This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator ...This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator is proposed for solving the convection-dominated non-symmetric eigenvalue problem with non-smooth eigenfunctions or multiple eigenvalues. Numerical examples confirm our theoretical analysis.展开更多
In this paper,we design a new error estimator and give a posteriori error analysis for a poroelasticity model.To better overcome“locking phenomenon”on pressure and displacement,we proposed a new error estimators bas...In this paper,we design a new error estimator and give a posteriori error analysis for a poroelasticity model.To better overcome“locking phenomenon”on pressure and displacement,we proposed a new error estimators based on multiphysics discontinuous Galerkin method for the poroelasticity model.And we prove the upper and lower bound of the proposed error estimators,which are numerically demonstrated to be computationally very efficient.Finally,we present numerical examples to verify and validate the efficiency of the proposed error estimators,which show that the adaptive scheme can overcome“locking phenomenon”and greatly reduce the computation cost.展开更多
In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existenc...In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.展开更多
A maximum a posteriori（ MAP） algorithm is proposed to improve the accuracy of super resolution（ SR） reconstruction in traditional methods. The algorithm applies both joints image registration and SR reconstruction...A maximum a posteriori（ MAP） algorithm is proposed to improve the accuracy of super resolution（ SR） reconstruction in traditional methods. The algorithm applies both joints image registration and SR reconstruction in the framework,but separates them in the process of iteratiion. Firstly,we estimate the shifting parameters through two lowresolution（ LR） images and use the parameters to reconstruct initial HR images. Then,we update the shifting parameters using HR images. The aforementioned steps are repeated until the ideal HR images are obtained. The metrics such as PSNR and SSIM are used to fully evaluate the quality of the reconstructed image. Experimental results indicate that the proposed method can enhance image resolution efficiently.展开更多
In this paper, a posteriori error estimates for the generalized Schwartz method with Dirichlet boundary conditions on the interfaces for advection-diffusion equation with second order boundary value problems are prove...In this paper, a posteriori error estimates for the generalized Schwartz method with Dirichlet boundary conditions on the interfaces for advection-diffusion equation with second order boundary value problems are proved by using the Euler time scheme combined with Galerkin spatial method. Furthermore, an asymptotic behavior in Sobolev norm is de- duced using Benssoussau-Lions＇ algorithm. Finally, the results of some numerical experiments are presented to support the theory.展开更多
Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level met...Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.展开更多
A nonlinear Galerkin mixed element (NGME) method and a posteriori error exstimator based on the method are established for the stationary Navier-Stokes equations. The existence and error estimates of the NGME solution...A nonlinear Galerkin mixed element (NGME) method and a posteriori error exstimator based on the method are established for the stationary Navier-Stokes equations. The existence and error estimates of the NGME solution are first discussed, and then a posteriori error estimator based on the NGME method is derived.展开更多
In this paper, a posteriori error estimates were derived for piecewise linear finite element approximations to parabolic obstacle problems. The instrumental ingredient was introduced as a new interpolation operator wh...In this paper, a posteriori error estimates were derived for piecewise linear finite element approximations to parabolic obstacle problems. The instrumental ingredient was introduced as a new interpolation operator which has optimal approximation properties and preserves positivity. With the help of the interpolation operator the upper and lower bounds were obtained.展开更多
A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illus...A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illustrate the accuracy and feasibility of this method.展开更多
In this article, we use streamline diffusion method for the linear second order hyperbolic initial-boundary value problem. More specifically, we prove a posteriori error estimates for this method for the linear wave e...In this article, we use streamline diffusion method for the linear second order hyperbolic initial-boundary value problem. More specifically, we prove a posteriori error estimates for this method for the linear wave equation. We observe that this error estimates make finite element method increasingly powerful rather than other methods.展开更多
The main aim of this paper is to give an anisotropic posteriori error estimator. We firstly study the convergence of bilineax finite element for the second order problem under anisotropic meshes. By using some novel a...The main aim of this paper is to give an anisotropic posteriori error estimator. We firstly study the convergence of bilineax finite element for the second order problem under anisotropic meshes. By using some novel approaches and techniques, the optimal error estimates and some superconvergence results axe obtained without the regulaxity assumption and quasi-uniform assumption requirements on the meshes. Then, based on these results, we give an anisotropic posteriori error estimate for the second problem.展开更多
