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Shock-Capturing Particle Hydrodynamics with Reproducing Kernels 认领 引用
1
作者 Stephan Rosswog 《Computer Modeling in Engineering & Sciences》 SCIE EI 2025年第5期1713-1741,共29页
We present and explore a new shock-capturing particle hydrodynamics approach.Our starting point is a commonly used discretization of smoothed particle hydrodynamics.We enhance this discretization with Roe’s approx-im... We present and explore a new shock-capturing particle hydrodynamics approach.Our starting point is a commonly used discretization of smoothed particle hydrodynamics.We enhance this discretization with Roe’s approx-imate Riemann solver,we identify its dissipative terms,and in these terms,we use slope-limited linear reconstruction.All gradients needed for our method are calculated with linearly reproducing kernels that are constructed to enforce the two lowest-order consistency relations.We scrutinize our reproducing kernel implementation carefully on a“glass-like”particle distribution,and we find that constant and linear functions are recovered to machine precision.We probe our method in a series of challenging 3D benchmark problems ranging from shocks over instabilities to Schulz-Rinne-type vorticity-creating shocks.All of our simulations show excellent agreement with analyticeference solutions. 展开更多
关键词 Ideal hydrodynamics reproducing kernels shocks instabilities smoothed particle hydrodynamics
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Analysis of variable coefficient advection-diffusion problems via complex variable reproducing kernel particle method 认领 引用 被引量：1
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作者 翁云杰 程玉民 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第9期197-202,共6页
The complex variable reproducing kernel particle method （CVRKPM） of solving two-dimensional variable coefficient advection-diffusion problems is presented in this paper. The advantage of the CVRKPM is that the shape... The complex variable reproducing kernel particle method （CVRKPM） of solving two-dimensional variable coefficient advection-diffusion problems is presented in this paper. The advantage of the CVRKPM is that the shape function of a two-dimensional problem is formed with a one-dimensional basis function. The Galerkin weak form is employed to obtain the discretized system equation, and the penalty method is used to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional variable coefficient advection-diffusion problems are obtained. Two numerical examples are given to show that the method in this paper has greater accuracy and computational efficiency than the conventional meshless method such as reproducing the kernel particle method （RKPM） and the element- free Galerkin （EFG） method. 展开更多
关键词 meshless method reproducing kernel particle method （RKPM） complex variable reproducingkernel particle method （CVRKPM） advection-diffusion problem
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The complex variable reproducing kernel particle method for two-dimensional elastodynamics 认领 引用 被引量：25
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作者 陈丽 程玉民 《Chinese Physics B》 SCIE EI CAS 2010年第9期59-70,共12页
On the basis of the reproducing kernel particle method （RKPM）, a new meshless method, which is called the complex variable reproducing kernel particle method （CVRKPM）, for two-dimensional elastodynamics is present... On the basis of the reproducing kernel particle method （RKPM）, a new meshless method, which is called the complex variable reproducing kernel particle method （CVRKPM）, for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM. 展开更多
关键词 meshless method reproducing kernel particle method complex variable reproducing kernel particle method elastodvnamics
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An Interpretable Denoising Layer for Neural Networks Based on Reproducing Kernel Hilbert Space and its Application in Machine Fault Diagnosis 认领 引用 被引量：11
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作者 Baoxuan Zhao Changming Cheng +3 位作者 Guowei Tu Zhike Peng Qingbo He Guang Meng 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2021年第3期104-114,共11页
Deep learning algorithms based on neural networks make remarkable achievements in machine fault diagnosis,while the noise mixed in measured signals harms the prediction accuracy of networks.Existing denoising methods ... Deep learning algorithms based on neural networks make remarkable achievements in machine fault diagnosis,while the noise mixed in measured signals harms the prediction accuracy of networks.Existing denoising methods in neural networks,such as using complex network architectures and introducing sparse techniques,always suffer from the difficulty of estimating hyperparameters and the lack of physical interpretability.To address this issue,this paper proposes a novel interpretable denoising layer based on reproducing kernel Hilbert space(RKHS)as the first layer for standard neural networks,with the aim to combine the advantages of both traditional signal processing technology with physical interpretation