The discrete scheme called discrete operator difference for differential equations was given. Several difference elements for plate bending problems and plane problems were given. By investigating these elements, the ...The discrete scheme called discrete operator difference for differential equations was given. Several difference elements for plate bending problems and plane problems were given. By investigating these elements, the ability of the discrete forms expressing to the element functions was talked about. In discrete operator difference method, the displacements of the elements can be reproduced exactly in the discrete forms whether the displacements are conforming or not. According to this point, discrete operator difference method is a method with good performance.展开更多
In this paper, we discuss some singulal integral operators, singular quadrature operators and discrethation matrices associated with singular integral equations of the first kind, and obtain some useful Properties for...In this paper, we discuss some singulal integral operators, singular quadrature operators and discrethation matrices associated with singular integral equations of the first kind, and obtain some useful Properties for them. Using these operators we give a unified framework for various collocation methods of numerical solutions of singular integral equations of the fine kind, which appears very simple.展开更多
To evaluate the operator health risk exposed to whole-body vibration(WBV) while the electric-shovel loads the ore on the truck body, the semi-truck mathematical model and 3-D virtual prototype were built to simulate t...To evaluate the operator health risk exposed to whole-body vibration(WBV) while the electric-shovel loads the ore on the truck body, the semi-truck mathematical model and 3-D virtual prototype were built to simulate the high shockwave of truck cab under the shovel loading. Discrete element method was utilized to accurately estimate the impacting force on the truck body. Based on the ISO 2631-5 criteria, the Sed is about 0.56 MPa in both models, which means that the dump operators have a high probability of adverse health effects over long-term exposure to these vibrations. The 4-DOF operator model was built to investigate the biodynamic response of seated-human body exposed to WBV in terms of the transmission of vibrations through the body. The results show that the response peak is in the frequency range of 4-6 Hz corresponding to the primary body resonant frequency.展开更多
We define discrete total differential forms on lattice space by. changing coefficients of discrete differential forms from functions only of n to functions also of dependent variables un and their partial differences....We define discrete total differential forms on lattice space by. changing coefficients of discrete differential forms from functions only of n to functions also of dependent variables un and their partial differences. And the discrete exterior derivative extends to be discrete total differential map which is also nilpotent. Then a discrete horizontal complex can be derived and be proved to be exact by constructing homotopy operators.展开更多
Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequali...Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.展开更多
To investigate impact of time delays on the small signal stability of power systems, the least-damped eigenvalues with the smallest damping ratios have been calculated by eigen-analysis methods based on Solution Opera...To investigate impact of time delays on the small signal stability of power systems, the least-damped eigenvalues with the smallest damping ratios have been calculated by eigen-analysis methods based on Solution Operator Discretization (SOD) with Pseudo-Spectral collocation (PS) and Implicit Runge-Kutta (IRK) methods. This paper evolves SOD-PSIIRK into their partial counterparts, i.e., PSOD-PSIIRK, with greatly enhanced efficiency and reliability in analyzing large-scale time delayed power systems. Compared with SOD-PSIIRK, PSOD-PSIIRK are characterized in constructing low order discretization matrices of solution operator as well as efficiently and directly solving the embedded Matrix-Inverse-Vector Products (MIVPs). The dimensions of the discretization matrices of solution operator are largely reduced as only the retarded state variables are discretized, rather than all state variables as in SOD-PSIIRK. Meanwhile, the proposed PSOD-PSIIRK optimize the most computationally expensive operations in SOD-PSIIRK by avoiding the iterative solutions to the two embedded MIVPs. PSOD-PS/IRK directly and efficiently compute the MIVPs via factorizing the Kronecker product-like discretization matrices of the solution operator into Schur complements. The Central China-North China ultra-high-voltage power grid with 80577 state variables serves to validate the proposed PSOD-PSIIRK and shows that compared with SOD-PSIIRK, the computational time consumed by PSOD-PSIIRK is cut down by 49.96 times without loss of any accuracy.展开更多