Interferogram noise reduction is a very important processing step in Interferometric Synthetic Aperture Radar(InSAR) technique. The most difficulty for this step is to remove the noises and preserve the fringes simult...Interferogram noise reduction is a very important processing step in Interferometric Synthetic Aperture Radar(InSAR) technique. The most difficulty for this step is to remove the noises and preserve the fringes simultaneously. To solve the dilemma, a new interferogram noise reduction algorithm based on the Maximum A Posteriori(MAP) estimate is introduced in this paper. The algorithm is solved under the Total Generalized Variation(TGV) minimization assumption, which exploits the phase characteristics up to the second order differentiation. The ideal noise-free phase consisting of piecewise smooth areas is involved in this assumption, which is coincident with the natural terrain. In order to overcome the phase wraparound effect, complex plane filter is utilized in this algorithm. The simulation and real data experiments show the algorithm can reduce the noises effectively and meanwhile preserve the interferogram fringes very well.展开更多
The paper presents an algorithm of automatic target detection in Synthetic Aperture Radar(SAR) images based on Maximum A Posteriori(MAP). The algorithm is divided into three steps. First, it employs Gaussian mixture d...The paper presents an algorithm of automatic target detection in Synthetic Aperture Radar(SAR) images based on Maximum A Posteriori(MAP). The algorithm is divided into three steps. First, it employs Gaussian mixture distribution to approximate and estimate multi-modal histogram of SAR image. Then, based on the principle of MAP, when a priori probability is both unknown and learned respectively, the sample pixels are classified into different classes c = {target,shadow, background}. Last, it compares the results of two different target detections. Simulation results preferably indicate that the presented algorithm is fast and robust, with the learned a priori probability, an approach to target detection is reliable and promising.展开更多
The present study regards the numerical approximation of solutions of systems of Korteweg-de Vries type,coupled through their nonlinear terms.In our previous work[9],we constructed conservative and dissipative finite ...The present study regards the numerical approximation of solutions of systems of Korteweg-de Vries type,coupled through their nonlinear terms.In our previous work[9],we constructed conservative and dissipative finite element methods for these systems and presented a priori error estimates for the semidiscrete schemes.In this sequel,we present a posteriori error estimates for the semidiscrete and fully discrete approximations introduced in[9].The key tool employed to effect our analysis is the dispersive reconstruction devel-oped by Karakashian and Makridakis[20]for related discontinuous Galerkin methods.We conclude by providing a set of numerical experiments designed to validate the a posteriori theory and explore the effectivity of the resulting error indicators.展开更多
In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the m...In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator.展开更多
One important issue for the simulation of flexible multibody systems is the reduction of the flexible bodies de- grees of freedom. As far as safety questions are concerned knowledge about the error introduced by the r...One important issue for the simulation of flexible multibody systems is the reduction of the flexible bodies de- grees of freedom. As far as safety questions are concerned knowledge about the error introduced by the reduction of the flexible degrees of freedom is helpful and very important. In this work, an a-posteriori error estimator for linear first order systems is extended for error estimation of me- chanical second order systems. Due to the special second order structure of mechanical systems, an improvement of the a-posteriori error estimator is achieved. A major advan- tage of the a-posteriori error estimator is that the estimator is independent of the used reduction technique. Therefore, it can be used for moment-matching based, Gramian matrices based or modal based model reduction techniques. The capability of the proposed technique is demon- strated by the a-posteriori error estimation of a mechanical system, and a sensitivity analysis of the parameters involved in the error estimation process is conducted.展开更多
A posteriori error computations in the space-time coupled and space-time decoupled finite element methods for initial value problems are essential:1)to determine the accuracy of the computed evolution,2)if the errors ...A posteriori error computations in the space-time coupled and space-time decoupled finite element methods for initial value problems are essential:1)to determine the accuracy of the computed evolution,2)if the errors in the coupled solutions are higher than an acceptable threshold,then a posteriori error computations provide measures for designing adaptive processes to improve the accuracy of the solution.How well the space-time approximation in each of the two methods satisfies the equations in the mathematical model over the space-time domain in the point wise sense is the absolute measure of the accuracy of the computed solution.When L2-norm of the space-time residual over the space-time domain of the computations approaches zero,the approximation φh(x,t)(,)→φ(x,t),the theoretical solution.Thus,the proximity of ||E||L_(2) ,the L_(2)-norm of the space-time residual function,to zero is a measure of the accuracy