In generator design field,waveform total harmonic distortion(THD)and telephone harmonic factor(THF)are parameters commonly used to measure the impact of generator no-load voltage harmonics on the power communication q...In generator design field,waveform total harmonic distortion(THD)and telephone harmonic factor(THF)are parameters commonly used to measure the impact of generator no-load voltage harmonics on the power communication quality.Tubular hydrogenerators are considered the optimal generator for exploiting low-head,high-flow hydro resources,and they have seen increasingly widespread application in China's power systems recent years.However,owing to the compact and constrained internal space of such generators,their internal magnetic-field harmonics are pronounced.Therefore,accurate calculation of their THD and THF is crucial during the analysis and design stages to ensure the quality of power communication.Especially in the electromagnetic field finite element modeling analysis of such generators,the type and order of the finite element meshes may have a significant impact on the THD and THF calculation results,which warrants in-depth research.To address this,this study takes a real 34 MW large tubular hydrogenerator as an example,and establishes its electromagnetic field finite element model under no-load conditions.Two types of meshes,five mesh densities,and two mesh orders are analyzed to reveal the effect of electromagnetic field finite element mesh types and orders on the calculation results of THD and THF for such generators.展开更多
We explore an intersection-based remap method between meshes consisting of isoparametric elements.We present algorithms for the case of serendipity isoparametric elements(QUAD8 elements)and piece-wise constant(cell-ce...We explore an intersection-based remap method between meshes consisting of isoparametric elements.We present algorithms for the case of serendipity isoparametric elements(QUAD8 elements)and piece-wise constant(cell-centered)discrete fields.We demonstrate convergence properties of this remap method with a few numerical experiments.展开更多
In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state pr...In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.展开更多
We consider the mixed discontinuous Galerkin(DG)finite element approximation of the Stokes equation and provide the analysis for the[P_(k)]^d-P_(k-1)element on the tensor product meshes.Comparing to the previous stabi...We consider the mixed discontinuous Galerkin(DG)finite element approximation of the Stokes equation and provide the analysis for the[P_(k)]^d-P_(k-1)element on the tensor product meshes.Comparing to the previous stability proof with[Q_(k)]^(d)-Q_(k-1)discontinuous finite elements in the existing references,our first contribution is to extend the formal proof to the[P_(k)]^d-P_(k-1)discontinuous elements on the tensor product meshes.Numerical infsup tests have been performed to compare Q_(x)and P_(k)types of elements and validate the well-posedness in both settings.Secondly,our contribution is to design the enhanced pressure-robust discretization by only modifying the body source assembling on[P_(k)]^d-P_(k-1)schemes to improve the numerical simulation further.The produced numerical velocity solution via our enhancement shows viscosity and pressure independence and thus outperforms the solution produced by standard discontinuous Galerkin schemes.Robustness analysis and numerical tests have been provided to validate the scheme's robustness.展开更多
Abdominal wall defects and incisional hernias represent a challenging problem. In particular, when a synthetic mesh is applied to contaminated wounds, its removal is required in 50%-90% of cases. Biosynthetic meshes a...Abdominal wall defects and incisional hernias represent a challenging problem. In particular, when a synthetic mesh is applied to contaminated wounds, its removal is required in 50%-90% of cases. Biosynthetic meshes are the newest tool available to surgeons and they could have a role in ventral hernia repair in a potential-ly contaminated field. We describe the use of a sheet of bovine pericardium graft in the reconstruction of abdominal wall defect in two patients. Bovine pericardium graft was placed in the retrorectus space and secured to the anterior abdominal wall using polypropylene sutures in a tension-free manner. We experienced no evidence of recurrence at 4 and 5 years follow-up.展开更多
A parallel virtual machine （PVM） protocol based parallel computation of 3-D hypersonic flows with chemical non-equilibrium on hybrid meshes is presented. The numerical simulation for hypersonic flows with chemical n...A parallel virtual machine （PVM） protocol based parallel computation of 3-D hypersonic flows with chemical non-equilibrium on hybrid meshes is presented. The numerical simulation for hypersonic flows with chemical non-equilibrium reactions encounters the stiffness problem, thus taking huge CPU time. Based on the domain decomposition method, a high efficient automatic domain decomposer for three-dimensional hybrid meshes is developed, and then implemented to the numerical simulation of hypersonic flows. Control equations are multicomponent N-S equations, and spatially discretized scheme is used by a cell-centered finite volume algorithm with a five-stage Runge-Kutta time step. The chemical kinetic model is a seven species model with weak ionization. A point-implicit method is used to solve the chemical source term. Numerical results on PC-Cluster are verified on a bi-ellipse model compared with references.展开更多