In this paper, we propose a nearly analytic exponential time difference （NETD） method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approxima...In this paper, we propose a nearly analytic exponential time difference （NETD） method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approximate the high-order spatial differential operators and transform the seismic wave equations into semi-discrete ordinary differential equations （ODEs）. Then, the converted ODE system is solved by the exponential time difference （ETD） method. We investigate the properties of NETD in detail, including the stability condition for 1-D and 2-D cases, the theoretical and relative errors, the numerical dispersion relation for the 2-D acoustic case, and the computational efficiency. In order to further validate the method, we apply it to simulating acoustic/elastic wave propagation in mul- tilayer models which have strong contrasts and complex heterogeneous media, e.g., the SEG model and the Mar- mousi model. From our theoretical analyses and numerical results, the NETD can suppress numerical dispersion effectively by using the displacement and gradient to approximate the high-order spatial derivatives. In addition, because NETD is based on the structure of the Lie group method which preserves the quantitative properties of differential equations, it can achieve more accurate results than the classical methods.展开更多
In this paper,we focus on inferring graph Laplacian matrix from the spatiotemporal signal which is defined as“time-vertex signal”.To realize this,we first represent the signals on a joint graph which is the Cartesia...In this paper,we focus on inferring graph Laplacian matrix from the spatiotemporal signal which is defined as“time-vertex signal”.To realize this,we first represent the signals on a joint graph which is the Cartesian product graph of the time-and vertex-graphs.By assuming the signals follow a Gaussian prior distribution on the joint graph,a meaningful representation that promotes the smoothness property of the joint graph signal is derived.Furthermore,by decoupling the joint graph,the graph learning framework is formulated as a joint optimization problem which includes signal denoising,timeand vertex-graphs learning together.Specifically,two algorithms are proposed to solve the optimization problem,where the discrete second-order difference operator with reversed sign(DSODO)in the time domain is used as the time-graph Laplacian operator to recover the signal and infer a vertex-graph in the first algorithm,and the time-graph,as well as the vertex-graph,is estimated by the other algorithm.Experiments on both synthetic and real-world datasets demonstrate that the proposed algorithms can effectively infer meaningful time-and vertex-graphs from noisy and incomplete data.展开更多
We develop a stabilizer free weak Galerkin (SFWG) finite element method for Brinkman equations. The main idea is to use high order polynomials to compute the discrete weak gradient and then the stabilizing term is rem...We develop a stabilizer free weak Galerkin (SFWG) finite element method for Brinkman equations. The main idea is to use high order polynomials to compute the discrete weak gradient and then the stabilizing term is removed from the numerical formulation. The SFWG scheme is very simple and easy to implement on polygonal meshes. We prove the well-posedness of the scheme and derive optimal order error estimates in energy and L2 norm. The error results are independent of the permeability tensor, hence the SFWG method is stable and accurate for both the Stokes and Darcy dominated problems. Finally, we present some numerical experiments to verify the efficiency and stability of the SFWG method.展开更多
We investigate the regularity properties of discrete multisublinear fractional maximal operators,both in the centered and uncentered versions.We prove that these operators are bounded and continuous from l^1（Z^d）...We investigate the regularity properties of discrete multisublinear fractional maximal operators,both in the centered and uncentered versions.We prove that these operators are bounded and continuous from l^1（Z^d）×l^1（Z^d）×…×l^1（Z^d）to BV（Z^d）,where BV（Z^d）is the set of functions of bounded variation defined on Zd.Moreover,two pointwise estimates for the partial derivatives of discrete multisublinear fractional maximal functions are also given.As applications,we present the regularity properties for discrete fractional maximal operator,which are new even in the linear case.展开更多
This paper proposed a discrete operation mode for a punchthrough（PT） phototransistor,which is suitable for low power application,since the bias current is only necessary during the read-out phase.Moreover,simulation...This paper proposed a discrete operation mode for a punchthrough（PT） phototransistor,which is suitable for low power application,since the bias current is only necessary during the read-out phase.Moreover,simulation results show that with the new operation mode,the photocurrent is much larger than that of continuous operation mode.An ultra-high responsivity of 2×10~7A/W at 10^（-9） W/cm^2 is obtained with a small detector size of 1μm^2.In CMOS image sensor applications,with an integration time of 10 ms,a normalized pixel responsivity of 220 V·m^2/W·s·μm^2 is obtained without any auxiliary amplifier.展开更多