or the error in the computed solution.In this paper,we present a methodology and a computational framework for computing L2 E in the a posteriori error computations for both space-time coupled and space-time decoupled finite element methods.It is shown that the proposed a posteriori computations require h,p,k framework in both space-time coupled as well as space-time decoupled finite element methods to ensure that space-time integrals over space-time discretization are Riemann,hence the proposed a posteriori computations can not be performed in finite difference and finite volume methods of solving initial value problems.High-order global differentiability in time in the integration methods is essential in space-time decoupled method for posterior computations.This restricts the use of methods like Euler’s method,Runge-Kutta methods,etc.,in the time integration of ODE’s in time.Mathematical and computational details including model problem studies are presented in the paper.To authors knowledge,it is the first presentation of the proposed a posteriori error computation methodology and computational infrastructure for initial value problems.展开更多
In this paper,we study a posteriori error estimates of the L1 scheme for time discretizations of time fractional parabolic differential equations,whose solutions have generally the initial singularity.To derive optima...In this paper,we study a posteriori error estimates of the L1 scheme for time discretizations of time fractional parabolic differential equations,whose solutions have generally the initial singularity.To derive optimal order a posteriori error estimates,the quadratic reconstruction for the L1 method and the necessary fractional integral reconstruction for the first-step integration are introduced.By using these continuous,piecewise time reconstructions,the upper and lower error bounds depending only on the discretization parameters and the data of the problems are derived.Various numerical experiments for the one-dimensional linear fractional parabolic equations with smooth or nonsmooth exact solution are used to verify and complement our theoretical results,with the convergence ofαorder for the nonsmooth case on a uniform mesh.To recover the optimal convergence order 2-αon a nonuniform mesh,we further develop a time adaptive algorithm by means of barrier function recently introduced.The numerical implementations are performed on nonsmooth case again and verify that the true error and a posteriori error can achieve the optimal convergence order in adaptive mesh.展开更多
In this paper,we consider the electromagnetic wave scattering problem from a periodic chiral structure.The scattering problem is simplified to a two-dimensional problem,and is discretized by a finite volume method com...In this paper,we consider the electromagnetic wave scattering problem from a periodic chiral structure.The scattering problem is simplified to a two-dimensional problem,and is discretized by a finite volume method combined with the perfectly matched layer(PML)technique.A residual-type a posteriori error estimate of the PML finite volume method is analyzed and the upper and lower bounds on the error are established in the H^(1)-norm.The crucial part of the a posteriori error analysis is to derive the error representation formula and use a L^(2)-orthogonality property of the residual which plays a similar role as the Galerkin orthogonality.An adaptive PML finite volume method is proposed to solve the scattering problem.The PML parameters such as the thickness of the layer and the medium property are determined through sharp a posteriori error estimate.Finally,numerical experiments are presented to illustrate the efficiency of the proposed method.展开更多
Gamma-ray imaging systems are powerful tools in radiographic diagnosis.However,the recorded images suffer from degradations such as noise,blurring,and downsampling,consequently failing to meet high-precision diagnosti...Gamma-ray imaging systems are powerful tools in radiographic diagnosis.However,the recorded images suffer from degradations such as noise,blurring,and downsampling,consequently failing to meet high-precision diagnostic requirements.In this paper,we propose a novel single-image super-resolution algorithm to enhance the spatial resolution of gamma-ray imaging systems.A mathematical model of the gamma-ray imaging system is established based on maximum a posteriori estimation.Within the plug-and-play framework,the half-quadratic splitting method is employed to decouple the data fidelit term and the regularization term.An image denoiser using convolutional neural networks is adopted as an implicit image prior,referred to as a deep denoiser prior,eliminating the need to explicitly design a regularization term.Furthermore,the impact of the image boundary condition on reconstruction results is considered,and a method for estimating image boundaries is introduced.The results show that the proposed algorithm can effectively addresses boundary artifacts.By increasing the pixel number of the reconstructed images,the proposed algorithm is capable of recovering more details.Notably,in both simulation and real experiments,the proposed algorithm is demonstrated to achieve subpixel resolution,surpassing the Nyquist sampling limit determined by the camera pixel size.展开更多
基金Supported by the National Natural Science Foundation of China (Grant Nos.1236108412001130)。
文摘This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator is proposed for solving the convection-dominated non-symmetric eigenvalue problem with non-smooth eigenfunctions or multiple eigenvalues. Numerical examples confirm our theoretical analysis.
