It has been proven that carrier smoothing and differential global positioning system （DGPS） are effective to improve the accuracy of pseudorange by reducing the noise in it and eliminating almost all the common mode...It has been proven that carrier smoothing and differential global positioning system （DGPS） are effective to improve the accuracy of pseudorange by reducing the noise in it and eliminating almost all the common mode errors between the ground station and user. However, another issue coming with local area augmentation system （LAAS） is how to find an adaptive smoothing window width to minimize the error on account of ionosphere delay and multipath. Based on the errors analysis in carrier smoothing process, a novel algorithm is formulated to design adaptive Hatch filter whose smoothing window width flexibly varies with the characteristic of ionosphere delay and multipath in the differential carrier smoothing process. By conducting the simulation in LAAS and after compared with traditional Hatch filers, it reveals that not only the accuracy of differential correction, but also the accuracy and the robustness of positioning results are significantly improved by using the designed adaptive Hatch filter.展开更多
In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-depe...In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.展开更多
We propose a method based on the Poynting vector that combines angle-domain imaging and image amplitude correction to overcome the shortcomings of reverse-time migration that cannot handle different angles during wave...We propose a method based on the Poynting vector that combines angle-domain imaging and image amplitude correction to overcome the shortcomings of reverse-time migration that cannot handle different angles during wave propagation. First, the local image matrix （LIM） and local illumination matrix are constructed, and the wavefield propagation directions are decomposed. The angle-domain imaging conditions are established in the local imaging matrix to remove low-wavenumber artifacts. Next, the angle-domain common image gathers are extracted and the dip angle is calculated, and the amplitude-corrected factors in the dip angle domain are calculated. The partial images are corrected by factors corresponding to the different angles and then are superimposed to perform the amplitude correction of the final image. Angle-domain imaging based on the Poynting vector improves the computation efficiency compared with local plane-wave decomposition. Finally, numerical simulations based on the SEG/EAGE velocity model are used to validate the proposed method.展开更多
In this paper,we will develop a first order and a second order convex splitting,and a first order linear energy stable fully discrete local discontinuous Galerkin(LDG)methods for the modified phase field crystal(MPFC)...In this paper,we will develop a first order and a second order convex splitting,and a first order linear energy stable fully discrete local discontinuous Galerkin(LDG)methods for the modified phase field crystal(MPFC)equation.In which,the first order linear scheme is based on the invariant energy quadratization approach.The MPFC equation is a damped wave equation,and to preserve an energy stability,it is necessary to introduce a pseudo energy,which all increase the difficulty of constructing numerical methods comparing with the phase field crystal(PFC)equation.Due to the severe time step restriction of explicit timemarchingmethods,we introduce the first order and second order semi-implicit schemes,which are proved to be unconditionally energy stable.In order to improve the temporal accuracy,the semi-implicit spectral deferred correction(SDC)method combining with the first order convex splitting scheme is employed.Numerical simulations of the MPFC equation always need long time to reach steady state,and then adaptive time-stepping method is necessary and of paramount importance.The schemes at the implicit time level are linear or nonlinear and we solve them by multigrid solver.Numerical experiments of the accuracy and long time simulations are presented demonstrating the capability and efficiency of the proposed methods,and the effectiveness of the adaptive time-stepping strategy.展开更多
This paper presents a high order time discretization method by combining the semi-implicit spectral deferred correction method with energy stable linear schemes to simulate a series of phase field problems.We start wi...This paper presents a high order time discretization method by combining the semi-implicit spectral deferred correction method with energy stable linear schemes to simulate a series of phase field problems.We start with the linear scheme,which is based on the invariant energy quadratization approach and is proved to be linear unconditionally energy stable.The scheme also takes advantage of avoiding nonlinear iteration and the restriction of time step to guarantee the nonlinear system uniquely solvable.Moreover,the scheme leads to linear algebraic system to solve at each iteration,and we employ the multigrid solver to solve it efficiently.Numerical re-sults are given to illustrate that the combination of local discontinuous Galerkin(LDG)spatial discretization and the high order temporal scheme is a practical,accurate and efficient simulation tool when solving phase field problems.Namely,we can obtain high order accuracy in both time and space by solving some simple linear algebraic equations.展开更多
High resolution Fresnel zone plates for nanoscale three-dimensional imaging of materials by both soft and hard x-rays are increasingly needed by the broad applications in nanoscience and nanotechnology.When the outmos...High resolution Fresnel zone plates for nanoscale three-dimensional imaging of materials by both soft and hard x-rays are increasingly needed by the broad applications in nanoscience and nanotechnology.When the outmost zone-width is shrinking down to 50 nm or even below,patterning the zone plates with high aspect ratio by electron beam lithography still remains a challenge because of the proximity effect.The uneven charge distribution in the exposed resist is still frequently observed even after standard proximity effect correction(PEC),because of the large variety in the line width.This work develops a new strategy,nicknamed as local proximity effect correction(LPEC),efficiently modifying the deposited energy over the whole zone plate on the top of proximity effect correction.By this way,50 nm zone plates with the aspect ratio from 4:1 up to 15:1 and the duty cycle close to 0.5 have been fabricated.Their imaging capability in soft(1.3 keV)and hard(9 keV)x-ray,respectively,has been demonstrated in Shanghai Synchrotron Radiation Facility(SSRF)with the resolution of 50 nm.The local proximity effect correction developed in this work should also be generally significant for the generation of zone plates with high resolutions beyond 50 nm.展开更多
基金supported by the National Natural Science Foundationof China (60974104)the National Defense Technical Foundation of Shipbuilding Industry (08J3.8.8)
文摘It has been proven that carrier smoothing and differential global positioning system （DGPS） are effective to improve the accuracy of pseudorange by reducing the noise in it and eliminating almost all the common mode errors between the ground station and user. However, another issue coming with local area augmentation system （LAAS） is how to find an adaptive smoothing window width to minimize the error on account of ionosphere delay and multipath. Based on the errors analysis in carrier smoothing process, a novel algorithm is formulated to design adaptive Hatch filter whose smoothing window width flexibly varies with the characteristic of ionosphere delay and multipath in the differential carrier smoothing process. By conducting the simulation in LAAS and after compared with traditional Hatch filers, it reveals that not only the accuracy of differential correction, but also the accuracy and the robustness of positioning results are significantly improved by using the designed adaptive Hatch filter.
