The phase field model can coherently address the relatively complex fracture phenomenon,such as crack nucleation,branching,deflection,etc.The model has been extensively implemented in the finite element package Abaqus...The phase field model can coherently address the relatively complex fracture phenomenon,such as crack nucleation,branching,deflection,etc.The model has been extensively implemented in the finite element package Abaqus to solve brittle fracture problems in recent studies.However,accurate numerical analysis typically requires fine meshes to model the evolving crack path effectively.A broad region must be discretized without prior knowledge of the crack path,further augmenting the computational expenses.In this proposed work,we present an automated framework utilizing a posteriori error-indicator(MISESERI)to demarcate and sufficiently refine the mesh along the anticipated crack path.This eliminates the need for manual mesh refinement based on previous experimental/computational results or heuristic judgment.The proposed Python-based framework integrates the preanalysis,sufficient mesh refinement,and subsequent phase-field model-based numerical analysis with user-defined subroutines in a single streamlined pass.The novelty of the proposed work lies in integrating Abaqus’s native error estimation and mesh refinement capability,tailored explicitly for phase-field simulations.The proposed methodology aims to reduce the computational resource requirement,thereby enhancing the efficiency of the phase-field simulations while preserving the solution accuracy,making the framework particularly advantageous for complex fracture problems where the computational/experimental results are limited or unavailable.Several benchmark numerical problems are solved to showcase the effectiveness and accuracy of the proposed approach.The numerical examples present the proposed approach’s efficacy in the case of a complex mixed-mode fracture problem.The results show significant reductions in computational resources compared to traditional phase-field methods,which is promising.展开更多
To deal with the problem of low computational precision at the nodes near the source and satisfy the requirements for computational efficiency in inversion imaging and finite-element numerical simulations of the direc...To deal with the problem of low computational precision at the nodes near the source and satisfy the requirements for computational efficiency in inversion imaging and finite-element numerical simulations of the direct current method, we propose a new mesh refinement and recoarsement method for a two-dimensional point source. We introduce the mesh refinement and mesh recoarsement into the traditional structured mesh subdivision. By refining the horizontal grids, the singularity owing to the point source is minimized and the topography is simulated. By recoarsening the horizontal grids, the number of grid cells is reduced significantly and computational efficiency is improved. Model tests show that the proposed method solves the singularity problem and reduces the number of grid cells by 80% compared to the uniform grid refinement.展开更多
In the present paper, high-order finite volume schemes on unstructured grids developed in our previous papers are extended to solve three-dimensional inviscid and viscous flows. The highorder variational reconstructio...In the present paper, high-order finite volume schemes on unstructured grids developed in our previous papers are extended to solve three-dimensional inviscid and viscous flows. The highorder variational reconstruction technique in terms of compact stencil is improved to reduce local condition numbers. To further improve the efficiency of computation, the adaptive mesh refinement technique is implemented in the framework of high-order finite volume methods. Mesh refinement and coarsening criteria are chosen to be the indicators for certain flow structures. One important challenge of the adaptive mesh refinement technique on unstructured grids is the dynamic load balancing in parallel computation. To solve this problem, the open-source library p4 est based on the forest of octrees is adopted. Several two-and three-dimensional test cases are computed to verify the accuracy and robustness of the proposed numerical schemes.展开更多
Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement...Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid Chttp：//lsec. cc. ac. cn/phg/）, a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simukaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the biseetioning refinement procedure.展开更多
In electrical impedance tomography （EIT）, distribution of the internal resistivity or conductivity of an unknown object is esti- mated using measured boundary voltage data induced by different current patterns with ...In electrical impedance tomography （EIT）, distribution of the internal resistivity or conductivity of an unknown object is esti- mated using measured boundary voltage data induced by different current patterns with various reconstruction algorithms. The reconstruction algorithms usually employ the Newton-Raphson iteration scheme to visualize the resistivity distribution inside the object. Accuracy of the imaging process depends not only on the algorithm used, but also on the scheme of finite element discretization. In this paper an adaptive mesh refinement is used in a modified reconstruction algorithm for the regularized Err. The method has a major impact on efficient solution of the forward problem as well as on achieving improved image resolution. Computer simulations indicate that the Newton-Raphson reconstruction algorithm for Err using adaptive mesh refinement performs better than the classical Newton-Raphson algorithm in terms of reconstructed image resolution.展开更多