The compressive deformation behavior in the longitudinal direction of graded Ti–6Al–4V meshes fabricated by electron beam melting was investigated using experiments and finite element methods（FEM）.The results indi...The compressive deformation behavior in the longitudinal direction of graded Ti–6Al–4V meshes fabricated by electron beam melting was investigated using experiments and finite element methods（FEM）.The results indicate that the overall strain along the longitudinal direction is the sum of the net strain carried by each uniform mesh constituent and the deformation behavior fits the Reuss model well. The layer thickness and the sectional area have no effect on the elastic modulus, whereas the strength increases with the sectional area due to the edge effect of each uniform mesh constituent. By optimizing3 D graded/gradient design, meshes with balanced superior properties, such as high strength, energy absorption and low elastic modulus, can be fabricated by electron beam melting.展开更多
The Wilson finite element method is considered to solve a class of two- dimensional second order elliptic boundary value problems. By using of the particular structure of the element and some new techniques, we obtain...The Wilson finite element method is considered to solve a class of two- dimensional second order elliptic boundary value problems. By using of the particular structure of the element and some new techniques, we obtain the superclose and global superconvergence on anisotropic meshes. Numerical example is also given to confirm our theoretical analysis.展开更多
The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application,...The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application, some parametrization results might behave better than others. In this paper, we will propose a method to parametrize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result. Here the parametrization results are obtained by minimizing discrete har- monic energy subject to spherical constraints. Then some applications are given to illustrate the advantages of our results. Based on PHT-splines, parametric surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parametrization has been obtained.展开更多
In this paper, we present an infrared transparent frequency selective surface（ITFSS） based on iterative metallic meshes, which possesses the properties of high transmittance in infrared band and band-pass effect in ...In this paper, we present an infrared transparent frequency selective surface（ITFSS） based on iterative metallic meshes, which possesses the properties of high transmittance in infrared band and band-pass effect in millimeter wave band. Cross-slot units are designed on the iterative metallic meshes, which is composed of two same square metallic meshes with a misplaced overlap. In the infrared band of 3–5 μm, the ITFSS has an average transmittance of 80% with a Mg F2 substrate. In the millimeter wave band, a transmittance of-0.74 d B at the resonance frequency of 39.4 GHz is obtained. Moreover, theoretical simulations of the ITFSS diffractive characteristics and transmittance response are also investigated in detail. This ITFSS may be an efficient way to achieve the metamaterial millimeter wave/infrared functional film.展开更多
The paper presents a finite volume numerical method universally applicable for solving both linear and nonlinear aeroacoustics problems on arbitrary unstructured meshes. It is based on the vertexcentered multi-paramet...The paper presents a finite volume numerical method universally applicable for solving both linear and nonlinear aeroacoustics problems on arbitrary unstructured meshes. It is based on the vertexcentered multi-parameter scheme offering up to the 6th accuracy order achieved on the Cartesian meshes. An adaptive dissipation is added for the numerical treatment of possible discontinuities. The scheme properties are studied on a series of test cases, its efficiency is demonstrated at simulating the noise suppression in resonance-type liners.展开更多
A systematic methodology for formulating,implementing,solving and verifying discrete adjoint of the compressible Reynolds-averaged Navier-Stokes（RANS） equations for aerodynamic design optimization on unstructured me...A systematic methodology for formulating,implementing,solving and verifying discrete adjoint of the compressible Reynolds-averaged Navier-Stokes（RANS） equations for aerodynamic design optimization on unstructured meshes is proposed.First,a general adjoint formulation is constructed for the entire optimization problem,including parameterization,mesh deformation,flow solution and computation of the objective function,which is followed by detailed formulations of matrix-vector products arising in the adjoint model.According to this formulation,procedural components of implementing the required matrix-vector products are generated by means of automatic differentiation（AD） in a structured and modular manner.Furthermore,a duality-preserving iterative algorithm is employed to solve flow adjoint equations arising in the adjoint model,ensuring identical convergence rates for the tangent and the adjoint models.A three-step strategy is adopted to verify the adjoint computation.The proposed method has several remarkable features：the use of AD techniques avoids tedious and error-prone manual derivation and programming;duality is strictly preserved so that consistent and highly accurate discrete sensitivities can be obtained;and comparable efficiency to hand-coded implementation can be achieved.Upon the current discrete adjoint method,a gradient-based optimization framework has been developed and applied to a drag reduction problem.展开更多