基金supported by the National Natural Science Foundation of China(Grant Nos.12371393 and 11971150)Natural Science Foundation of Henan(Grant No.242300421047).
文摘In this paper,we design a new error estimator and give a posteriori error analysis for a poroelasticity model.To better overcome“locking phenomenon”on pressure and displacement,we proposed a new error estimators based on multiphysics discontinuous Galerkin method for the poroelasticity model.And we prove the upper and lower bound of the proposed error estimators,which are numerically demonstrated to be computationally very efficient.Finally,we present numerical examples to verify and validate the efficiency of the proposed error estimators,which show that the adaptive scheme can overcome“locking phenomenon”and greatly reduce the computation cost.
基金supported by the National Basic Research Program under the Grant 2005CB321701the National Natural Science Foundation of China under the Grants 60474027 and 10771211.
文摘In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.
基金Supported by the National Natural Science Foundation of China(61405191)
文摘A maximum a posteriori（ MAP） algorithm is proposed to improve the accuracy of super resolution（ SR） reconstruction in traditional methods. The algorithm applies both joints image registration and SR reconstruction in the framework,but separates them in the process of iteratiion. Firstly,we estimate the shifting parameters through two lowresolution（ LR） images and use the parameters to reconstruct initial HR images. Then,we update the shifting parameters using HR images. The aforementioned steps are repeated until the ideal HR images are obtained. The metrics such as PSNR and SSIM are used to fully evaluate the quality of the reconstructed image. Experimental results indicate that the proposed method can enhance image resolution efficiently.
文摘In this paper, a posteriori error estimates for the generalized Schwartz method with Dirichlet boundary conditions on the interfaces for advection-diffusion equation with second order boundary value problems are proved by using the Euler time scheme combined with Galerkin spatial method. Furthermore, an asymptotic behavior in Sobolev norm is de- duced using Benssoussau-Lions＇ algorithm. Finally, the results of some numerical experiments are presented to support the theory.
文摘Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.
文摘A nonlinear Galerkin mixed element (NGME) method and a posteriori error exstimator based on the method are established for the stationary Navier-Stokes equations. The existence and error estimates of the NGME solution are first discussed, and then a posteriori error estimator based on the NGME method is derived.
基金Project supported by National Natural Science Foundation ofChina (Grant No .10471089)
文摘In this paper, a posteriori error estimates were derived for piecewise linear finite element approximations to parabolic obstacle problems. The instrumental ingredient was introduced as a new interpolation operator which has optimal approximation properties and preserves positivity. With the help of the interpolation operator the upper and lower bounds were obtained.
文摘A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illustrate the accuracy and feasibility of this method.
文摘In this article, we use streamline diffusion method for the linear second order hyperbolic initial-boundary value problem. More specifically, we prove a posteriori error estimates for this method for the linear wave equation. We observe that this error estimates make finite element method increasingly powerful rather than other methods.
