The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition (POD)and discrete empirical interpolation method (DEIM). Instead of using the classical DEIM to directly approxima...The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition (POD)and discrete empirical interpolation method (DEIM). Instead of using the classical DEIM to directly approximate thenonlinear term of a system, our approach extracts the main part of the nonlinear term with a linear approximation beforeapproximating the residual with the DEIM. We construct the linear term by Taylor series expansion and dynamic modedecomposition (DMD), respectively, so as to obtain a more accurate reconstruction of the nonlinear term. In addition, anovel error prediction model is devised for the POD-DEIM reduced systems by employing neural networks with the aid oferror data. The error model is cheaply computable and can be adopted as a remedy model to enhance the reduction accuracy.Finally, numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.展开更多
In this paper,an efcient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible fow in porous media.The cornerstone of the proposed model is that the fu...In this paper,an efcient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible fow in porous media.The cornerstone of the proposed model is that the full approximate storage multigrid method is used to accelerate the solution of fow equation in original full-order space,and the discrete empirical interpolation method(DEIM)is applied to speed up the solution of Peng-Robinson equation of state in reduced-order subspace.The multigrid-DEIM semi-reduced-order model combines the computation both in full-order space and in reducedorder subspace,which not only preserves good prediction accuracy of full-order model,but also gains dramatic computational acceleration by multigrid and DEIM.Numerical performances including accuracy and acceleration of the proposed model are carefully evaluated by comparing with that of the standard semi-implicit method.In addition,the selection of interpolation points for constructing the low-dimensional subspace for solving the Peng-Robinson equation of state is demonstrated and carried out in detail.Comparison results indicate that the multigrid-DEIM semi-reduced-order model can speed up the simulation substantially at the same time preserve good computational accuracy with negligible errors.The general acceleration is up to 50-60 times faster than that of standard semi-implicit method in two-dimensional simulations,but the average relative errors of numerical results between these two methods only have the order of magnitude 10^(−4)-10^(−6)%.展开更多
A new method as a post-processing step is presented to improve the shape quality of triangular meshes, which uses a topological clean up procedure and discrete smoothing interpolate (DSI) algorithm together. T...A new method as a post-processing step is presented to improve the shape quality of triangular meshes, which uses a topological clean up procedure and discrete smoothing interpolate (DSI) algorithm together. This method can improve the angle distribution of mesh element. while keeping the resulting meshes conform to the predefined constraints which are inputted as a PSLG.展开更多
Fiber-reinforced composites are an ideal material for the lightweight design of aerospace structures. Especially in recent years, with the rapid development of composite additive manufacturing technology, the design o...Fiber-reinforced composites are an ideal material for the lightweight design of aerospace structures. Especially in recent years, with the rapid development of composite additive manufacturing technology, the design optimization of variable stiffness of fiber-reinforced composite laminates has attracted widespread attention from scholars and industry. In these aerospace composite structures, numerous cutout panels and shells serve as access points for maintaining electrical, fuel, and hydraulic systems. The traditional fiber-reinforced composite laminate subtractive drilling manufacturing inevitably faces the problems of interlayer delamination, fiber fracture, and burr of the laminate. Continuous fiber additive manufacturing technology offers the potential for integrated design optimization and manufacturing with high structural performance. Considering the integration of design and manufacturability in continuous fiber additive manufacturing, the paper proposes linear and nonlinear filtering strategies based on the Normal Distribution Fiber Optimization (NDFO) material interpolation scheme to overcome the challenge of discrete fiber optimization results, which are difficult to apply directly to continuous fiber additive manufacturing. With minimizing structural compliance as the objective function, the proposed approach provides a strategy to achieve continuity of discrete fiber paths in the variable stiffness design optimization of composite laminates with regular and irregular holes. In the variable stiffness design optimization model, the number of candidate fiber laying angles in the NDFO material interpolation scheme is considered as design variable. The sensitivity information of structural compliance with respect to the number of candidate fiber laying angles is obtained using the analytical sensitivity analysis method. Based on the proposed variable stiffness design optimization method for complex perforated composite laminates, the numerical examples consider the variable stiffness design optimization of typical non-perforated and perforated composite laminates with circular, square, and irregular holes, and systematically discuss the number of candidate discrete fiber laying angles, discrete fiber continuous filtering strategies, and filter radius on structural compliance, continuity, and manufacturability. The optimized discrete fiber angles of variable stiffness laminates are converted into continuous fiber laying paths using a streamlined process for continuous fiber additive manufacturing. Meanwhile, the optimized non-perforated and perforated MBB beams after discrete fiber continuous treatment, are manufactured using continuous fiber co-extrusion additive manufacturing technology to verify the effectiveness of the variable stiffness fiber optimization framework proposed in this paper.展开更多