Expression, occlusion, and pose variations are three main challenges for 3D face recognition. A novel method is presented to address 3D face recognition using scale-invariant feature transform(SIFT) features on 3D mes...Expression, occlusion, and pose variations are three main challenges for 3D face recognition. A novel method is presented to address 3D face recognition using scale-invariant feature transform(SIFT) features on 3D meshes. After preprocessing, shape index extrema on the 3D facial surface are selected as keypoints in the difference scale space and the unstable keypoints are removed after two screening steps. Then, a local coordinate system for each keypoint is established by principal component analysis(PCA).Next, two local geometric features are extracted around each keypoint through the local coordinate system. Additionally, the features are augmented by the symmetrization according to the approximate left-right symmetry in human face. The proposed method is evaluated on the Bosphorus, BU-3DFE, and Gavab databases, respectively. Good results are achieved on these three datasets. As a result, the proposed method proves robust to facial expression variations, partial external occlusions and large pose changes.展开更多
In this paper, the nonconforming mortar finite element with a class of meshes is studied without considering the global regularity condition or quasi-uniformly assumption. Meanwhile, the superclose result coincides wi...In this paper, the nonconforming mortar finite element with a class of meshes is studied without considering the global regularity condition or quasi-uniformly assumption. Meanwhile, the superclose result coincides with conventional methods is obtained by means of integral identities techniques.展开更多
In this paper,we propose a new method to achieve automatic matching of multi-scale roads under the constraints of smaller scale data.The matching process is:Firstly,meshes are extracted from two different scales road ...In this paper,we propose a new method to achieve automatic matching of multi-scale roads under the constraints of smaller scale data.The matching process is:Firstly,meshes are extracted from two different scales road data.Secondly,several basic meshes in the larger scale road network will be merged into a composite one which is matched with one mesh in the smaller scale road network,to complete the N∶1(N>1)and 1∶1 matching.Thirdly,meshes of the two different scale road data with M∶N(M>1,N>1)matching relationships will be matched.Finally,roads will be classified into two categories under the constraints of meshes:mesh boundary roads and mesh internal roads,and then matchings between the two scales meshes will be carried out within their own categories according to the matching relationships.The results show that roads of different scales will be more precisely matched using the proposed method.展开更多
Higher-order displacement-based finite element methods are useful for simulating bending problems and potentially addressing mesh-locking associated with nearly-incompressible elasticity,yet are computationally expens...Higher-order displacement-based finite element methods are useful for simulating bending problems and potentially addressing mesh-locking associated with nearly-incompressible elasticity,yet are computationally expensive.To address the computational expense,the paper presents a matrix-free,displacement-based,higher-order,hexahedral finite element implementation of compressible and nearly-compressible(ν→0.5)linear isotropic elasticity at small strain with p-multigrid preconditioning.The cost,solve time,and scalability of the implementation with respect to strain energy error are investigated for polynomial order p=1,2,3,4 for compressible elasticity,and p=2,3,4 for nearly-incompressible elasticity,on different number of CPU cores for a tube bending problem.In the context of this matrix-free implementation,higher-order polynomials(p=3,4)generally are faster in achieving better accuracy in the solution than lower-order polynomials(p=1,2).However,for a beam bending simulation with stress concentration(singularity),it is demonstrated that higher-order finite elements do not improve the spatial order of convergence,even though accuracy is improved.展开更多
The nonconforming Wilson’s brick classically is restricted to regular hexahedral meshes. Lesaint and Zlamal[6] relaxed this constraint for the two-dimensional analonue of this element In this paper we extend their re...The nonconforming Wilson’s brick classically is restricted to regular hexahedral meshes. Lesaint and Zlamal[6] relaxed this constraint for the two-dimensional analonue of this element In this paper we extend their results to three dimensions and prove that and where u is the exact solution, u_h is the approximate solution and is the usual norm for the Sobolev space H^1(?).展开更多