Feature lines are fundamental shape descriptors and have been extensively applied to computer graphics, computer-aided design, image processing, and non-photorealistic renderingi This paper introduces a unified variat...Feature lines are fundamental shape descriptors and have been extensively applied to computer graphics, computer-aided design, image processing, and non-photorealistic renderingi This paper introduces a unified variational framework for detecting generic feature lines on polygonal meshes. The classic Mumford-Shah model is extended to surfaces. Using F-convergence method and discrete differential geometry, we discretize the proposed variational model to sequential coupled sparse linear systems. Through quadratic polyno- mials fitting, we develop a method for extracting valleys of functions defined on surfaces. Our approach provides flexible and intuitive control over the detecting procedure, and is easy to implement. Several measure functions are devised for different types of feature lines, and we apply our approach to various polygonal meshes ranging from synthetic to measured models. The experiments demonstrate both the effectiveness of our algorithms and the visual quality of results.展开更多
We propose a direct solver for the three-dimensional Poisson equation with a variable coefficient,and an algorithm to directly solve the associated sparse linear systems that exploits the sparsity pattern of the coeff...We propose a direct solver for the three-dimensional Poisson equation with a variable coefficient,and an algorithm to directly solve the associated sparse linear systems that exploits the sparsity pattern of the coefficient matrix.Introducing some appropriate finite difference operators,we derive a second-order scheme for the solver,and then two suitable high-order compact schemes are also discussed.For a cube containing N nodes,the solver requires O(N^(3/2)log^(2)N)arithmetic operations and O(NlogN)memory to store the necessary information.Its efficiency is illustrated with examples,and the numerical results are analysed.展开更多
A stabilizer-free weak Galerkin finite element method is proposed for the Stokes equations in this paper.Here we omit the stabilizer term in the new method by increasing the degree of polynomial approximating spaces f...A stabilizer-free weak Galerkin finite element method is proposed for the Stokes equations in this paper.Here we omit the stabilizer term in the new method by increasing the degree of polynomial approximating spaces for the weak gradient operators.The new algorithm is simple in formulation and the computational complexity is also reduced.The corresponding approximating spaces consist of piecewise polynomials of degree k≥1 for the velocity and k-1 for the pressure,respectively.Optimal order error estimates have been derived for the velocity in both H^(1) and L^(2) norms and for the pressure in L^(2) norm.Numerical examples are presented to illustrate the accuracy and convergency of the method.展开更多
文摘The discrete scheme called discrete operator difference for differential equations was given. Several difference elements for plate bending problems and plane problems were given. By investigating these elements, the ability of the discrete forms expressing to the element functions was talked about. In discrete operator difference method, the displacements of the elements can be reproduced exactly in the discrete forms whether the displacements are conforming or not. According to this point, discrete operator difference method is a method with good performance.
文摘In this paper, we discuss some singulal integral operators, singular quadrature operators and discrethation matrices associated with singular integral equations of the first kind, and obtain some useful Properties for them. Using these operators we give a unified framework for various collocation methods of numerical solutions of singular integral equations of the fine kind, which appears very simple.
基金Project(2006BAB11B03)supported by the National Key Technology Research and Development Program of ChinaProject(Z1011030055010004)supported by Beijing Municipal Science Program of China
文摘To evaluate the operator health risk exposed to whole-body vibration(WBV) while the electric-shovel loads the ore on the truck body, the semi-truck mathematical model and 3-D virtual prototype were built to simulate the high shockwave of truck cab under the shovel loading. Discrete element method was utilized to accurately estimate the impacting force on the truck body. Based on the ISO 2631-5 criteria, the Sed is about 0.56 MPa in both models, which means that the dump operators have a high probability of adverse health effects over long-term exposure to these vibrations. The 4-DOF operator model was built to investigate the biodynamic response of seated-human body exposed to WBV in terms of the transmission of vibrations through the body. The results show that the response peak is in the frequency range of 4-6 Hz corresponding to the primary body resonant frequency.
文摘We define discrete total differential forms on lattice space by. changing coefficients of discrete differential forms from functions only of n to functions also of dependent variables un and their partial differences. And the discrete exterior derivative extends to be discrete total differential map which is also nilpotent. Then a discrete horizontal complex can be derived and be proved to be exact by constructing homotopy operators.
基金Supported by Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515012429)Guangzhou Huashang College Research Team Project(Grant No.2021HSKT03)。
文摘Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.