文摘The main aim of this paper is to give an anisotropic posteriori error estimator. We firstly study the convergence of bilineax finite element for the second order problem under anisotropic meshes. By using some novel approaches and techniques, the optimal error estimates and some superconvergence results axe obtained without the regulaxity assumption and quasi-uniform assumption requirements on the meshes. Then, based on these results, we give an anisotropic posteriori error estimate for the second problem.
文摘Interferogram noise reduction is a very important processing step in Interferometric Synthetic Aperture Radar(InSAR) technique. The most difficulty for this step is to remove the noises and preserve the fringes simultaneously. To solve the dilemma, a new interferogram noise reduction algorithm based on the Maximum A Posteriori(MAP) estimate is introduced in this paper. The algorithm is solved under the Total Generalized Variation(TGV) minimization assumption, which exploits the phase characteristics up to the second order differentiation. The ideal noise-free phase consisting of piecewise smooth areas is involved in this assumption, which is coincident with the natural terrain. In order to overcome the phase wraparound effect, complex plane filter is utilized in this algorithm. The simulation and real data experiments show the algorithm can reduce the noises effectively and meanwhile preserve the interferogram fringes very well.
文摘The paper presents an algorithm of automatic target detection in Synthetic Aperture Radar(SAR) images based on Maximum A Posteriori(MAP). The algorithm is divided into three steps. First, it employs Gaussian mixture distribution to approximate and estimate multi-modal histogram of SAR image. Then, based on the principle of MAP, when a priori probability is both unknown and learned respectively, the sample pixels are classified into different classes c = {target,shadow, background}. Last, it compares the results of two different target detections. Simulation results preferably indicate that the presented algorithm is fast and robust, with the learned a priori probability, an approach to target detection is reliable and promising.
基金This work was supported in part by the National Science Foundation under grant DMS-1620288。
文摘The present study regards the numerical approximation of solutions of systems of Korteweg-de Vries type,coupled through their nonlinear terms.In our previous work[9],we constructed conservative and dissipative finite element methods for these systems and presented a priori error estimates for the semidiscrete schemes.In this sequel,we present a posteriori error estimates for the semidiscrete and fully discrete approximations introduced in[9].The key tool employed to effect our analysis is the dispersive reconstruction devel-oped by Karakashian and Makridakis[20]for related discontinuous Galerkin methods.We conclude by providing a set of numerical experiments designed to validate the a posteriori theory and explore the effectivity of the resulting error indicators.
文摘In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator.
文摘One important issue for the simulation of flexible multibody systems is the reduction of the flexible bodies de- grees of freedom. As far as safety questions are concerned knowledge about the error introduced by the reduction of the flexible degrees of freedom is helpful and very important. In this work, an a-posteriori error estimator for linear first order systems is extended for error estimation of me- chanical second order systems. Due to the special second order structure of mechanical systems, an improvement of the a-posteriori error estimator is achieved. A major advan- tage of the a-posteriori error estimator is that the estimator is independent of the used reduction technique. Therefore, it can be used for moment-matching based, Gramian matrices based or modal based model reduction techniques. The capability of the proposed technique is demon- strated by the a-posteriori error estimation of a mechanical system, and a sensitivity analysis of the parameters involved in the error estimation process is conducted.
基金grateful for the facilities provided by the Computational Mechanics Laboratory of the Department of Mechanical Engineering.