Mesh motion strategy is one of the key points in many fluid-structure interaction problems. One popular technique used to solve this problem is known as the spring analogy method. In this paper a new mesh update appro...Mesh motion strategy is one of the key points in many fluid-structure interaction problems. One popular technique used to solve this problem is known as the spring analogy method. In this paper a new mesh update approach based on the spring analogy method is presented for the effective treatment of mesh moving boundary problems. The proposed mesh update technique is developed to avoid the generation of squashed invalid elements and maintain mesh quality by considering each element shape and grid scale to the definition of the spring stiffness. The method is applied to several 2D and 3D boundary correction problems for fully unstructured meshes and evaluated by a mesh quality indicator. With these applications,it is demonstrated that the present method preserves mesh quality even under large motions of bodies. We highlight the advantages of this method with respect to robustness and mesh quality.展开更多
A high-order leap-frog based non-dissipative discontinuous Galerkin time- domain method for solving Maxwell＇s equations is introduced and analyzed. The pro- posed method combines a centered approximation for the eval...A high-order leap-frog based non-dissipative discontinuous Galerkin time- domain method for solving Maxwell＇s equations is introduced and analyzed. The pro- posed method combines a centered approximation for the evaluation of fluxes at the in- terface between neighboring elements, with a Nth-order leap-frog time scheme. More- over, the interpolation degree is defined at the element level and the mesh is refined locally in a non-conforming way resulting in arbitrary level hanging nodes. The method is proved to be stable under some CFL-like condition on the time step. The convergence of the semi-discrete approximation to Maxwelrs equations is established rigorously and bounds on the global divergence error are provided. Numerical experiments with high- order elements show the potential of the method.展开更多
This paper concerns a discontinuous Galerkin(DG)method for a one-dimensional singularly perturbed problem which possesses essential characteristic of second order convection-diffusion problem after some simple transfo...This paper concerns a discontinuous Galerkin(DG)method for a one-dimensional singularly perturbed problem which possesses essential characteristic of second order convection-diffusion problem after some simple transformations.We derive an optimal convergence of the DG method for eight layer-adapted meshes in a general framework.The convergence rate is valid independent of the small parameter.Furthermore,we establish a sharper L^(2)-error estimate if the true solution has a special regular component.Numerical experiments are also given.展开更多
基金sponsored by the National Natural Science Foundation,Youth Foundation of China,Grant/Award Number:51607146Sichuan Natural Sciences Fund,Grant/Award Number:2023NSFSC0295。
文摘In generator design field,waveform total harmonic distortion(THD)and telephone harmonic factor(THF)are parameters commonly used to measure the impact of generator no-load voltage harmonics on the power communication quality.Tubular hydrogenerators are considered the optimal generator for exploiting low-head,high-flow hydro resources,and they have seen increasingly widespread application in China's power systems recent years.However,owing to the compact and constrained internal space of such generators,their internal magnetic-field harmonics are pronounced.Therefore,accurate calculation of their THD and THF is crucial during the analysis and design stages to ensure the quality of power communication.Especially in the electromagnetic field finite element modeling analysis of such generators,the type and order of the finite element meshes may have a significant impact on the THD and THF calculation results,which warrants in-depth research.To address this,this study takes a real 34 MW large tubular hydrogenerator as an example,and establishes its electromagnetic field finite element model under no-load conditions.Two types of meshes,five mesh densities,and two mesh orders are analyzed to reveal the effect of electromagnetic field finite element mesh types and orders on the calculation results of THD and THF for such generators.
基金This work was performed under the auspices of the National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory under Contract No.89233218CNA000001.
文摘We explore an intersection-based remap method between meshes consisting of isoparametric elements.We present algorithms for the case of serendipity isoparametric elements(QUAD8 elements)and piece-wise constant(cell-centered)discrete fields.We demonstrate convergence properties of this remap method with a few numerical experiments.
基金supported by the NSFC Grant No.11872210 and Grant No.MCMS-I-0120G01Chi-Wang Shu:Research is supported by the AFOSR Grant FA9550-20-1-0055 and the NSF Grant DMS-2010107Jianxian Qiu:Research is supported by the NSFC Grant No.12071392.
