Based on the fact that the singular boundary integrals in the sense of Cauchy principal value can be represented approximately by the mean values of two companion nearly singular boundary integrals, a vary general app...Based on the fact that the singular boundary integrals in the sense of Cauchy principal value can be represented approximately by the mean values of two companion nearly singular boundary integrals, a vary general approach was developed in the paper. In the approach, the approximate formulation before discretization was constructed to cope with the difficulties encountered in the corner treatment in the formulations of hypersingular boundary integral equations. This makes it possible to solve the hypersingular boundary integral equation numerically in a non regularized form and in a local manner by using conforming C 0 quadratic boundary elements and standard Gaussian quadratures similar to those employed in the conventional displacement BIE formulations. The approximate formulation is very convenient to use because the corner information is comprised naturally in the representations of those approximate integrals. Numerical examples in plane elasticity show that with the present approach, the compatible or better results can be achieved in comparison with those of the conventional BIE formulations.展开更多
0 IntroductionWe consider here seepage problem with the free boundaryon the free boundary ψ=0, =y.By an inverse formulation of seepage problem,the free boundary problem is inverted to the boundaryproblem with the fix...0 IntroductionWe consider here seepage problem with the free boundaryon the free boundary ψ=0, =y.By an inverse formulation of seepage problem,the free boundary problem is inverted to the boundaryproblem with the fixed boundary in the complex potential plane. With classical analysis, the problem ischanged into the Cauchy integral equation problemThis paper discussed the approximate property and approximate method by Chebyshev polynomials.1 Approximate展开更多
In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate pa...In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.展开更多
The Burton-Miller boundary integral formulation is solved by a complex variable boundary element-free method(CVBEFM)for the boundary-only meshless analysis of acoustic problems with arbitrary wavenumbers.To regularize...The Burton-Miller boundary integral formulation is solved by a complex variable boundary element-free method(CVBEFM)for the boundary-only meshless analysis of acoustic problems with arbitrary wavenumbers.To regularize both strongly singular and hypersingular integrals and to avoid the computation of the solid angle and its normal derivative,a weakly singular Burton-Miller formulation is derived by considering the normal derivative of the solid angle and adopting the singularity subtraction procedures.To facilitate the implementation of the CVBEFM and the approximation of gradients of the boundary variables,a stabilized complex variable moving least-square approximation is selected in the meshless discretization procedure.The results show the accuracy and efficiency of the present CVBEFM and reveal that the method can produce satisfactory results for all wavenumbers,even for extremely large wavenumbers such as k=10000.展开更多
The advection-diffusion equation y_t~ε-εy_(xx)~ε+ M y_x~ε= 0,(x, t) ∈(0, 1) ×(0, T) is null controllable for any strictly positive values of the diffusion coefficient ε and of the controllability time T. We...The advection-diffusion equation y_t~ε-εy_(xx)~ε+ M y_x~ε= 0,(x, t) ∈(0, 1) ×(0, T) is null controllable for any strictly positive values of the diffusion coefficient ε and of the controllability time T. We discuss here the behavior of the cost of control when the coefficient ε goes to zero, according to the values of T. It is actually known that this cost is uniformly bounded with respect to ε if T is greater than a minimal time T_M, with T_M in the interval [1, 2×3^(1/2)]/M for M > 0 and in the interval [2×2^(1/2), 2(1 +3^(1/2))]/|M | for M < 0. The exact value of TM is however unknown.We investigate in this work the determination of the minimal time T_M employing two distincts but complementary approaches. In a first one, we numerically estimate the cost of controllability, reformulated as the solution of a generalized eigenvalue problem for the underlying control operator, with respect to the parameter T and ε. This allows notably to exhibit the structure of initial data leading to large costs of control. At the practical level, this evaluation requires the non trivial and challenging approximation of null controls for the advection-diffusion equation. In the second approach, we perform an asymptotic analysis, with respect to the parameter ε, of the optimality system associated to the control of minimal L^2-norm. The matched asymptotic expansion method is used to describe the multiple boundary layers.展开更多
