多
关键词 隐含主题 自动抽取 文本特征 无监督TF-IDF算法 LDA模型 Gibbs快速抽样法
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两块多级布局方式的轻重货物混合装箱优化算法 认领 引用
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作者 潘卫平 《自动化与仪器仪表》 2026年第6期8-11,共4页
讨论轻重货物混合装箱问题,即在一个集装箱中装入长方体形状的轻质货物和重质货物,在满足集装箱的载重约束下最大化集装箱的空间利用率。为了简化装载操作,货物在集装箱中按层排放。提出一种两块多级布局方式的确定性优化算法。这种布... 讨论轻重货物混合装箱问题,即在一个集装箱中装入长方体形状的轻质货物和重质货物,在满足集装箱的载重约束下最大化集装箱的空间利用率。为了简化装载操作,货物在集装箱中按层排放。提出一种两块多级布局方式的确定性优化算法。这种布局方式将集装箱底面划分成2个块,在每个块中货物按照多级方式排列。多级布局方式由多个级正交组合而成,其中每个级由方向相同的同种货物组成。首先构造递归算法确定每个级中货物的布局方式,然后采用隐式枚举算法确定最优两块划分。采用实际生产中的例题验证本算法,结果表明所提算法可以有效提高集装箱空间利用率,并且计算时间较短。 展开更多
关键词 装箱问题 多级布局方式 递归算法 隐式枚举 轻重货物
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双屈服面土体弹塑性模型的返回映射算法及其数值实现 认领 引用
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作者 赛冬拉·马学义 崔溦 +1 位作者 张宇 王操 《岩土工程学报》 EI CAS CSCD 北大核心 2026年第4期845-855,875,共11页
双屈服面本构模型能更好的描述土体的力学行为,其数值积分算法是准确计算土体应力与变形的关键。基于双重塑性机制弹塑性模型,建立了双屈服面模型的隐式返回映射算法,并推导了相应的一致性切线模量。考虑双屈服面交点处采用Newton算法... 双屈服面本构模型能更好的描述土体的力学行为,其数值积分算法是准确计算土体应力与变形的关键。基于双重塑性机制弹塑性模型,建立了双屈服面模型的隐式返回映射算法,并推导了相应的一致性切线模量。考虑双屈服面交点处采用Newton算法易出现数值奇异和不收敛等应力积分问题,在塑性修正过程提出了两阶段迭代算法,即先引入塑性增量理论确定迭代初值,再通过Newton算法进行迭代修正。最后通过ABAQUS提供的UMAT接口编制了数值求解程序,结合钙质砂三轴试验结果对模型进行了分析论证。结果表明,数值程序可以有效反映不同围压对砂土应力-应变曲线的影响,能够准确描述钙质砂剪胀与剪缩的体变行为,另外新迭代算法的计算效率优于常规迭代算法,有效解决了数值奇异与不收敛问题,表明了算法的优越性、程序的正确性和实用性。 展开更多
关键词 双屈服面模型 隐式积分算法 两阶段迭代算法 一致性切线模量 二次开发
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基于多尺度离散速度方法的高速飞行器跨流域流动数值模拟 认领 引用
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作者 张庆典 钟诚文 +1 位作者 卓丛山 刘沙 《空气动力学学报》 CSCD 北大核心 2026年第7期139-153,共15页
针对高空稀薄气体环境下飞行器跨流域流动特性预测难题,本文采用多尺度离散速度方法,并结合定常隐式算法,对高速飞行器开展跨流域数值模拟研究。针对9°钝锥、70°钝锥、Apollo 6返回舱及X-38飞行器等典型三维外形,分别开展了... 针对高空稀薄气体环境下飞行器跨流域流动特性预测难题,本文采用多尺度离散速度方法,并结合定常隐式算法,对高速飞行器开展跨流域数值模拟研究。针对9°钝锥、70°钝锥、Apollo 6返回舱及X-38飞行器等典型三维外形,分别开展了跨流域流动条件下的数值模拟。相关结果表明,该方法能够准确捕捉跨流域流场的非平衡效应和主要流动特征,升阻力系数、表面压力系数及热流系数等关键参数与直接模拟蒙特卡罗方法或相关实验数据等参考结果吻合良好(以X-38算例为例,升力系数相对误差1.31%,阻力系数相对误差2.69%)。特别地,针对X-38飞行器算例的对比分析表明,采用定常隐式算法后,多尺度离散速度方法在获得与直接模拟蒙特卡罗方法相当结果的同时,显示出一定的效率优势(总核时从DSMC的4281核时降低至3072核时,节约约28%)和工程应用潜力。上述结果验证了多尺度离散速度方法的有效性和准确性,可为跨流域飞行器气动特性预测和气动设计提供方法支撑。 展开更多
关键词 多尺度离散速度方法 隐式算法 跨流域流动 稀薄气体 非平衡效应
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基于BDF2-AB2的钢铸件凝固多物理场耦合模拟方法 认领 引用
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作者 李嘉韦 潘思源 +6 位作者 江北竹 张宇昕 石宇航 殷亚军 李文 沈旭 周建新 《铸造》 CAS 2026年第8期869-876,共8页
