Superconvergence and H(div) projection for discontinuous Galerkin methods

We introduce and analyse a projection of the discontinuous Galerkin (DG) velocity approximations that preserve the local mass conservation property. The projected velocities have the additional property of continuous normal component. Both theoretical and numerical convergence rates are obtained which show that the accuracy of the DG velocity field is maintained. Superconvergence properties of the DG methods are shown. Finally, numerical simulations of complicated flow and transport problem illustrate the benefits of the projection. Copyright © 2003 John Wiley & Sons, Ltd.     

DERIVATION AND ANALYSIS OF A NEW RECONSTRUCTION FORMULA FROM CONE-BEAM PROJECTIONS

A new method to compute the first derivative of 3-D Radon transform is given for cone-beam data taken from any orbit. Smith [Ⅰ1] and Grangeat [5] even derived cone-beam inversion formulas which are the basic work in fully 3-D image reconstruction algorithm and are used extensively now. In this paper we will give a new inversion formula and a simple necessary and sufficient condition which guarantees the complete reconstruction algorithm.     

Dealing with pressure: FEM solution strategies for the pressure in the time‐dependent Navier–Stokes equations

This paper presents a survey of solution methods for calculating the pressure in the time‐dependent Navier–Stokes equations. The primary focus is on the treatment of the pressure‐Poisson equation deriving from index‐1 DAE formulations of the Navier–Stokes equations. Based on extensive operational experience with a variety of solution strategies, the combination of a stabilized pressure‐Poisson operator with an A‐conjugate projection and SSOR preconditioned conjugate gradient method has been found to yield the overall best performance relative to the resolve cost of a high performance direct solver. Copyright © 2002 John Wiley & Sons, Ltd.     

Pointwise supercloseness of quadratic serendipity block finite elements for a variable coefficient elliptic equation

For a variable coefficient elliptic boundary value problem in three dimensions, using the properties of the interpolation operator of projection type, we derive the weak estimate of the first type for the quadratic serendipity block finite element. In addition, the estimate for the W^1,1 ‐seminorm of the discrete derivative Green's function is given. Finally, we prove that the derivatives of the finite element approximation and the corresponding interpolant of projection type are superclose in the pointwise sense of the L^∞ ‐norm. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1253‐1261, 2011     

On a Family of Gradient-Type Projection Methods for Nonlinear Ill-Posed Problems

Abstract

We propose and analyze a family of successive projection methods whose step direction is the same as the Landweber method for solving nonlinear ill-posed problems that satisfy the Tangential Cone Condition (TCC). This family encompasses the Landweber method, the minimal error method, and the steepest descent method; thus, providing an unified framework for the analysis of these methods. Moreover, we define new methods in this family, which are convergent for the constant of the TCC in a range twice as large as the one required for the Landweber and other gradient type methods. The TCC is widely used in the analysis of iterative methods for solving nonlinear ill-posed problems. The key idea in this work is to use the TCC in order to construct special convex sets possessing a separation property, and to successively project onto these sets. Numerical experiments are presented for a nonlinear two-dimensional elliptic parameter identification problem, validating the efficiency of our method.     

Accurate and efficient algorithm for simulation of fringe projection system

Because of intrinsic drawbacks of existing algorithm for optical simulation: first, there is an accuracy problem, finite-precision machine arithmetic introduces error into line-surface intersection calculation. Second, these algorithms do not or partially consider process of shadow modeling. In this paper, we present an algorithm based on geometric analysis to simulate fringe projection system, a variable-step-iterative (VSI) algorithm is used to search line-surface intersection point, which can avoid many difficult problems. The proposed algorithm can accurately identify the shadow. Simulation results shows the reconstructed RMS errors obtained by our algorithm are far smaller than those obtained by previous reported algorithm. Simulation results validate our VSI algorithm can obtain more accurate results than many previous intersection point algorithms. Simulation results indicate our shadow modeling algorithm exceeds many existing shadow modeling algorithm, and is equivalent to shadow volumes algorithm, but our shadow algorithm runs faster than shadow volumes algorithm.     

fMRI pain activation in the periaqueductal gray in healthy volunteers during the cold pressor test

The periaqueductal gray (PAG), a brain area belonging to the descending pain modulatory system, plays a crucial role in pain perception. Little information is available on the relationship between PAG activation and perceived pain intensity. In this study, we acquired functional magnetic resonance imaging (fMRI) scans from the PAG during the cold pressor test, a model for tonic pain, in 12 healthy volunteers. fMRI data were acquired with a 12-channel head-coil and a 3-Tesla scanner and analyzed with Statistical Parametric Mapping (SPM8) software.     

DMZ内视场光学分割型航摄相机子影像高准确度几何拼接

针对内视场光学分割型相机,利用子影像同名像点虚拟影像坐标相等这一约束条件,提出一种高准确度子影像几何拼接方法.首先在分析各CCD几何安置误差的基础上,设计拼接关系并给出拼接参量计算方法;其次结合SIFT等高准确度影像匹配算子对拼接模型进行优化选择,给出子影像拼接流程;最后采用附加参量自检校技术进行畸变参量再精化处理.利用所提方法对一款自行设计的数字大面阵复合相机进行几何拼接试验,结果表明该方法能够有效解决高准确度子影像几何拼接、高量测性能大幅面虚拟影像生成问题,拼接后影像内符准确度可达子像元级,满足航测作业对数字航摄相机测图准确度和摄影效率的应用要求.