A full-wave analysis of the electromagnetic problem of a three-dimensional （3-D） antenna radiating through a 3-D dielectric radome is preserued. The problem is formulated using the Poggio-Miller-Chang-Harrington- Wu...A full-wave analysis of the electromagnetic problem of a three-dimensional （3-D） antenna radiating through a 3-D dielectric radome is preserued. The problem is formulated using the Poggio-Miller-Chang-Harrington- Wu（PMCHW） approach for homogeneous dielectric objects and the electric field integral equation for conducting objects. The integral equations are discretized by the method of moment （MoM）, in which the conducting and dielectric surface/interfaces are represented by curvilinear triangular patches and the unknown equivalent electric and magnetic currents are expanded using curvilinear RWG basis functions. The resultant matrix equation is then solved by the multilevel fast multipole algorithm （MLFMA） and fast far-field approximation （FAFFA） is used to further accelerate the computation. The radiation patterns of dipole arrays in the presence of radomes are presented. The numerical results demonstrate the accuracy and versatility of this method.展开更多
To facilitate the commercialization of wave energy in an array or farm environment, effective control strategies for improving energy extraction efficiency of the system are important. In this paper, we develop and ap...To facilitate the commercialization of wave energy in an array or farm environment, effective control strategies for improving energy extraction efficiency of the system are important. In this paper, we develop and apply model-predictive control(MPC) to a heaving point-absorber array, where the optimization problem is cast into a convex quadratic programming(QP)formulation,which can be efficiently solved by a standard QP solver. We introduced a term for penalizing large slew rates in the cost function to ensure the convexity of this function. Constraints on both range of the states and the input capacity can be accommodated. The convex formulation reduces the computational hurdles imposed on conventional nonlinear MPC. For illustration of the control principles,a point-absorber approximation is adopted to simplify the representation of the hydrodynamic coefficients among the array by exploiting the small devices to wavelength assumption. The energycapturing capabilities of a two-cylinder array in regular and irregular waves are investigated. The performance of the MPC for this two-WEC array is compared to that for a single WEC, and the behavior of the individual devices in head or beam wave configuration is explained. Also shown is the reactive power required by the power takeoff system to achieve the performance.展开更多
The incompressible Navier Stokes equations are solved via variables of vorticity and velocity. Firstly, a rigorous variational framework with the equivalence between the velocity pressure and the vorticity velocity fo...The incompressible Navier Stokes equations are solved via variables of vorticity and velocity. Firstly, a rigorous variational framework with the equivalence between the velocity pressure and the vorticity velocity formulations is presented in a Lipschitz domain. Next, a class of Galerkin finite element approximations of the corresponding variational form is introduced, and a convergence analysis is given for the Stokes problem. Finally, an iterative finite element solver for the Navier Stokes problem is proposed.展开更多
文摘Based on the fact that the singular boundary integrals in the sense of Cauchy principal value can be represented approximately by the mean values of two companion nearly singular boundary integrals, a vary general approach was developed in the paper. In the approach, the approximate formulation before discretization was constructed to cope with the difficulties encountered in the corner treatment in the formulations of hypersingular boundary integral equations. This makes it possible to solve the hypersingular boundary integral equation numerically in a non regularized form and in a local manner by using conforming C 0 quadratic boundary elements and standard Gaussian quadratures similar to those employed in the conventional displacement BIE formulations. The approximate formulation is very convenient to use because the corner information is comprised naturally in the representations of those approximate integrals. Numerical examples in plane elasticity show that with the present approach, the compatible or better results can be achieved in comparison with those of the conventional BIE formulations.
文摘0 IntroductionWe consider here seepage problem with the free boundaryon the free boundary ψ=0, =y.By an inverse formulation of seepage problem,the free boundary problem is inverted to the boundaryproblem with the fixed boundary in the complex potential plane. With classical analysis, the problem ischanged into the Cauchy integral equation problemThis paper discussed the approximate property and approximate method by Chebyshev polynomials.1 Approximate
基金supported by the National Key Research and Development Plan(Grant No.2020YFB1709401)the National Natural Science Foundation of China(Grant Nos.12202092,12032008,and 11821202)the China Postdoctoral Science Foundation(Grant No.ZX20220734).
文摘In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.
