We report a linear-scaling random Green's function(rGF) method for large-scale electronic structure calculation. In this method, the rGF is defined on a set of random states and is efficiently calculated by projec...We report a linear-scaling random Green's function(rGF) method for large-scale electronic structure calculation. In this method, the rGF is defined on a set of random states and is efficiently calculated by projecting onto Krylov subspace. With the rGF method, the Fermi–Dirac operator can be obtained directly, avoiding the polynomial expansion to Fermi–Dirac function. To demonstrate the applicability, we implement the rGF method with the density-functional tight-binding method. It is shown that the Krylov subspace can maintain at small size for materials with different gaps at zero temperature, including H_(2)O and Si clusters. We find with a simple deflation technique that the rGF self-consistent calculation of H_(2)O clusters at T = 0 K can reach an error of~ 1 me V per H_(2)O molecule in total energy, compared to deterministic calculations. The rGF method provides an effective stochastic method for large-scale electronic structure simulation.展开更多
The collocation method is a widely used numerical method for science and engineering problems governed by partial differential equations.This paper provides a comprehensive review of collocation methods and their appl...The collocation method is a widely used numerical method for science and engineering problems governed by partial differential equations.This paper provides a comprehensive review of collocation methods and their applications,focused on elasticity,heat conduction,electromagnetic field analysis,and fluid dynamics.The merits of the collocation method can be attributed to the need for element mesh,simple implementation,high computational efficiency,and ease in handling irregular domain problems since the collocation method is a type of node-based numerical method.Beginning with the fundamental principles of the collocation method,the discretization process in the continuous domain is elucidated,and how the collocation method approximation solutions for solving differential equations are explained.Delving into the historical development of the collocation methods,their earliest applications and key milestones are traced,thereby demonstrating their evolution within the realm of numerical computation.The mathematical foundations of collocation methods,encompassing the selection of interpolation functions,definition of weighting functions,and derivation of integration rules,are examined in detail,emphasizing their significance in comprehending the method’s effectiveness and stability.At last,the practical application of the collocation methods in engineering contexts is emphasized,including heat conduction simulations,electromagnetic coupled field analysis,and fluid dynamics simulations.These specific case studies can underscore collocation method’s broad applicability and effectiveness in addressing complex engineering challenges.In conclusion,this paper puts forward the future development trend of the collocation method through rigorous analysis and discussion,thereby facilitating further advancements in research and practical applications within these fields.展开更多
A versatile analytical method(VAM) for calculating the harmonic components of the magnetomotive force(MMF) generated by diverse armature windings in AC machines has been proposed, and the versatility of this method ha...A versatile analytical method(VAM) for calculating the harmonic components of the magnetomotive force(MMF) generated by diverse armature windings in AC machines has been proposed, and the versatility of this method has been established in early literature. However, its practical applications and significance in advancing the analysis of AC machines need further elaboration. This paper aims to complement VAM by augmenting its theory, offering additional insights into its conclusions, as well as demonstrating its utility in assessing armature windings and its application of calculating torque for permanent magnet synchronous machines(PMSM). This work contributes to advancing the analysis of AC machines and underscores the potential for improved design and performance optimization.展开更多