and network modeling strategy with parameter adaption.By investigating the influencing mechanism of parameters on the regularization procedure in RKHS,the key parameter that dynamically controls the signal smoothness with low computational cost is selected as the only trainable parameter of the proposed layer.Besides,the forward and backward propagation algorithms of the designed layer are formulated to ensure that the selected parameter can be automatically updated together with other parameters in the neural network.Moreover,exponential and piecewise functions are introduced in the weight updating process to keep the trainable weight within a reasonable range and avoid the ill-conditioned problem.Experiment studies verify the effectiveness and compatibility of the proposed layer design method in intelligent fault diagnosis of machinery in noisy environments. 展开更多
关键词 Machine fault diagnosis Reproducing kernel Hilbert space(RKHS) Regularization problem Denoising layer Neural network
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h-ADAPTIVITY ANALYSIS BASED ON MULTIPLE SCALE REPRODUCING KERNEL PARTICLE METHOD 认领 引用 被引量：4
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作者 ZHANG Zhi-qian ZHOU Jin-xiong +2 位作者 WANG Xue-ming ZHANG Yan-fen ZHANG Ling 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第8期1064-1071,共8页
An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes（SNN） and local-Delaunay-tri... An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes（SNN） and local-Delaunay-triangulation（LDT） techniques, which were suitable and effective for h-adaptivity analysis on 2-D problems with the regular or irregular distribution of the nodes. The results of multiresolution and h- adaptivity analyses on 2-D linear elastostatics and bending plate problems demonstrate that the improper high-gradient indicator will reduce the convergence property of the h- adaptivity analysis, and that the efficiency of the LDT node refinement strategy is better than SNN, and that the presented h-adaptivity analysis scheme is provided with the validity, stability and good convergence property. 展开更多
关键词 meshfree method reproducing kernel particle method multiresolution analysis adaptive analysis
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An interpolating reproducing kernel particle method for two-dimensional scatter points 认领 引用 被引量：3
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作者 秦义校 刘营营 +1 位作者 李中华 杨明 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第7期238-241,共4页
An interpolating reproducing kernel particle method for two-dimensional （2D） scatter points is introduced. It elim- inates the dependency of gridding in numerical calculations. The interpolating shape function in th... An interpolating reproducing kernel particle method for two-dimensional （2D） scatter points is introduced. It elim- inates the dependency of gridding in numerical calculations. The interpolating shape function in the interpolating repro- ducing kernel particle method satisfies the property of the Kronecker delta function. This method offers a mathematics basis for recognition technology and simulation analysis, which can be expressed as simultaneous differential equations in science or project problems. Mathematical examples are given to show the validity of the interpolating reproducing kernel particle method. 展开更多
关键词 interpolating reproducing kernel particle method point interpolating characteristic scatter points
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Adaptive multi-step piecewise interpolation reproducing kernel method for solving the nonlinear time-fractional partial differential equation arising from financial economics 认领 引用 被引量：2
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作者 杜明婧 孙宝军 凯歌 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第3期53-57,共5页
This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)metho... This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)method which deals with this problem is very troublesome.This paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel(AMPIRK)method for the first time.This method has three obvious advantages which are as follows.Firstly,the piecewise number is reduced.Secondly,the calculation accuracy is improved.Finally,the waste time caused by too many fragments is avoided.Then four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the others.The research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics. 展开更多
关键词 time-fractional partial differential equation adaptive multi-step reproducing kernel method method numerical solution
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AHermitian C2 Differential Reproducing Kernel Interpolation Meshless Method for the 3D Microstructure-Dependent Static Flexural Analysis of Simply Supported and Functionally Graded Microplates 认领 引用 被引量：2
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作者 Chih-Ping Wu Ruei-Syuan Chang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第10期917-949,共33页