基金Project supported by the National Natural Science Foundation of China(No.11971085)the Innovation Research Group Project in Universities of Chongqing of China(No.CXQT19018)+1 种基金the Science and Technology Research Program of Chongqing Municipal Education Commission of China(No.KJZD-M201800501)and the Science and Technology Research Program of Chongqing University of Education of China(No.KY201927C)。
文摘The Burton-Miller boundary integral formulation is solved by a complex variable boundary element-free method(CVBEFM)for the boundary-only meshless analysis of acoustic problems with arbitrary wavenumbers.To regularize both strongly singular and hypersingular integrals and to avoid the computation of the solid angle and its normal derivative,a weakly singular Burton-Miller formulation is derived by considering the normal derivative of the solid angle and adopting the singularity subtraction procedures.To facilitate the implementation of the CVBEFM and the approximation of gradients of the boundary variables,a stabilized complex variable moving least-square approximation is selected in the meshless discretization procedure.The results show the accuracy and efficiency of the present CVBEFM and reveal that the method can produce satisfactory results for all wavenumbers,even for extremely large wavenumbers such as k=10000.
文摘The advection-diffusion equation y_t~ε-εy_(xx)~ε+ M y_x~ε= 0,(x, t) ∈(0, 1) ×(0, T) is null controllable for any strictly positive values of the diffusion coefficient ε and of the controllability time T. We discuss here the behavior of the cost of control when the coefficient ε goes to zero, according to the values of T. It is actually known that this cost is uniformly bounded with respect to ε if T is greater than a minimal time T_M, with T_M in the interval [1, 2×3^(1/2)]/M for M > 0 and in the interval [2×2^(1/2), 2(1 +3^(1/2))]/|M | for M < 0. The exact value of TM is however unknown.We investigate in this work the determination of the minimal time T_M employing two distincts but complementary approaches. In a first one, we numerically estimate the cost of controllability, reformulated as the solution of a generalized eigenvalue problem for the underlying control operator, with respect to the parameter T and ε. This allows notably to exhibit the structure of initial data leading to large costs of control. At the practical level, this evaluation requires the non trivial and challenging approximation of null controls for the advection-diffusion equation. In the second approach, we perform an asymptotic analysis, with respect to the parameter ε, of the optimality system associated to the control of minimal L^2-norm. The matched asymptotic expansion method is used to describe the multiple boundary layers.
基金the National Natural Science Foundation of China (60431010)
文摘A full-wave analysis of the electromagnetic problem of a three-dimensional （3-D） antenna radiating through a 3-D dielectric radome is preserued. The problem is formulated using the Poggio-Miller-Chang-Harrington- Wu（PMCHW） approach for homogeneous dielectric objects and the electric field integral equation for conducting objects. The integral equations are discretized by the method of moment （MoM）, in which the conducting and dielectric surface/interfaces are represented by curvilinear triangular patches and the unknown equivalent electric and magnetic currents are expanded using curvilinear RWG basis functions. The resultant matrix equation is then solved by the multilevel fast multipole algorithm （MLFMA） and fast far-field approximation （FAFFA） is used to further accelerate the computation. The radiation patterns of dipole arrays in the presence of radomes are presented. The numerical results demonstrate the accuracy and versatility of this method.
文摘To facilitate the commercialization of wave energy in an array or farm environment, effective control strategies for improving energy extraction efficiency of the system are important. In this paper, we develop and apply model-predictive control(MPC) to a heaving point-absorber array, where the optimization problem is cast into a convex quadratic programming(QP)formulation,which can be efficiently solved by a standard QP solver. We introduced a term for penalizing large slew rates in the cost function to ensure the convexity of this function. Constraints on both range of the states and the input capacity can be accommodated. The convex formulation reduces the computational hurdles imposed on conventional nonlinear MPC. For illustration of the control principles,a point-absorber approximation is adopted to simplify the representation of the hydrodynamic coefficients among the array by exploiting the small devices to wavelength assumption. The energycapturing capabilities of a two-cylinder array in regular and irregular waves are investigated. The performance of the MPC for this two-WEC array is compared to that for a single WEC, and the behavior of the individual devices in head or beam wave configuration is explained. Also shown is the reactive power required by the power takeoff system to achieve the performance.
文摘The incompressible Navier Stokes equations are solved via variables of vorticity and velocity. Firstly, a rigorous variational framework with the equivalence between the velocity pressure and the vorticity velocity formulations is presented in a Lipschitz domain. Next, a class of Galerkin finite element approximations of the corresponding variational form is introduced, and a convergence analysis is given for the Stokes problem. Finally, an iterative finite element solver for the Navier Stokes problem is proposed.