文摘In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.
基金sponsored by the Natural Science Fund of Heilongjiang Province(No.F201404)
文摘We propose a method based on the Poynting vector that combines angle-domain imaging and image amplitude correction to overcome the shortcomings of reverse-time migration that cannot handle different angles during wave propagation. First, the local image matrix （LIM） and local illumination matrix are constructed, and the wavefield propagation directions are decomposed. The angle-domain imaging conditions are established in the local imaging matrix to remove low-wavenumber artifacts. Next, the angle-domain common image gathers are extracted and the dip angle is calculated, and the amplitude-corrected factors in the dip angle domain are calculated. The partial images are corrected by factors corresponding to the different angles and then are superimposed to perform the amplitude correction of the final image. Angle-domain imaging based on the Poynting vector improves the computation efficiency compared with local plane-wave decomposition. Finally, numerical simulations based on the SEG/EAGE velocity model are used to validate the proposed method.
基金Research of R.Guo is supported by NSFC grant No.11601490Research of Y.Xu is supported by NSFC grant No.11371342,11626253,91630207.
文摘In this paper,we will develop a first order and a second order convex splitting,and a first order linear energy stable fully discrete local discontinuous Galerkin(LDG)methods for the modified phase field crystal(MPFC)equation.In which,the first order linear scheme is based on the invariant energy quadratization approach.The MPFC equation is a damped wave equation,and to preserve an energy stability,it is necessary to introduce a pseudo energy,which all increase the difficulty of constructing numerical methods comparing with the phase field crystal(PFC)equation.Due to the severe time step restriction of explicit timemarchingmethods,we introduce the first order and second order semi-implicit schemes,which are proved to be unconditionally energy stable.In order to improve the temporal accuracy,the semi-implicit spectral deferred correction(SDC)method combining with the first order convex splitting scheme is employed.Numerical simulations of the MPFC equation always need long time to reach steady state,and then adaptive time-stepping method is necessary and of paramount importance.The schemes at the implicit time level are linear or nonlinear and we solve them by multigrid solver.Numerical experiments of the accuracy and long time simulations are presented demonstrating the capability and efficiency of the proposed methods,and the effectiveness of the adaptive time-stepping strategy.
基金Research of R.Guo is supported by NSFC grant No.11601490Research of Y.Xu is supported by NSFC grant No.11722112,91630207.
文摘This paper presents a high order time discretization method by combining the semi-implicit spectral deferred correction method with energy stable linear schemes to simulate a series of phase field problems.We start with the linear scheme,which is based on the invariant energy quadratization approach and is proved to be linear unconditionally energy stable.The scheme also takes advantage of avoiding nonlinear iteration and the restriction of time step to guarantee the nonlinear system uniquely solvable.Moreover,the scheme leads to linear algebraic system to solve at each iteration,and we employ the multigrid solver to solve it efficiently.Numerical re-sults are given to illustrate that the combination of local discontinuous Galerkin(LDG)spatial discretization and the high order temporal scheme is a practical,accurate and efficient simulation tool when solving phase field problems.Namely,we can obtain high order accuracy in both time and space by solving some simple linear algebraic equations.
基金Project supported by the National Natural Science Foundation of China(Grant No.U1732104)China Postdoctoral Science Foundation(Grant No.2017M611443)Shanghai STCSM2019-11-20 Grant,China(Grant No.19142202700)。
文摘High resolution Fresnel zone plates for nanoscale three-dimensional imaging of materials by both soft and hard x-rays are increasingly needed by the broad applications in nanoscience and nanotechnology.When the outmost zone-width is shrinking down to 50 nm or even below,patterning the zone plates with high aspect ratio by electron beam lithography still remains a challenge because of the proximity effect.The uneven charge distribution in the exposed resist is still frequently observed even after standard proximity effect correction(PEC),because of the large variety in the line width.This work develops a new strategy,nicknamed as local proximity effect correction(LPEC),efficiently modifying the deposited energy over the whole zone plate on the top of proximity effect correction.By this way,50 nm zone plates with the aspect ratio from 4:1 up to 15:1 and the duty cycle close to 0.5 have been fabricated.Their imaging capability in soft(1.3 keV)and hard(9 keV)x-ray,respectively,has been demonstrated in Shanghai Synchrotron Radiation Facility(SSRF)with the resolution of 50 nm.The local proximity effect correction developed in this work should also be generally significant for the generation of zone plates with high resolutions beyond 50 nm.