This work develops a Hermitian C2 differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredepend... This work develops a Hermitian C2 differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C2 differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC2DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C2 DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant. 展开更多
关键词 Consistent/modified couple stress theory differential reproducing kernel methods microplates point collocation methods static flexural 3D microstructure-dependent analysis
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Application of Reproducing Kernel Particle Method in an Analysis of Elasto-plastic Deformation Under Taylor Impact 认领 引用 被引量：1
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作者 ZHAO Guang-ming SONG Shun-cheng MENG Xiang-rui 《Journal of China University of Mining and Technology》 2006年第4期485-489,共5页
The Reproducing Kernel Particle Method (RKPM) is one of several new meshless numerical methods de- veloped internationally in recent years. The ideal elasto-plastic constitutive model of material under a Taylor impact... The Reproducing Kernel Particle Method (RKPM) is one of several new meshless numerical methods de- veloped internationally in recent years. The ideal elasto-plastic constitutive model of material under a Taylor impact is characterized by the Jaumann stress- and strain-rates. An updated Lagrangian format is used for the calculation in a nu- merical analysis. With the RKPM, this paper deals with the calculation model for the Taylor impact and deduces the control equation for the impact process. A program was developed to simulate numerically the Taylor impact of projec- tiles composed of several kinds of material. The simulation result is in good accordance with both the test results and the Taylor analysis outcome. Since the meshless method is not limited by meshes, it is believed to be widely applicable to such complicated processes as the Taylor impact, including large deformation and strain and to the study of the dy- namic qualities of materials. 展开更多
关键词 Reproducing Kernel Particle Method Taylor impact large deformation meshless method
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ANALYSIS OF THREE-DIMENSIONAL UPSETTING PROCESS BY THE RIGID-PLASTIC REPRODUCING KERNEL PARTICLE METHOD 认领 引用 被引量：2
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作者 Y. H. Liu J. Chen S. Yu X. W. Chen 《Acta Metallurgica Sinica(English Letters)》 EI CAS 2006年第5期371-378,共8页
A meshless approach, called the rigid-plastic reproducing kernel particle method （RKPM）, is presented for three-dimensional （3D） bulk metal forming simulation. The approach is a combination of RKPM with the flow t... A meshless approach, called the rigid-plastic reproducing kernel particle method （RKPM）, is presented for three-dimensional （3D） bulk metal forming simulation. The approach is a combination of RKPM with the flow theory of 3D rigid-plastic mechanics. For the treatments of essential boundary conditions and incompressibility constraint, the boundary singular kernel method and the modified penalty method are utilized, respectively. The arc-tangential friction model is employed to treat the contact conditions. The compression of rectangular blocks, a typical 3D upsetting operation, is analyzed for different friction conditions and the numerical results are compared with those obtained using commercial rigid-plastic FEM （finite element method） software Deform^3D. As results show, when handling 3D plastic deformations, the proposed approach eliminates the need of expensive meshing and remeshing procedures which are unavoidable in conventional FEM and can provide results that are in good agreement with finite element predictions. 展开更多
关键词 meshless reproducing kernel particle method（RKPM） three-dimensional upsetting incompressibility modified penalty method
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A Geometrically Exact Triangular Shell Element Based on Reproducing Kernel DMS-Splines 认领 引用
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作者 Hanjiang Chang Qiang Tian Haiyan Hu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第7期825-860,共36页
Tomodel amultibody systemcomposed of shell components,a geometrically exact Kirchho-Love triangular shell element is proposed.The middle surface of the shell element is described by using the DMS-splines,which can exa... Tomodel amultibody systemcomposed of shell components,a geometrically exact Kirchho-Love triangular shell element is proposed.The middle surface of the shell element is described by using the DMS-splines,which can exactly represent arbitrary topology piecewise polynomial triangular surfaces.The proposed shell element employs only nodal displacement and can automatically maintain C1 continuity properties at the element boundaries.A reproducing DMS-spline kernel skill is also introduced to improve computation stability and accuracy.The proposed triangular shell element based on reproducing kernel DMS-splines can achieve an almost optimal convergent rate.Finally,the proposed shell element is validated via three static problems of shells and the dynamic simulation of aexible multibody system undergoing both overall motions and large deformations. 展开更多