The task of indoor visual localization, utilizing camera visual information for user pose calculation, was a core component of Augmented Reality (AR) and Simultaneous Localization and Mapping (SLAM). Existing indoor l...The task of indoor visual localization, utilizing camera visual information for user pose calculation, was a core component of Augmented Reality (AR) and Simultaneous Localization and Mapping (SLAM). Existing indoor localization technologies generally used scene-specific 3D representations or were trained on specific datasets, making it challenging to balance accuracy and cost when applied to new scenes. Addressing this issue, this paper proposed a universal indoor visual localization method based on efficient image retrieval. Initially, a Multi-Layer Perceptron (MLP) was employed to aggregate features from intermediate layers of a convolutional neural network, obtaining a global representation of the image. This approach ensured accurate and rapid retrieval of reference images. Subsequently, a new mechanism using Random Sample Consensus (RANSAC) was designed to resolve relative pose ambiguity caused by the essential matrix decomposition based on the five-point method. Finally, the absolute pose of the queried user image was computed, thereby achieving indoor user pose estimation. The proposed indoor localization method was characterized by its simplicity, flexibility, and excellent cross-scene generalization. Experimental results demonstrated a positioning error of 0.09 m and 2.14° on the 7Scenes dataset, and 0.15 m and 6.37° on the 12Scenes dataset. These results convincingly illustrated the outstanding performance of the proposed indoor localization method.展开更多
To study the safety and stability of large slopes, taking the right side slope of the Yuxi’an tunnel of the Yuchu Expressway Bridge in Yunnan Province as an example, limit equilibrium and finite element analysis were...To study the safety and stability of large slopes, taking the right side slope of the Yuxi’an tunnel of the Yuchu Expressway Bridge in Yunnan Province as an example, limit equilibrium and finite element analysis were applied to engineering examples to calculate the stability coefficient of the slope before and after excavation in the natural state. After comparative analysis, it was concluded that the former had a clear mechanical model and concept, which could quickly provide stability results;the latter could accurately determine the sliding surface of the slope and simulate the stress state changes of the rock and soil mass. The stability coefficients calculated by the two methods were within the stable range, but their values were different. On this basis, combined with the calculation principles, advantages and disadvantages of the two methods, a comprehensive analysis method of slope stability based on the limit equilibrium and finite element methods was proposed, and the rationality of the stability coefficient calculated by this method was judged for a slope case.展开更多
商业油流是储量起算标准的重要经济评价指标之一。中国石油行业标准Q/ SY 01180—2020《石油天然气经济可采储量评价规范》中给出的常规油藏稳定递减单井商业油流的计算方法,对生产初期产量递减较快、中后期产量递减相对平缓的“分段式...商业油流是储量起算标准的重要经济评价指标之一。中国石油行业标准Q/ SY 01180—2020《石油天然气经济可采储量评价规范》中给出的常规油藏稳定递减单井商业油流的计算方法,对生产初期产量递减较快、中后期产量递减相对平缓的“分段式”递减的特低渗油藏适用性较差。为此,基于常规油藏单一递减率的单井商业油流计算方法,应用盈亏平衡原理,结合“分段式”递减规律,建立了一种符合“分段式”递减规律的油藏单井商业油流计算模型,并以辽河坳陷太阳组为例,结合其油藏相关物性参数、单井投资及成本费用、油气价格等参数,利用所建立的“分段式”递减油藏单井商业油流计算模型,确定了评价油价为60美元/桶条件下的单井商业油流。研究结果对同类型油藏具有借鉴意义。展开更多
基金financial support from the National Natural Science Foundation of China (Grant No. 12227901)the financial support from the National Natural Science Foundation of China (Grant Nos. 11974263 and 12174291)。
文摘We report a linear-scaling random Green's function(rGF) method for large-scale electronic structure calculation. In this method, the rGF is defined on a set of random states and is efficiently calculated by projecting onto Krylov subspace. With the rGF method, the Fermi–Dirac operator can be obtained directly, avoiding the polynomial expansion to Fermi–Dirac function. To demonstrate the applicability, we implement the rGF method with the density-functional tight-binding method. It is shown that the Krylov subspace can maintain at small size for materials with different gaps at zero temperature, including H_(2)O and Si clusters. We find with a simple deflation technique that the rGF self-consistent calculation of H_(2)O clusters at T = 0 K can reach an error of~ 1 me V per H_(2)O molecule in total energy, compared to deterministic calculations. The rGF method provides an effective stochastic method for large-scale electronic structure simulation.
基金the National Natural Science Foundation of China for financial support to this work under Grant NSFC No.12072064.