钢铸件凝固过程数值模拟对于缺陷预测与工艺优化具有重要意义,但其强非线性特性对算法稳定性与计算效率提出了严峻挑战。为此,本研究提出一种基于BDF2-AB2混合时间积分格式的多物理场耦合求解方法,详细介绍了数学模型建立及数值离散方法... 钢铸件凝固过程数值模拟对于缺陷预测与工艺优化具有重要意义,但其强非线性特性对算法稳定性与计算效率提出了严峻挑战。为此,本研究提出一种基于BDF2-AB2混合时间积分格式的多物理场耦合求解方法,详细介绍了数学模型建立及数值离散方法,并将其与经典显式欧拉法进行了对比。结果表明,在相同网格规模下,BDF2-AB2方法的单步计算成本与显式欧拉法相当,且在稳定性方面具有显著优势。显式欧拉法在时间步长增至0.0005 s时发生数值失稳,而BDF2-AB2格式在步长达到0.01 s时才发生数值失稳,其稳定步长上限约为显式欧拉法的20倍。在工程算例中,BDF2-AB2方法能够准确模拟三维铸锭的凝固过程及宏观偏析行为,可为铸件凝固过程的高效、高精度数值模拟提供有效的计算手段。 展开更多
关键词 BDF2-AB2时间离散 凝固模拟 数值稳定性 计算效率 隐式算法 铸钢 宏观偏析 多物理场耦合
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ON A CLASS OF GENERALIZED NONLINEAR IMPLICIT QUASIVARIATIONAL INCLUSIONS 认领 引用 被引量：2
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作者 丁协平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第10期1087-1098,共12页
In this paper, a new class of generalized nonlinear implicit quasivariational inclusions involving a set-valued maximal monotone wrapping are studied. A existence theorem of solutions for this class of generalized non... In this paper, a new class of generalized nonlinear implicit quasivariational inclusions involving a set-valued maximal monotone wrapping are studied. A existence theorem of solutions for this class of generalized nonlinear implicit quasivariational inclusions is Proved without compactness assumptions. A new iterative algorithm for finding approximate solutions of the generalized nonlinear implicit quasivariational inclusions is suggested and analysed and the convergence of iterative sequence generated by the new algorithm is also given, As special cases, some known results in this field are also discussed. 展开更多
关键词 generalized nonlinear implicit quasivariational inclusion maximal monotone mapping iterative algorithm Hilbert space
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Full-vectorial finite-difference beam propagation method based on the modified alternating direction implicit method 认领 引用 被引量：1
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作者 肖金标 孙小菡 《Chinese Physics B》 CAS 2006年第8期1824-1830,共7页
A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first ... A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method. 展开更多
关键词 beam propagation method alternating direction implicit algorithm finite difference optical waveguides integrated optics
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