基金supported in part by the National Natural Science Foundation of China(No.51677107,52077126)。
文摘To investigate impact of time delays on the small signal stability of power systems, the least-damped eigenvalues with the smallest damping ratios have been calculated by eigen-analysis methods based on Solution Operator Discretization (SOD) with Pseudo-Spectral collocation (PS) and Implicit Runge-Kutta (IRK) methods. This paper evolves SOD-PSIIRK into their partial counterparts, i.e., PSOD-PSIIRK, with greatly enhanced efficiency and reliability in analyzing large-scale time delayed power systems. Compared with SOD-PSIIRK, PSOD-PSIIRK are characterized in constructing low order discretization matrices of solution operator as well as efficiently and directly solving the embedded Matrix-Inverse-Vector Products (MIVPs). The dimensions of the discretization matrices of solution operator are largely reduced as only the retarded state variables are discretized, rather than all state variables as in SOD-PSIIRK. Meanwhile, the proposed PSOD-PSIIRK optimize the most computationally expensive operations in SOD-PSIIRK by avoiding the iterative solutions to the two embedded MIVPs. PSOD-PS/IRK directly and efficiently compute the MIVPs via factorizing the Kronecker product-like discretization matrices of the solution operator into Schur complements. The Central China-North China ultra-high-voltage power grid with 80577 state variables serves to validate the proposed PSOD-PSIIRK and shows that compared with SOD-PSIIRK, the computational time consumed by PSOD-PSIIRK is cut down by 49.96 times without loss of any accuracy.
文摘In this paper, we propose a nearly analytic exponential time difference （NETD） method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approximate the high-order spatial differential operators and transform the seismic wave equations into semi-discrete ordinary differential equations （ODEs）. Then, the converted ODE system is solved by the exponential time difference （ETD） method. We investigate the properties of NETD in detail, including the stability condition for 1-D and 2-D cases, the theoretical and relative errors, the numerical dispersion relation for the 2-D acoustic case, and the computational efficiency. In order to further validate the method, we apply it to simulating acoustic/elastic wave propagation in mul- tilayer models which have strong contrasts and complex heterogeneous media, e.g., the SEG model and the Mar- mousi model. From our theoretical analyses and numerical results, the NETD can suppress numerical dispersion effectively by using the displacement and gradient to approximate the high-order spatial derivatives. In addition, because NETD is based on the structure of the Lie group method which preserves the quantitative properties of differential equations, it can achieve more accurate results than the classical methods.
基金supported by the National Natural Science Foundation of China(Grant No.61966007)Key Laboratory of Cognitive Radio and Information Processing,Ministry of Education(No.CRKL180106,No.CRKL180201)+1 种基金Guangxi Key Laboratory of Wireless Wideband Communication and Signal Processing,Guilin University of Electronic Technology(No.GXKL06180107,No.GXKL06190117)Guangxi Colleges and Universities Key Laboratory of Satellite Navigation and Position Sensing.
文摘In this paper,we focus on inferring graph Laplacian matrix from the spatiotemporal signal which is defined as“time-vertex signal”.To realize this,we first represent the signals on a joint graph which is the Cartesian product graph of the time-and vertex-graphs.By assuming the signals follow a Gaussian prior distribution on the joint graph,a meaningful representation that promotes the smoothness property of the joint graph signal is derived.Furthermore,by decoupling the joint graph,the graph learning framework is formulated as a joint optimization problem which includes signal denoising,timeand vertex-graphs learning together.Specifically,two algorithms are proposed to solve the optimization problem,where the discrete second-order difference operator with reversed sign(DSODO)in the time domain is used as the time-graph Laplacian operator to recover the signal and infer a vertex-graph in the first algorithm,and the time-graph,as well as the vertex-graph,is estimated by the other algorithm.Experiments on both synthetic and real-world datasets demonstrate that the proposed algorithms can effectively infer meaningful time-and vertex-graphs from noisy and incomplete data.
基金supported by the National Natural Science Foundation of China(Grant Nos.1901015,12271208,11971198,91630201,11871245,11771179,11826101)by the Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education,Jilin University.
文摘We develop a stabilizer free weak Galerkin (SFWG) finite element method for Brinkman equations. The main idea is to use high order polynomials to compute the discrete weak gradient and then the stabilizing term is removed from the numerical formulation. The SFWG scheme is very simple and easy to implement on polygonal meshes. We prove the well-posedness of the scheme and derive optimal order error estimates in energy and L2 norm. The error results are independent of the permeability tensor, hence the SFWG method is stable and accurate for both the Stokes and Darcy dominated problems. Finally, we present some numerical experiments to verify the efficiency and stability of the SFWG method.