The present study provides a three-dimensional volume-of-fluid method based on the adaptive mesh refinement technique.The projection method on the adaptive mesh is introduced for solving the incompressible Navier-Stok...The present study provides a three-dimensional volume-of-fluid method based on the adaptive mesh refinement technique.The projection method on the adaptive mesh is introduced for solving the incompressible Navier-Stokes equations.The octree structure mesh is employed to solve the flow velocities and the pressure.The developed solver is applied to simulate the deformation of the cubic droplet driven by the surface tension without the effect of the gravity.The numerical results well predict the shape evolution of the droplet.展开更多
High-order schemes based on block-structured adaptive mesh refinement method are prepared to solve computational aeroacoustic （CAA） problems with an aim at improving computational efficiency. A number of numerical i...High-order schemes based on block-structured adaptive mesh refinement method are prepared to solve computational aeroacoustic （CAA） problems with an aim at improving computational efficiency. A number of numerical issues associated with high-order schemes on an adaptively refined mesh, such as stability and accuracy are addressed. Several CAA benchmark problems are used to demonstrate the feasibility and efficiency of the approach.展开更多
In this study,a numerical model for simulating two-phase flow is developed.The Cartesian grid with Adaptive Mesh Refinement(AMR)is adopted to reduce the computational cost.An explicit projection method is used for the...In this study,a numerical model for simulating two-phase flow is developed.The Cartesian grid with Adaptive Mesh Refinement(AMR)is adopted to reduce the computational cost.An explicit projection method is used for the time integration and the Finite Difference Method(FDM)is applied on a staggered grid for the discretization of spatial derivatives.The Volume of Fluid(VOF)method with Piecewise-Linear Interface Calculation(PLIC)is extended to the AMR grid to capture the gas-water interface accurately.A coarse-fine interface treatment method is developed to preserve the flux conservation at the interfaces.Several two-dimensional(2D)and three-dimensional(3D)benchmark cases are carried out for the validation of the model.2D and 3D shear flow tests are conducted to validate the extension of the VOF method to the AMR grid.A 2D linear sloshing case is considered in which the model is proved to have 2nd-order accuracy in space.The efficiency of applying the AMR grid is discussed with a nonlinear sloshing problem.Finally,2D solitary wave past stage and 2D/3D dam break are simulated to demonstrate that the model is able to simulate violent interface problems.展开更多
A new method for estimating the posterior error of linear triangular element is presented. According to the specified accuracy, the element size and node spacing function of adaptive h-version mesh refinement are pred...A new method for estimating the posterior error of linear triangular element is presented. According to the specified accuracy, the element size and node spacing function of adaptive h-version mesh refinement are predicted. The main domain is divided by the isolines of node spacing into subregions in which mesh regeneration is realized. This remeshing refinement process implements mesh subdivision and mesh de-refinement in onecycle.展开更多
In recent years, due to the rapid development of computer hardware and the urgent need of complex engineering problems, great support has been provided in the related fields of unstructured mesh generation. A large nu...In recent years, due to the rapid development of computer hardware and the urgent need of complex engineering problems, great support has been provided in the related fields of unstructured mesh generation. A large number of research results show that the adaptive analysis is an effective way to improve the efficiency and precision of the numerical calculation. The reliable error estimation and the powerful mesh generation are two key problems in the process of adaptive numerical analysis. H-type refinement strategy adding the new nodes in the high error area, gradually refines the mesh to reduce the size of the element to achieve the purpose of mesh adaptation;this strategy is simple, intuitive and easy to program. Although the calculation accuracy of unstructured triangle and tetrahedron elements is not high, these elements are suitable for discretization of any complex problem domain, and have a wider range of application in academic and engineering fields.展开更多
从三维Mesh数据中分割建筑物立面以识别对象,是三维场景理解的关键,但现有方法多依赖高成本的精细标注数据。针对该问题,提出了一种半监督学习方法,引入一种基于对比学习和一致性正则化的半监督语义分割(semi-supervised semantic segme...从三维Mesh数据中分割建筑物立面以识别对象,是三维场景理解的关键,但现有方法多依赖高成本的精细标注数据。针对该问题,提出了一种半监督学习方法,引入一种基于对比学习和一致性正则化的半监督语义分割(semi-supervised semantic segmentation based on contrastive learning and consistency regularization,SS_CC)方法,用于分割三维Mesh数据的建筑物立面。在SS_CC方法中,改进后的对比学习模块利用正负样本之间的类可分性,能够更有效地利用类特征信息;提出的基于特征空间的一致性正则化损失函数,从挖掘全局特征的角度增强了对所提取建筑物立面特征的鉴别力。实验结果表明,所提出的SS_CC方法在F1分数、mIoU指标上优于当前一些主流方法,且在建筑物的墙面和窗户上的分割效果相对更好。展开更多
