Dual-primal FETI algorithms for edge finite-element approximations in 3D

^** Email: toselli{at}sam.math.ethz.ch A family of dual-primal finite-element tearing and interconnectingmethods for edge-element approximations in 3D is proposed andanalysed. The key part of this work relies on the observationthat for these finite-element spaces there is a strong couplingbetween degrees of freedom associated with subdomain edges andfaces and a local change of basis is therefore necessary. Theprimal constraints are associated with subdomain edges. We proposethree methods. They ensure a condition number that is independentof the number of substructures and possibly large jumps of oneof the coefficients of the original problem, and only dependson the number of unknowns associated with a single substructure,as for the corresponding methods for continuous nodal elements.A polylogarithmic dependence is shown for two algorithms. Numericalresults validating our theoretical bounds are given.     

Influence of the halo upon angular distributions for elastic scattering and breakup

The angular distributions for elastic scattering and breakup of halo nuclei are analysed using a near-side/far-side decomposition within the framework of the dynamical eikonal approximation. This analysis is performed for ¹¹Be impinging on Pb at 69 MeV/nucleon. These distributions exhibit very similar features. In particular they are both near-side dominated, as expected from Coulomb-dominated reactions. The general shape of these distributions is sensitive mostly to the projectile-target interactions, but is also affected by the extension of the halo. This suggests the elastic scattering not to be affected by a loss of flux towards the breakup channel.     

Comment on “Entanglement of two interacting bosons in a two-dimensional isotropic harmonic trap” [Phys. Lett. A 373 (2009) 3833]

The correct form of the Schmidt decomposition of the stationary wave functions for a system of two interacting particles trapped in a two-dimensional harmonic potential is given.     

Fast algorithms for spherical harmonic expansions,III

We accelerate the computation of spherical harmonic transforms, using what is known as the butterfly scheme. This provides a convenient alternative to the approach taken in the second paper from this series on “Fast algorithms for spherical harmonic expansions”. The requisite precomputations become manageable when organized as a “depth-first traversal” of the program’s control-flow graph, rather than as the perhaps more natural “breadth-first traversal” that processes one-by-one each level of the multilevel procedure. We illustrate the results via several numerical examples.     

The influence of cell geometry on the Godunov scheme applied to the linear wave equation

By studying the structure of the discrete kernel of the linear acoustic operator discretized with a Godunov scheme, we clearly explain why the behaviour of the Godunov scheme applied to the linear wave equation deeply depends on the space dimension and, especially, on the type of mesh. This approach allows us to explain why, in the periodic case, the Godunov scheme applied to the resolution of the compressible Euler or Navier–Stokes system is accurate at low Mach number when the mesh is triangular or tetrahedral and is not accurate when the mesh is a 2D (or 3D) cartesian mesh. This approach confirms also the fact that a Godunov scheme remains accurate when it is modified by simply centering the discretization of the pressure gradient.     

LDPC一致校验矩阵的LU分解算法

不同于Turbo码,LDPC是数学结构非常好的一类高速码。对其结构进行系统研究,不但对实际编码方案很有帮助,而且也有很高的理论价值。二进制低密度码（MN码）编码的基础为Gaussian消元法（消去法）。丈中推导了MN码的一致校验矩阵的基于初等变换的Gaussian消元法。研究表明,基于初等变换的Gaussian消元法结合“minprod”算法在进行LU分解时,可以有效地保持MN码一致校验矩阵的稀疏性。     

一种图像快速配准算法的研究

在基于小波分解和互信息测度的图像配准方法的基础上,提出一种改进的快速图像配准算法。首先,对图像进行小波分解,以分解后的图像的近似分量进行配准,利用互信息最大化作为相似性测度,并结合粒子群优化算法和鲍威尔算法为优化策略搜索最优配准参数。实验结果显示,此方法在得到较高的配准精度和鲁棒性的情况下,还大大减少了运算量,提高了配准的速度。     

基于直方图散度和小波分解的图像配准算法

针对基于互信息的图像配准方法运行时间长、抗噪声差的问题,提出了一种基于新的相似性测度的图像配准算法,在分析两幅图像的联合直方图点集分布情况的基础上,定义了直方图点集的散度公式,并将其作为相似性测度.为加速参数的搜索过程,配准是在小波域内进行的,并使用遗传算法与Powell算法相结合的方法来优化参数.实验证明,相对于基于互信息的图像配准算法,本算法参数优化方法选择可以更灵活,时间消耗更少,噪声鲁棒性更优.     

一种改进的小波基线校正方法的研究

通过对小波变换基线校正中最佳分解尺度方法的研究,提出了一种新的基于小波变换的最佳分解尺度确定方法,不但有效地提高了基线校正效果,而且具有简单、快速的优点.将该方法应用于血糖光谱数据预处理中进行基线校正,取得了较好的效果.通过人体口服葡萄糖耐量试验(OGTT)得到人体无创检测近红外光谱和对应血糖浓度值,然后采用该方法对上述光谱进行基线校正并建立多元回归模型,采用交互验证的方式对模型及基线校正的效果进行了评价.实验结果表明,血糖浓度预测值和参考值间的相关系数为0.75,预测均方根误差(RMSEP)为1.36 mmol/L,与原始光谱预测结果和其他小波分解尺度下的预测结果相比,RMSEP降低了将近39%,相关系数提高了0.64,预测精度得到较大幅度提高.     

宽带数字接收机的研究及实现

针对雷达侦察接收机带宽较大,处理速度成为后续数字信号处理的瓶颈,提出一种基于多相结构的宽带数字信道化接收机设计方案,通过信道化降低后续信号处理速度,提高信号的频率分辨率并节省硬件资源。模块仿真测试结果表明该方案可行且实用。