基金supported by National Natural Science Foundation of China (Grant Nos. 11371295, 11471041 and 11526122)Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (Grant No. 2015RCJJ053)+2 种基金Research Award Fund for Outstanding Young Scientists of Shandong Province (Grant No. BS2015SF012)Outstanding Young Scientific and Technological Top-Notch Talents of College of Mathematics and Systems Science (Grant No. Sxy2016K01)Natural Science Foundation of Fujian Province of China (Grant No. 2015J01025)
文摘We investigate the regularity properties of discrete multisublinear fractional maximal operators,both in the centered and uncentered versions.We prove that these operators are bounded and continuous from l^1（Z^d）×l^1（Z^d）×…×l^1（Z^d）to BV（Z^d）,where BV（Z^d）is the set of functions of bounded variation defined on Zd.Moreover,two pointwise estimates for the partial derivatives of discrete multisublinear fractional maximal functions are also given.As applications,we present the regularity properties for discrete fractional maximal operator,which are new even in the linear case.
基金Project supported by the National Natural Science Foundation of China(Nos.61076046,61274023)the New Century Excellent Talents Support Program of the Ministry of Educationthe Opening Project of Science and Technology on Reliability Physics and Application Technology of Electronic Component Laboratory(No.ZHD201204)
文摘This paper proposed a discrete operation mode for a punchthrough（PT） phototransistor,which is suitable for low power application,since the bias current is only necessary during the read-out phase.Moreover,simulation results show that with the new operation mode,the photocurrent is much larger than that of continuous operation mode.An ultra-high responsivity of 2×10~7A/W at 10^（-9） W/cm^2 is obtained with a small detector size of 1μm^2.In CMOS image sensor applications,with an integration time of 10 ms,a normalized pixel responsivity of 220 V·m^2/W·s·μm^2 is obtained without any auxiliary amplifier.
文摘Feature lines are fundamental shape descriptors and have been extensively applied to computer graphics, computer-aided design, image processing, and non-photorealistic renderingi This paper introduces a unified variational framework for detecting generic feature lines on polygonal meshes. The classic Mumford-Shah model is extended to surfaces. Using F-convergence method and discrete differential geometry, we discretize the proposed variational model to sequential coupled sparse linear systems. Through quadratic polyno- mials fitting, we develop a method for extracting valleys of functions defined on surfaces. Our approach provides flexible and intuitive control over the detecting procedure, and is easy to implement. Several measure functions are devised for different types of feature lines, and we apply our approach to various polygonal meshes ranging from synthetic to measured models. The experiments demonstrate both the effectiveness of our algorithms and the visual quality of results.
基金supported by NFS No.11001257,was stimulated by Per-Gunnar Martinsson’s paper”A Fast Direct Solver for a Class of Elliptic Partial Differential Equations”.Professor Jingfang Huang suggested solving the Poisson equation with variable coefficient as a test case.We are very grateful to both of them for their selfless help.
文摘We propose a direct solver for the three-dimensional Poisson equation with a variable coefficient,and an algorithm to directly solve the associated sparse linear systems that exploits the sparsity pattern of the coefficient matrix.Introducing some appropriate finite difference operators,we derive a second-order scheme for the solver,and then two suitable high-order compact schemes are also discussed.For a cube containing N nodes,the solver requires O(N^(3/2)log^(2)N)arithmetic operations and O(NlogN)memory to store the necessary information.Its efficiency is illustrated with examples,and the numerical results are analysed.
基金supported in part by China Natural National Science Foundation(Nos.91630201,U1530116,11726102,11771179,93K172018Z01,11701210,JJKH20180113KJ,20190103029JH)by the Program for Cheung Kong Scholars of Ministry of Education of China,Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education.The research of Liu was partially supported by China Natural National Science Foundation(No.12001306)Guangdong Provincial Natural Science Foundation(No.2017A030310285).
文摘A stabilizer-free weak Galerkin finite element method is proposed for the Stokes equations in this paper.Here we omit the stabilizer term in the new method by increasing the degree of polynomial approximating spaces for the weak gradient operators.The new algorithm is simple in formulation and the computational complexity is also reduced.The corresponding approximating spaces consist of piecewise polynomials of degree k≥1 for the velocity and k-1 for the pressure,respectively.Optimal order error estimates have been derived for the velocity in both H^(1) and L^(2) norms and for the pressure in L^(2) norm.Numerical examples are presented to illustrate the accuracy and convergency of the method.