In this paper, a method to construct a surface with point interpolation and normal interpolation is presented. An algorithm to construct the discrete interpolation is also presented, which has the time com- plexity O ...In this paper, a method to construct a surface with point interpolation and normal interpolation is presented. An algorithm to construct the discrete interpolation is also presented, which has the time com- plexity O (Nlog N), where N in the number of scattered points.展开更多
A space-time coupled spectral element method based on Chebyshev polynomials is presented for solving time-dependent wave equations.Acoustic propagation problems in1＋1,2＋1,3＋1 dimensions with the Dirichlet boundary ...A space-time coupled spectral element method based on Chebyshev polynomials is presented for solving time-dependent wave equations.Acoustic propagation problems in1＋1,2＋1,3＋1 dimensions with the Dirichlet boundary conditions are simulated via space-time coupled spectral element method using quadrilateral,hexahedral and tesseractic elements respectively.Space-time coupled spectral element method can obtain high-order precision over time.With the same total number of nodes,higher numerical precision is obtained if the higher-order Chebyshev polynomials in space directions and lower-order Chebyshev polynomials in time direction are adopted.Numerical illustrations have indicated that the space-time algorithm provides higher precision than the semi-discretization.When space-time coupled spectral element method is used,time subdomain-by-subdomain approach is more economical than time domain approach.展开更多
Smooth interpolants defined over tetrahedra are currently being developed for they have many applications in geography, solid modeling, finite element analysis, etc. In this paper, we will characterize a certain class...Smooth interpolants defined over tetrahedra are currently being developed for they have many applications in geography, solid modeling, finite element analysis, etc. In this paper, we will characterize a certain class of C-1 discrete tetrahedral interpolants with only C-1 data required. As special cases of the class characterized, we give two C-1 discrete tetrahedral interpolants which have concise expressions.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11871400 and 11971386)the Natural Science Foundation of Shaanxi Province,China(Grant No.2017JM1019).
文摘The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition (POD)and discrete empirical interpolation method (DEIM). Instead of using the classical DEIM to directly approximate thenonlinear term of a system, our approach extracts the main part of the nonlinear term with a linear approximation beforeapproximating the residual with the DEIM. We construct the linear term by Taylor series expansion and dynamic modedecomposition (DMD), respectively, so as to obtain a more accurate reconstruction of the nonlinear term. In addition, anovel error prediction model is devised for the POD-DEIM reduced systems by employing neural networks with the aid oferror data. The error model is cheaply computable and can be adopted as a remedy model to enhance the reduction accuracy.Finally, numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.
基金This study is supported by the National Natural Science Foundation of China(Nos.51904031,51936001)the Beijing Natural Science Foundation(No.3204038)the Jointly Projects of Beijing Natural Science Foundation and Beijing Municipal Education Commission(No.KZ201810017023).
文摘In this paper,an efcient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible fow in porous media.The cornerstone of the proposed model is that the full approximate storage multigrid method is used to accelerate the solution of fow equation in original full-order space,and the discrete empirical interpolation method(DEIM)is applied to speed up the solution of Peng-Robinson equation of state in reduced-order subspace.The multigrid-DEIM semi-reduced-order model combines the computation both in full-order space and in reducedorder subspace,which not only preserves good prediction accuracy of full-order model,but also gains dramatic computational acceleration by multigrid and DEIM.Numerical performances including accuracy and acceleration of the proposed model are carefully evaluated by comparing with that of the standard semi-implicit method.In addition,the selection of interpolation points for constructing the low-dimensional subspace for solving the Peng-Robinson equation of state is demonstrated and carried out in detail.Comparison results indicate that the multigrid-DEIM semi-reduced-order model can speed up the simulation substantially at the same time preserve good computational accuracy with negligible errors.The general acceleration is up to 50-60 times faster than that of standard semi-implicit method in two-dimensional simulations,but the average relative errors of numerical results between these two methods only have the order of magnitude 10^(−4)-10^(−6)%.