文摘The collocation method is a widely used numerical method for science and engineering problems governed by partial differential equations.This paper provides a comprehensive review of collocation methods and their applications,focused on elasticity,heat conduction,electromagnetic field analysis,and fluid dynamics.The merits of the collocation method can be attributed to the need for element mesh,simple implementation,high computational efficiency,and ease in handling irregular domain problems since the collocation method is a type of node-based numerical method.Beginning with the fundamental principles of the collocation method,the discretization process in the continuous domain is elucidated,and how the collocation method approximation solutions for solving differential equations are explained.Delving into the historical development of the collocation methods,their earliest applications and key milestones are traced,thereby demonstrating their evolution within the realm of numerical computation.The mathematical foundations of collocation methods,encompassing the selection of interpolation functions,definition of weighting functions,and derivation of integration rules,are examined in detail,emphasizing their significance in comprehending the method’s effectiveness and stability.At last,the practical application of the collocation methods in engineering contexts is emphasized,including heat conduction simulations,electromagnetic coupled field analysis,and fluid dynamics simulations.These specific case studies can underscore collocation method’s broad applicability and effectiveness in addressing complex engineering challenges.In conclusion,this paper puts forward the future development trend of the collocation method through rigorous analysis and discussion,thereby facilitating further advancements in research and practical applications within these fields.
基金supported by the Natural Science Foundation of China under Grant U22A20214 and Grant 51837010。
文摘A versatile analytical method(VAM) for calculating the harmonic components of the magnetomotive force(MMF) generated by diverse armature windings in AC machines has been proposed, and the versatility of this method has been established in early literature. However, its practical applications and significance in advancing the analysis of AC machines need further elaboration. This paper aims to complement VAM by augmenting its theory, offering additional insights into its conclusions, as well as demonstrating its utility in assessing armature windings and its application of calculating torque for permanent magnet synchronous machines(PMSM). This work contributes to advancing the analysis of AC machines and underscores the potential for improved design and performance optimization.
文摘The task of indoor visual localization, utilizing camera visual information for user pose calculation, was a core component of Augmented Reality (AR) and Simultaneous Localization and Mapping (SLAM). Existing indoor localization technologies generally used scene-specific 3D representations or were trained on specific datasets, making it challenging to balance accuracy and cost when applied to new scenes. Addressing this issue, this paper proposed a universal indoor visual localization method based on efficient image retrieval. Initially, a Multi-Layer Perceptron (MLP) was employed to aggregate features from intermediate layers of a convolutional neural network, obtaining a global representation of the image. This approach ensured accurate and rapid retrieval of reference images. Subsequently, a new mechanism using Random Sample Consensus (RANSAC) was designed to resolve relative pose ambiguity caused by the essential matrix decomposition based on the five-point method. Finally, the absolute pose of the queried user image was computed, thereby achieving indoor user pose estimation. The proposed indoor localization method was characterized by its simplicity, flexibility, and excellent cross-scene generalization. Experimental results demonstrated a positioning error of 0.09 m and 2.14° on the 7Scenes dataset, and 0.15 m and 6.37° on the 12Scenes dataset. These results convincingly illustrated the outstanding performance of the proposed indoor localization method.
文摘To study the safety and stability of large slopes, taking the right side slope of the Yuxi’an tunnel of the Yuchu Expressway Bridge in Yunnan Province as an example, limit equilibrium and finite element analysis were applied to engineering examples to calculate the stability coefficient of the slope before and after excavation in the natural state. After comparative analysis, it was concluded that the former had a clear mechanical model and concept, which could quickly provide stability results;the latter could accurately determine the sliding surface of the slope and simulate the stress state changes of the rock and soil mass. The stability coefficients calculated by the two methods were within the stable range, but their values were different. On this basis, combined with the calculation principles, advantages and disadvantages of the two methods, a comprehensive analysis method of slope stability based on the limit equilibrium and finite element methods was proposed, and the rationality of the stability coefficient calculated by this method was judged for a slope case.
文摘商业油流是储量起算标准的重要经济评价指标之一。中国石油行业标准Q/ SY 01180—2020《石油天然气经济可采储量评价规范》中给出的常规油藏稳定递减单井商业油流的计算方法,对生产初期产量递减较快、中后期产量递减相对平缓的“分段式”递减的特低渗油藏适用性较差。为此,基于常规油藏单一递减率的单井商业油流计算方法,应用盈亏平衡原理,结合“分段式”递减规律,建立了一种符合“分段式”递减规律的油藏单井商业油流计算模型,并以辽河坳陷太阳组为例,结合其油藏相关物性参数、单井投资及成本费用、油气价格等参数,利用所建立的“分段式”递减油藏单井商业油流计算模型,确定了评价油价为60美元/桶条件下的单井商业油流。研究结果对同类型油藏具有借鉴意义。