关键词 DMS-splines reproducing kernel kirchhoff-love shell C1continuity multibody system dynamics
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Splitting Rolling Simulated by Reproducing Kernel Particle Method 认领 引用
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作者 CUI Qing-ling LIU Xiang-hua WANG Guo-dong 《Journal of Iron and Steel Research International》 SCIE CAS 2007年第3期42-46,共5页
During splitting rolling simulation,re-meshing is necessary to prevent the effect of severe mesh distortion when the conventional finite element method is used.However,extreme deformation cannot be solved by the finit... During splitting rolling simulation,re-meshing is necessary to prevent the effect of severe mesh distortion when the conventional finite element method is used.However,extreme deformation cannot be solved by the finite element method in splitting rolling.The reproducing kernel particle method can solve this problem because the continuum body is discretized by a set of nodes,and a finite element mesh is unnecessary,and there is no explicit limitation of mesh when the metal is split.To ensure stability in the large deformation elastoplastic analysis,the Lagrange material shape function was introduced.The transformation method was utilized to impose the essential boundary conditions.The splitting rolling method was simulated and the simulation results were in accordance with the experimental ones in the literature. 展开更多
关键词 elasto-plasticity large deformation reproducing kernel particle method splitting rolling
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Stability and dispersion analysis of reproducing kernel collocation method for transient dynamics 认领 引用
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作者 罗汉中 刘学文 黄醒春 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第6期777-788,共12页
A reproducing kernel collocation method based on strong formulation is introduced for transient dynamics. To study the stability property of this method, an algorithm based on the von Neumann hypothesis is proposed to... A reproducing kernel collocation method based on strong formulation is introduced for transient dynamics. To study the stability property of this method, an algorithm based on the von Neumann hypothesis is proposed to predict the critical time step. A numerical test is conducted to validate the algorithm. The numerical critical time step and the predicted critical time step are in good agreement. The results are compared with those obtained based on the radial basis collocation method, and they axe in good agreement. Several important conclusions for choosing a proper support size of the reproducing kernel shape function are given to improve the stability condition. 展开更多
关键词 reproducing kernel collocation method （RKCM） stability analysis disper-sion analysis transient dynamics
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Reproducing wavelet kernel method in nonlinear system identification 认领 引用
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作者 文香军 许晓鸣 蔡云泽 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2008年第2期248-254,共7页
By combining the wavelet decomposition with kernel method, a practical approach of universal multiscale wavelet kernels constructed in reproducing kernel Hilbert space （RKHS） is discussed, and an identification sche... By combining the wavelet decomposition with kernel method, a practical approach of universal multiscale wavelet kernels constructed in reproducing kernel Hilbert space （RKHS） is discussed, and an identification scheme using wavelet support vector machines （WSVM） estimator is proposed for nordinear dynamic systems. The good approximating properties of wavelet kernel function enhance the generalization ability of the proposed method, and the comparison of some numerical experimental results between the novel approach and some existing methods is encouraging. 展开更多
关键词 wavelet kernels support vector machine （SVM） reproducing kernel Hilbert space （RKHS） nonlinear system identification
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Using reproducing kernel for solving a class of partial differential equation with variable-coefficients 认领 引用
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作者 王玉兰 朝鲁 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第1期129-137,共9页
How to solve the partial differential equation has been attached importance to by all kinds of fields. The exact solution to a class of partial differential equation with variable-coefficient is obtained in reproducin... How to solve the partial differential equation has been attached importance to by all kinds of fields. The exact solution to a class of partial differential equation with variable-coefficient is obtained in reproducing kernel space. For getting the approximate solution, give an iterative method, convergence of the iterative method is proved. The numerical example shows that our method is effective and good practicability. 展开更多
关键词 iterative method exact solution approximate solution variable-coefficient partial differential equation reproducing kernel