文摘A new method as a post-processing step is presented to improve the shape quality of triangular meshes, which uses a topological clean up procedure and discrete smoothing interpolate (DSI) algorithm together. This method can improve the angle distribution of mesh element. while keeping the resulting meshes conform to the predefined constraints which are inputted as a PSLG.
基金supports for this research were provided by the National Natural Science Foundation of China(No.12272301,12002278,U1906233)the Guangdong Basic and Applied Basic Research Foundation,China(Nos.2023A1515011970,2024A1515010256)+1 种基金the Dalian City Supports Innovation and Entrepreneurship Projects for High-Level Talents,China(2021RD16)the Key R&D Project of CSCEC,China(No.CSCEC-2020-Z-4).
文摘Fiber-reinforced composites are an ideal material for the lightweight design of aerospace structures. Especially in recent years, with the rapid development of composite additive manufacturing technology, the design optimization of variable stiffness of fiber-reinforced composite laminates has attracted widespread attention from scholars and industry. In these aerospace composite structures, numerous cutout panels and shells serve as access points for maintaining electrical, fuel, and hydraulic systems. The traditional fiber-reinforced composite laminate subtractive drilling manufacturing inevitably faces the problems of interlayer delamination, fiber fracture, and burr of the laminate. Continuous fiber additive manufacturing technology offers the potential for integrated design optimization and manufacturing with high structural performance. Considering the integration of design and manufacturability in continuous fiber additive manufacturing, the paper proposes linear and nonlinear filtering strategies based on the Normal Distribution Fiber Optimization (NDFO) material interpolation scheme to overcome the challenge of discrete fiber optimization results, which are difficult to apply directly to continuous fiber additive manufacturing. With minimizing structural compliance as the objective function, the proposed approach provides a strategy to achieve continuity of discrete fiber paths in the variable stiffness design optimization of composite laminates with regular and irregular holes. In the variable stiffness design optimization model, the number of candidate fiber laying angles in the NDFO material interpolation scheme is considered as design variable. The sensitivity information of structural compliance with respect to the number of candidate fiber laying angles is obtained using the analytical sensitivity analysis method. Based on the proposed variable stiffness design optimization method for complex perforated composite laminates, the numerical examples consider the variable stiffness design optimization of typical non-perforated and perforated composite laminates with circular, square, and irregular holes, and systematically discuss the number of candidate discrete fiber laying angles, discrete fiber continuous filtering strategies, and filter radius on structural compliance, continuity, and manufacturability. The optimized discrete fiber angles of variable stiffness laminates are converted into continuous fiber laying paths using a streamlined process for continuous fiber additive manufacturing. Meanwhile, the optimized non-perforated and perforated MBB beams after discrete fiber continuous treatment, are manufactured using continuous fiber co-extrusion additive manufacturing technology to verify the effectiveness of the variable stiffness fiber optimization framework proposed in this paper.
文摘In this paper, a method to construct a surface with point interpolation and normal interpolation is presented. An algorithm to construct the discrete interpolation is also presented, which has the time com- plexity O (Nlog N), where N in the number of scattered points.
基金supported by the the State Plan for Development of Basic Research in Key Area(973Project)(2012CB026004)
文摘A space-time coupled spectral element method based on Chebyshev polynomials is presented for solving time-dependent wave equations.Acoustic propagation problems in1＋1,2＋1,3＋1 dimensions with the Dirichlet boundary conditions are simulated via space-time coupled spectral element method using quadrilateral,hexahedral and tesseractic elements respectively.Space-time coupled spectral element method can obtain high-order precision over time.With the same total number of nodes,higher numerical precision is obtained if the higher-order Chebyshev polynomials in space directions and lower-order Chebyshev polynomials in time direction are adopted.Numerical illustrations have indicated that the space-time algorithm provides higher precision than the semi-discretization.When space-time coupled spectral element method is used,time subdomain-by-subdomain approach is more economical than time domain approach.
文摘Smooth interpolants defined over tetrahedra are currently being developed for they have many applications in geography, solid modeling, finite element analysis, etc. In this paper, we will characterize a certain class of C-1 discrete tetrahedral interpolants with only C-1 data required. As special cases of the class characterized, we give two C-1 discrete tetrahedral interpolants which have concise expressions.