文摘A posteriori error computations in the space-time coupled and space-time decoupled finite element methods for initial value problems are essential:1)to determine the accuracy of the computed evolution,2)if the errors in the coupled solutions are higher than an acceptable threshold,then a posteriori error computations provide measures for designing adaptive processes to improve the accuracy of the solution.How well the space-time approximation in each of the two methods satisfies the equations in the mathematical model over the space-time domain in the point wise sense is the absolute measure of the accuracy of the computed solution.When L2-norm of the space-time residual over the space-time domain of the computations approaches zero,the approximation φh(x,t)(,)→φ(x,t),the theoretical solution.Thus,the proximity of ||E||L_(2) ,the L_(2)-norm of the space-time residual function,to zero is a measure of the accuracy or the error in the computed solution.In this paper,we present a methodology and a computational framework for computing L2 E in the a posteriori error computations for both space-time coupled and space-time decoupled finite element methods.It is shown that the proposed a posteriori computations require h,p,k framework in both space-time coupled as well as space-time decoupled finite element methods to ensure that space-time integrals over space-time discretization are Riemann,hence the proposed a posteriori computations can not be performed in finite difference and finite volume methods of solving initial value problems.High-order global differentiability in time in the integration methods is essential in space-time decoupled method for posterior computations.This restricts the use of methods like Euler’s method,Runge-Kutta methods,etc.,in the time integration of ODE’s in time.Mathematical and computational details including model problem studies are presented in the paper.To authors knowledge,it is the first presentation of the proposed a posteriori error computation methodology and computational infrastructure for initial value problems.
基金supported by the Natural Science Foundation of China(Grants 12271367,12071403)by the Shanghai Science and Technology Planning Projects(Grant 20JC1414200).
文摘In this paper,we study a posteriori error estimates of the L1 scheme for time discretizations of time fractional parabolic differential equations,whose solutions have generally the initial singularity.To derive optimal order a posteriori error estimates,the quadratic reconstruction for the L1 method and the necessary fractional integral reconstruction for the first-step integration are introduced.By using these continuous,piecewise time reconstructions,the upper and lower error bounds depending only on the discretization parameters and the data of the problems are derived.Various numerical experiments for the one-dimensional linear fractional parabolic equations with smooth or nonsmooth exact solution are used to verify and complement our theoretical results,with the convergence ofαorder for the nonsmooth case on a uniform mesh.To recover the optimal convergence order 2-αon a nonuniform mesh,we further develop a time adaptive algorithm by means of barrier function recently introduced.The numerical implementations are performed on nonsmooth case again and verify that the true error and a posteriori error can achieve the optimal convergence order in adaptive mesh.
基金supported in part by the NSF of China(Grant No.12171141)by the Science and Technology Attack Plan Project of Henan province(Grant No.222102210049)supported in part by the NSF of China(Grant No.62102134).
文摘In this paper,we consider the electromagnetic wave scattering problem from a periodic chiral structure.The scattering problem is simplified to a two-dimensional problem,and is discretized by a finite volume method combined with the perfectly matched layer(PML)technique.A residual-type a posteriori error estimate of the PML finite volume method is analyzed and the upper and lower bounds on the error are established in the H^(1)-norm.The crucial part of the a posteriori error analysis is to derive the error representation formula and use a L^(2)-orthogonality property of the residual which plays a similar role as the Galerkin orthogonality.An adaptive PML finite volume method is proposed to solve the scattering problem.The PML parameters such as the thickness of the layer and the medium property are determined through sharp a posteriori error estimate.Finally,numerical experiments are presented to illustrate the efficiency of the proposed method.
基金supported by the National Natural Science Foundation of China(Grant No.12175183)。
文摘Gamma-ray imaging systems are powerful tools in radiographic diagnosis.However,the recorded images suffer from degradations such as noise,blurring,and downsampling,consequently failing to meet high-precision diagnostic requirements.In this paper,we propose a novel single-image super-resolution algorithm to enhance the spatial resolution of gamma-ray imaging systems.A mathematical model of the gamma-ray imaging system is established based on maximum a posteriori estimation.Within the plug-and-play framework,the half-quadratic splitting method is employed to decouple the data fidelit term and the regularization term.An image denoiser using convolutional neural networks is adopted as an implicit image prior,referred to as a deep denoiser prior,eliminating the need to explicitly design a regularization term.Furthermore,the impact of the image boundary condition on reconstruction results is considered,and a method for estimating image boundaries is introduced.The results show that the proposed algorithm can effectively addresses boundary artifacts.By increasing the pixel number of the reconstructed images,the proposed algorithm is capable of recovering more details.Notably,in both simulation and real experiments,the proposed algorithm is demonstrated to achieve subpixel resolution,surpassing the Nyquist sampling limit determined by the camera pixel size.