文摘In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.
文摘We consider the mixed discontinuous Galerkin(DG)finite element approximation of the Stokes equation and provide the analysis for the[P_(k)]^d-P_(k-1)element on the tensor product meshes.Comparing to the previous stability proof with[Q_(k)]^(d)-Q_(k-1)discontinuous finite elements in the existing references,our first contribution is to extend the formal proof to the[P_(k)]^d-P_(k-1)discontinuous elements on the tensor product meshes.Numerical infsup tests have been performed to compare Q_(x)and P_(k)types of elements and validate the well-posedness in both settings.Secondly,our contribution is to design the enhanced pressure-robust discretization by only modifying the body source assembling on[P_(k)]^d-P_(k-1)schemes to improve the numerical simulation further.The produced numerical velocity solution via our enhancement shows viscosity and pressure independence and thus outperforms the solution produced by standard discontinuous Galerkin schemes.Robustness analysis and numerical tests have been provided to validate the scheme's robustness.
文摘Abdominal wall defects and incisional hernias represent a challenging problem. In particular, when a synthetic mesh is applied to contaminated wounds, its removal is required in 50%-90% of cases. Biosynthetic meshes are the newest tool available to surgeons and they could have a role in ventral hernia repair in a potential-ly contaminated field. We describe the use of a sheet of bovine pericardium graft in the reconstruction of abdominal wall defect in two patients. Bovine pericardium graft was placed in the retrorectus space and secured to the anterior abdominal wall using polypropylene sutures in a tension-free manner. We experienced no evidence of recurrence at 4 and 5 years follow-up.
文摘A parallel virtual machine （PVM） protocol based parallel computation of 3-D hypersonic flows with chemical non-equilibrium on hybrid meshes is presented. The numerical simulation for hypersonic flows with chemical non-equilibrium reactions encounters the stiffness problem, thus taking huge CPU time. Based on the domain decomposition method, a high efficient automatic domain decomposer for three-dimensional hybrid meshes is developed, and then implemented to the numerical simulation of hypersonic flows. Control equations are multicomponent N-S equations, and spatially discretized scheme is used by a cell-centered finite volume algorithm with a five-stage Runge-Kutta time step. The chemical kinetic model is a seven species model with weak ionization. A point-implicit method is used to solve the chemical source term. Numerical results on PC-Cluster are verified on a bi-ellipse model compared with references.
基金supported by 863 Project(No.2015AA033702)the National Basic Research Program of China(Nos.2012CB619103,2012CB933901 and 2012CB933902)+1 种基金the National Natural Science Foundation of China(Nos.51271182 and 51271180)the Shandong Provincial Natural Science Foundation,China(No.ZR2014JL031)
文摘The compressive deformation behavior in the longitudinal direction of graded Ti–6Al–4V meshes fabricated by electron beam melting was investigated using experiments and finite element methods（FEM）.The results indicate that the overall strain along the longitudinal direction is the sum of the net strain carried by each uniform mesh constituent and the deformation behavior fits the Reuss model well. The layer thickness and the sectional area have no effect on the elastic modulus, whereas the strength increases with the sectional area due to the edge effect of each uniform mesh constituent. By optimizing3 D graded/gradient design, meshes with balanced superior properties, such as high strength, energy absorption and low elastic modulus, can be fabricated by electron beam melting.
基金Project supported by the National Natural Science Foundation of China (No. 10371113)
文摘The Wilson finite element method is considered to solve a class of two- dimensional second order elliptic boundary value problems. By using of the particular structure of the element and some new techniques, we obtain the superclose and global superconvergence on anisotropic meshes. Numerical example is also given to confirm our theoretical analysis.
基金Project supported by the Outstanding Youth Grant of Natural Science Foundation of China (No. 60225002), the National Basic Research Program (973) of China (No. 2004CB318000), the National Natural Science Foundation of China (Nos. 60533060 and 60473132)
文摘The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application, some parametrization results might behave better than others. In this paper, we will propose a method to parametrize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result. Here the parametrization results are obtained by minimizing discrete har- monic energy subject to spherical constraints. Then some applications are given to illustrate the advantages of our results. Based on PHT-splines, parametric surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parametrization has been obtained.