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The choosing of reproducing kernel particle shape function with mathematic proof 认领 引用
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作者 夏茂辉 李金 《Chinese Physics B》 CAS 2007年第10期3067-3071,共5页
Many mechanical problems can be induced from differential equations with boundary conditions; there exist analytic and numerical methods for solving the differential equations. Usually it is not so easy to obtain anal... Many mechanical problems can be induced from differential equations with boundary conditions; there exist analytic and numerical methods for solving the differential equations. Usually it is not so easy to obtain analytic solutions. So it is necessary to give numerical solutions. The reproducing kernel particle （RKP） method is based on the Carlerkin Meshless method. According to the Sobolev space and Fourier transform, the RKP shape function is mathematically proved in this paper. 展开更多
关键词 point of interpolation particle reproducing kernel particle shape function
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ON APPROXIMATION BY SPHERICAL REPRODUCING KERNEL HILBERT SPACES 认领 引用
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作者 Zhixiang Chen 《Analysis in Theory and Applications》 2007年第4期325-333,共9页
The spherical approximation between two nested reproducing kernels Hilbert spaces generated from different smooth kernels is investigated. It is shown that the functions of a space can be approximated by that of the s... The spherical approximation between two nested reproducing kernels Hilbert spaces generated from different smooth kernels is investigated. It is shown that the functions of a space can be approximated by that of the subspace with better smoothness. Furthermore, the upper bound of approximation error is given. 展开更多
关键词 spherical harmonic polynomial radial basis function reproducing kernel Hilbert space error estimates
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Adaptive Single Piecewise Interpolation Reproducing Kernel Method for Solving Fractional Partial Differential Equation 认领 引用
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作者 DU Mingjing 《Journal of Donghua University(English Edition)》 CAS 2022年第5期454-460,共7页
It is well-known that using the traditional reproducing kernel method(TRKM) for solving the fractional partial differential equation(FPDE) is very intractable. In this study, the adaptive single piecewise interpolatio... It is well-known that using the traditional reproducing kernel method(TRKM) for solving the fractional partial differential equation(FPDE) is very intractable. In this study, the adaptive single piecewise interpolation reproducing kernel method(ASPIRKM) is determined to solve the FPDE. This improved method not only improves the calculation accuracy, but also reduces the waste of time. Two numerical examples show that the ASPIRKM is a more time-saving numerical method than the TRKM. 展开更多
关键词 fractional partial differential equation(FPDE) reproducing kernel method(RKM) single piecewise numerical solution
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Reproducing Kernel Particle Method for Non-Linear Fracture Analysis 认领 引用
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作者 曹中清 周本宽 陈大鹏 《Journal of Southwest Jiaotong University(English Edition)》 2006年第4期372-378,共7页
To study the non-linear fracture, a non-linear constitutive model for piezoelectric ceramics was proposed, in which the polarization switching and saturation were taken into account. Based on the model, the non-linear... To study the non-linear fracture, a non-linear constitutive model for piezoelectric ceramics was proposed, in which the polarization switching and saturation were taken into account. Based on the model, the non-linear fracture analysis was implemented using reproducing kernel particle method （RKPM）. Using local J-integral as a fracture criterion, a relation curve of fracture loads against electric fields was obtained. Qualitatively, the curve is in agreement with the experimental observations reported in literature. The reproducing equation, the shape function of RKPM, and the transformation method to impose essential boundary conditions for meshless methods were also introduced. The computation was implemented using object-oriented programming method. 展开更多
关键词 Meshless methods Reproducing kernel particle method Facture Piezoelectric ceramics
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Combining the complex variable reproducing kernel particle method and the finite element method for solving transient heat conduction problems 认领 引用 被引量：10
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作者 陈丽 马和平 程玉民 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第5期67-74,共8页
In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE metho... In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method. 展开更多
关键词 complex variable reproducing kernel particle method finite element method combined method,transient heat conduction
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