文摘The phase field model can coherently address the relatively complex fracture phenomenon,such as crack nucleation,branching,deflection,etc.The model has been extensively implemented in the finite element package Abaqus to solve brittle fracture problems in recent studies.However,accurate numerical analysis typically requires fine meshes to model the evolving crack path effectively.A broad region must be discretized without prior knowledge of the crack path,further augmenting the computational expenses.In this proposed work,we present an automated framework utilizing a posteriori error-indicator(MISESERI)to demarcate and sufficiently refine the mesh along the anticipated crack path.This eliminates the need for manual mesh refinement based on previous experimental/computational results or heuristic judgment.The proposed Python-based framework integrates the preanalysis,sufficient mesh refinement,and subsequent phase-field model-based numerical analysis with user-defined subroutines in a single streamlined pass.The novelty of the proposed work lies in integrating Abaqus’s native error estimation and mesh refinement capability,tailored explicitly for phase-field simulations.The proposed methodology aims to reduce the computational resource requirement,thereby enhancing the efficiency of the phase-field simulations while preserving the solution accuracy,making the framework particularly advantageous for complex fracture problems where the computational/experimental results are limited or unavailable.Several benchmark numerical problems are solved to showcase the effectiveness and accuracy of the proposed approach.The numerical examples present the proposed approach’s efficacy in the case of a complex mixed-mode fracture problem.The results show significant reductions in computational resources compared to traditional phase-field methods,which is promising.
基金financially supported by the National Natural Science Foundation of China(No.41574127 and 41174104)the National Key Technology R&D Program for the 13th five-year plan(No.2016ZX05018006-006)
文摘To deal with the problem of low computational precision at the nodes near the source and satisfy the requirements for computational efficiency in inversion imaging and finite-element numerical simulations of the direct current method, we propose a new mesh refinement and recoarsement method for a two-dimensional point source. We introduce the mesh refinement and mesh recoarsement into the traditional structured mesh subdivision. By refining the horizontal grids, the singularity owing to the point source is minimized and the topography is simulated. By recoarsening the horizontal grids, the number of grid cells is reduced significantly and computational efficiency is improved. Model tests show that the proposed method solves the singularity problem and reduces the number of grid cells by 80% compared to the uniform grid refinement.
基金supported by the National Natural Science Foundation of China(Nos.91752114 and 11672160)
文摘In the present paper, high-order finite volume schemes on unstructured grids developed in our previous papers are extended to solve three-dimensional inviscid and viscous flows. The highorder variational reconstruction technique in terms of compact stencil is improved to reduce local condition numbers. To further improve the efficiency of computation, the adaptive mesh refinement technique is implemented in the framework of high-order finite volume methods. Mesh refinement and coarsening criteria are chosen to be the indicators for certain flow structures. One important challenge of the adaptive mesh refinement technique on unstructured grids is the dynamic load balancing in parallel computation. To solve this problem, the open-source library p4 est based on the forest of octrees is adopted. Several two-and three-dimensional test cases are computed to verify the accuracy and robustness of the proposed numerical schemes.
基金supported by the 973 Program of China 2005CB321702China NSF 10531080.
文摘Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid Chttp：//lsec. cc. ac. cn/phg/）, a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simukaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the biseetioning refinement procedure.
基金Project supported by National Natural Science Foundation of China（Grant No. 60075009）
文摘In electrical impedance tomography （EIT）, distribution of the internal resistivity or conductivity of an unknown object is esti- mated using measured boundary voltage data induced by different current patterns with various reconstruction algorithms. The reconstruction algorithms usually employ the Newton-Raphson iteration scheme to visualize the resistivity distribution inside the object. Accuracy of the imaging process depends not only on the algorithm used, but also on the scheme of finite element discretization. In this paper an adaptive mesh refinement is used in a modified reconstruction algorithm for the regularized Err. The method has a major impact on efficient solution of the forward problem as well as on achieving improved image resolution. Computer simulations indicate that the Newton-Raphson reconstruction algorithm for Err using adaptive mesh refinement performs better than the classical Newton-Raphson algorithm in terms of reconstructed image resolution.