基金supported by the National Natural Science Foundation of China(Grant No.61401424)
文摘In this paper, we present an infrared transparent frequency selective surface（ITFSS） based on iterative metallic meshes, which possesses the properties of high transmittance in infrared band and band-pass effect in millimeter wave band. Cross-slot units are designed on the iterative metallic meshes, which is composed of two same square metallic meshes with a misplaced overlap. In the infrared band of 3–5 μm, the ITFSS has an average transmittance of 80% with a Mg F2 substrate. In the millimeter wave band, a transmittance of-0.74 d B at the resonance frequency of 39.4 GHz is obtained. Moreover, theoretical simulations of the ITFSS diffractive characteristics and transmittance response are also investigated in detail. This ITFSS may be an efficient way to achieve the metamaterial millimeter wave/infrared functional film.
基金Russian Foundation of Basic Research(No. 04-01-08034, 06-01-00293-a)
文摘The paper presents a finite volume numerical method universally applicable for solving both linear and nonlinear aeroacoustics problems on arbitrary unstructured meshes. It is based on the vertexcentered multi-parameter scheme offering up to the 6th accuracy order achieved on the Cartesian meshes. An adaptive dissipation is added for the numerical treatment of possible discontinuities. The scheme properties are studied on a series of test cases, its efficiency is demonstrated at simulating the noise suppression in resonance-type liners.
基金supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions of China
文摘A systematic methodology for formulating,implementing,solving and verifying discrete adjoint of the compressible Reynolds-averaged Navier-Stokes（RANS） equations for aerodynamic design optimization on unstructured meshes is proposed.First,a general adjoint formulation is constructed for the entire optimization problem,including parameterization,mesh deformation,flow solution and computation of the objective function,which is followed by detailed formulations of matrix-vector products arising in the adjoint model.According to this formulation,procedural components of implementing the required matrix-vector products are generated by means of automatic differentiation（AD） in a structured and modular manner.Furthermore,a duality-preserving iterative algorithm is employed to solve flow adjoint equations arising in the adjoint model,ensuring identical convergence rates for the tangent and the adjoint models.A three-step strategy is adopted to verify the adjoint computation.The proposed method has several remarkable features：the use of AD techniques avoids tedious and error-prone manual derivation and programming;duality is strictly preserved so that consistent and highly accurate discrete sensitivities can be obtained;and comparable efficiency to hand-coded implementation can be achieved.Upon the current discrete adjoint method,a gradient-based optimization framework has been developed and applied to a drag reduction problem.
基金Project(XDA06020300)supported by the"Strategic Priority Research Program"of the Chinese Academy of SciencesProject(12511501700)supported by the Research on the Key Technology of Internet of Things for Urban Community Safety Based on Video Sensor networks
文摘Expression, occlusion, and pose variations are three main challenges for 3D face recognition. A novel method is presented to address 3D face recognition using scale-invariant feature transform(SIFT) features on 3D meshes. After preprocessing, shape index extrema on the 3D facial surface are selected as keypoints in the difference scale space and the unstable keypoints are removed after two screening steps. Then, a local coordinate system for each keypoint is established by principal component analysis(PCA).Next, two local geometric features are extracted around each keypoint through the local coordinate system. Additionally, the features are augmented by the symmetrization according to the approximate left-right symmetry in human face. The proposed method is evaluated on the Bosphorus, BU-3DFE, and Gavab databases, respectively. Good results are achieved on these three datasets. As a result, the proposed method proves robust to facial expression variations, partial external occlusions and large pose changes.
基金Foundation item: Supported by the NSF of China(10371113)Supported by the Foundation of Overseas Scholar of China(2001(119))Supported by the project of Creative Engineering of Province of China(2002(219))
文摘In this paper, the nonconforming mortar finite element with a class of meshes is studied without considering the global regularity condition or quasi-uniformly assumption. Meanwhile, the superclose result coincides with conventional methods is obtained by means of integral identities techniques.
基金The National Natural Science Foundation of China(Nos.4110136241471386)。
文摘In this paper,we propose a new method to achieve automatic matching of multi-scale roads under the constraints of smaller scale data.The matching process is:Firstly,meshes are extracted from two different scales road data.Secondly,several basic meshes in the larger scale road network will be merged into a composite one which is matched with one mesh in the smaller scale road network,to complete the N∶1(N>1)and 1∶1 matching.Thirdly,meshes of the two different scale road data with M∶N(M>1,N>1)matching relationships will be matched.Finally,roads will be classified into two categories under the constraints of meshes:mesh boundary roads and mesh internal roads,and then matchings between the two scales meshes will be carried out within their own categories according to the matching relationships.The results show that roads of different scales will be more precisely matched using the proposed method.
基金The research relied on computational resources[29]provided by the University of Colorado Boulder Research Computing Group,which is supported by the National1302 CMES,2021,vol.129,no.3 Science Foundation(Awards ACI-1532235 and ACI-1532236)University of Colorado Boulder,and Colorado State University.
文摘Higher-order displacement-based finite element methods are useful for simulating bending problems and potentially addressing mesh-locking associated with nearly-incompressible elasticity,yet are computationally expensive.To address the computational expense,the paper presents a matrix-free,displacement-based,higher-order,hexahedral finite element implementation of compressible and nearly-compressible(ν→0.5)linear isotropic elasticity at small strain with p-multigrid preconditioning.The cost,solve time,and scalability of the implementation with respect to strain energy error are investigated for polynomial order p=1,2,3,4 for compressible elasticity,and p=2,3,4 for nearly-incompressible elasticity,on different number of CPU cores for a tube bending problem.In the context of this matrix-free implementation,higher-order polynomials(p=3,4)generally are faster in achieving better accuracy in the solution than lower-order polynomials(p=1,2).However,for a beam bending simulation with stress concentration(singularity),it is demonstrated that higher-order finite elements do not improve the spatial order of convergence,even though accuracy is improved.
文摘The nonconforming Wilson’s brick classically is restricted to regular hexahedral meshes. Lesaint and Zlamal[6] relaxed this constraint for the two-dimensional analonue of this element In this paper we extend their results to three dimensions and prove that and where u is the exact solution, u_h is the approximate solution and is the usual norm for the Sobolev space H^1(?).
基金the National Natural Science Foundation of China(No.50778111)the Doctoral Disciplinary Special Research Project of Chinese Ministry of Education(No.200802480056)the Key Project of Fund of Science Technology Development of Shanghai(No.07JC14023)
文摘Mesh motion strategy is one of the key points in many fluid-structure interaction problems. One popular technique used to solve this problem is known as the spring analogy method. In this paper a new mesh update approach based on the spring analogy method is presented for the effective treatment of mesh moving boundary problems. The proposed mesh update technique is developed to avoid the generation of squashed invalid elements and maintain mesh quality by considering each element shape and grid scale to the definition of the spring stiffness. The method is applied to several 2D and 3D boundary correction problems for fully unstructured meshes and evaluated by a mesh quality indicator. With these applications,it is demonstrated that the present method preserves mesh quality even under large motions of bodies. We highlight the advantages of this method with respect to robustness and mesh quality.
基金supported by a grant from the French National Ministry of Education and Research(MENSR,19755-2005)
文摘A high-order leap-frog based non-dissipative discontinuous Galerkin time- domain method for solving Maxwell＇s equations is introduced and analyzed. The pro- posed method combines a centered approximation for the evaluation of fluxes at the in- terface between neighboring elements, with a Nth-order leap-frog time scheme. More- over, the interpolation degree is defined at the element level and the mesh is refined locally in a non-conforming way resulting in arbitrary level hanging nodes. The method is proved to be stable under some CFL-like condition on the time step. The convergence of the semi-discrete approximation to Maxwelrs equations is established rigorously and bounds on the global divergence error are provided. Numerical experiments with high- order elements show the potential of the method.
基金Supported by the National Natural Science Foundation of China(11801396)National College Students Innovation and Entrepreneurship Training Project(202210332019Z)。
文摘This paper concerns a discontinuous Galerkin(DG)method for a one-dimensional singularly perturbed problem which possesses essential characteristic of second order convection-diffusion problem after some simple transformations.We derive an optimal convergence of the DG method for eight layer-adapted meshes in a general framework.The convergence rate is valid independent of the small parameter.Furthermore,we establish a sharper L^(2)-error estimate if the true solution has a special regular component.Numerical experiments are also given.