基金This work was supported by the National Natural Science Foun-dation of China(No.41776194).
文摘The present study provides a three-dimensional volume-of-fluid method based on the adaptive mesh refinement technique.The projection method on the adaptive mesh is introduced for solving the incompressible Navier-Stokes equations.The octree structure mesh is employed to solve the flow velocities and the pressure.The developed solver is applied to simulate the deformation of the cubic droplet driven by the surface tension without the effect of the gravity.The numerical results well predict the shape evolution of the droplet.
基金supported by the National Natural Science Foundation of China (11150110134)the Science Foundation of Aeronautics of China (20101271004)
文摘High-order schemes based on block-structured adaptive mesh refinement method are prepared to solve computational aeroacoustic （CAA） problems with an aim at improving computational efficiency. A number of numerical issues associated with high-order schemes on an adaptively refined mesh, such as stability and accuracy are addressed. Several CAA benchmark problems are used to demonstrate the feasibility and efficiency of the approach.
基金This work was financially supported by the National Natural Science Foundation of China(Nos.51779049,51879058,52071098,51979053).
文摘In this study,a numerical model for simulating two-phase flow is developed.The Cartesian grid with Adaptive Mesh Refinement(AMR)is adopted to reduce the computational cost.An explicit projection method is used for the time integration and the Finite Difference Method(FDM)is applied on a staggered grid for the discretization of spatial derivatives.The Volume of Fluid(VOF)method with Piecewise-Linear Interface Calculation(PLIC)is extended to the AMR grid to capture the gas-water interface accurately.A coarse-fine interface treatment method is developed to preserve the flux conservation at the interfaces.Several two-dimensional(2D)and three-dimensional(3D)benchmark cases are carried out for the validation of the model.2D and 3D shear flow tests are conducted to validate the extension of the VOF method to the AMR grid.A 2D linear sloshing case is considered in which the model is proved to have 2nd-order accuracy in space.The efficiency of applying the AMR grid is discussed with a nonlinear sloshing problem.Finally,2D solitary wave past stage and 2D/3D dam break are simulated to demonstrate that the model is able to simulate violent interface problems.
文摘A new method for estimating the posterior error of linear triangular element is presented. According to the specified accuracy, the element size and node spacing function of adaptive h-version mesh refinement are predicted. The main domain is divided by the isolines of node spacing into subregions in which mesh regeneration is realized. This remeshing refinement process implements mesh subdivision and mesh de-refinement in onecycle.
文摘In recent years, due to the rapid development of computer hardware and the urgent need of complex engineering problems, great support has been provided in the related fields of unstructured mesh generation. A large number of research results show that the adaptive analysis is an effective way to improve the efficiency and precision of the numerical calculation. The reliable error estimation and the powerful mesh generation are two key problems in the process of adaptive numerical analysis. H-type refinement strategy adding the new nodes in the high error area, gradually refines the mesh to reduce the size of the element to achieve the purpose of mesh adaptation;this strategy is simple, intuitive and easy to program. Although the calculation accuracy of unstructured triangle and tetrahedron elements is not high, these elements are suitable for discretization of any complex problem domain, and have a wider range of application in academic and engineering fields.
文摘从三维Mesh数据中分割建筑物立面以识别对象,是三维场景理解的关键,但现有方法多依赖高成本的精细标注数据。针对该问题,提出了一种半监督学习方法,引入一种基于对比学习和一致性正则化的半监督语义分割(semi-supervised semantic segmentation based on contrastive learning and consistency regularization,SS_CC)方法,用于分割三维Mesh数据的建筑物立面。在SS_CC方法中,改进后的对比学习模块利用正负样本之间的类可分性,能够更有效地利用类特征信息;提出的基于特征空间的一致性正则化损失函数,从挖掘全局特征的角度增强了对所提取建筑物立面特征的鉴别力。实验结果表明,所提出的SS_CC方法在F1分数、mIoU指标上优于当前一些主流方法,且在建筑物的墙面和窗户上的分割效果相对更好。
