Two-stage least squares and indirect least squares algorithms for simultaneous equations models

This paper analyzes the solution of simultaneous equations models. Efficient algorithms for the two-stage least squares method using QR-decomposition are developed and studied. The reduction of the execution time when the structure of the matrices in each equation is exploited is analyzed theoretically and experimentally. An efficient algorithm for the indirect least squares method is developed. Some techniques are used to accelerate the solution of the problem: parallel versions for multicore systems, and extensive use of the MKL library, thus obtaining efficient, portable versions of the algorithms.     

A NEW GENERALIZED ASYNCHRONOUS PARALLEL MULTISPLITTING ITERATION METHOD

1.IntroductionTosolvelargesparsesystemsoflinearandnonlinearequationsonthemultiprocessorsystems,manyauthorspresentedandstudiedvariousparalleliterativemethodsinthesenseofmultisplittinginrecentyears.FOrdetailsonecanreferto[1]-[9]andreferencestherein.Amo...     

Beam-displacement ray-mode theory of sound propagation in shallow water

A normal mode method for propagation modeling in common horizontally stratified shallow water, which is called beam-displacement ray-mode (BDRM) theory, is introduced. The peculiarity of this method is that the boundary effects on the sound field can be expressed by the equivalent boundary reflection coefficient, so BDRM theory can be extended to elastic bottom easily. Theoretical calculations of shallow-water sound field show that BDRM has high accuracy and fast speed. The pulse propagation in shallow water is also calculated by BDRM, and the calculated waveforms are in good agreement with the measured waveforms. Project support by the National Natural Science Foundation of China (Grant No. 1973405).     

Nd∶YVO4/Nd∶GdVO4双波长激光器的功率均衡实验研究

实验研究了Nd∶YVO4/Nd∶GdVO4双波长激光器在不同抽运功率条件下,通过调节热沉温度达到功率均衡时的输出特性.实验结果表明:对于Nd∶YVO4/Nd∶GdVO4双波长激光器,当提高抽运功率,需要重新降低热沉温度达到功率均衡输出,降温幅度与抽运功率增加之比为11.23℃/W.与此同时,随着抽运功率和热沉温度的变化,双波长激光器的中心波长会出现小幅度的漂移,左峰波长随抽运功率增加的蓝移速率为0.056 nm/W,右峰波长随抽运功率增加的蓝移速率为0.054 nm/W.实验还发现功率均衡条件下激光器的输出总功率随抽运功率的增加而增加,拟合斜效率为8.7%,当抽运功率为5.58 W时,输出最大总功率达到115.7 mW.     

The Crank‐Nicolson/Adams‐Bashforth scheme for the time‐dependent Navier‐Stokes equations with nonsmooth initial data

In this article, we study the stability and convergence of the Crank‐Nicolson/Adams‐Bashforth scheme for the two‐dimensional nonstationary Navier‐Stokes equations with a nonsmooth initial data. A finite element method is applied for the spatial approximation of the velocity and pressure. The time discretization is based on the implicit Crank‐Nicolson scheme for the linear terms and the explicit Adams‐Bashforth scheme for the nonlinear term. Moreover, we prove that the scheme is almost unconditionally stable for a nonsmooth initial data u₀ with div u₀ = 0, i.e., the time step τ satisfies: τ ≤ C₀ if u₀ ∈ H¹ ∩ L^∞; τ |log h| ≤ C₀ if u₀ ∈ H¹ for the mesh size h and some positive constant C₀. Finally, we obtain some error estimates for the discrete velocity and pressure under the above stability condition. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 28: 155‐187, 2012     

On a hierarchical error estimator combined with a stabilized method for the Navier–Stokes equations

This work combines two complementary strategies for solving the steady incompressible Navier–Stokes model with a zeroth‐order term, namely, a stabilized finite element method and a mesh–refinement approach based on an error estimator. First, equal order interpolation spaces are adopted to approximate both the velocity and the pressure while stability is recovered within the stabilization approach. Also designed to handle advection dominated flows under zeroth‐order term influence, the stabilized method incorporates a new parameter with a threefold asymptotic behavior. Mesh adaptivity driven by a new hierarchical error estimator and built on the stabilized method is the second ingredient. The estimator construction process circumvents the saturation assumption by using an enhancing space strategy which is shown to be equivalent to the error. Several numerical tests validate the methodology. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

光电导天线太赫兹辐射峰值调控研究

针对微结构光电导天线与飞秒激光之间相互作用效应以及辐射太赫兹波调控问题进行了研究。采用德鲁德-洛伦兹理论模型获得微结构光电导天线辐射光电流密度,通过时域有限差分把光电流密度迭代在激励网格上,结合麦克斯韦方程求解时变电磁场,并通过传输线格林函数获得多层介质近场到远场的辐射太赫兹波,建立了辐射光电流与辐射阻抗、电磁共振模式之间的关系模型,模拟仿真分析了微结构S型光电导天线太赫兹波辐射调控机理。研究结果表明：微结构改变了天线等效模型的辐射阻抗;同时得知耦合系数不为零时存在耦合作用,且随着耦合系数增大共振频率峰值发生辐射增强和位移;并通过设计S型光电导天线获得辐射峰值频率调整范围为0.50～0.80 THz之间,对比工形天线辐射峰值频率由原来的0.40 T移动到0.76 T,频率调整度75%,峰值辐射效率约提高70%。该研究工作为后续高功率光导天线太赫兹波辐射的共振中心频点以及结构设计奠定重要基础。     

一类半线性椭圆型方程爆炸解的存在性与渐近行为

设Ω是Ｒ＾Ｎ（Ｎ≥２）中的Ｃ＾２有界区域,对非线性项带有适当的梯度与无界系数ｋ（ｘ）,首先应用非线性变换将爆炸解问题,转化成等价的带奇异项的Ｄｉｒｉｃｈｌｅｔ问题,应用极大值原理得到爆炸解问题的最小爆炸速度。随后,应用摄动方法,结合上下解方法与椭圆型方程的估计理论得到了爆炸解的存在性。     

Full collocation methods for some boundary integral equations

In this paper we propose a fully discretized version of the collocation method applied to integral equations of the first kind with logarithmic kernel. After a stability and convergence analysis is given, we prove the existence of an asymptotic expansion of the error, which justifies the use of Richardson extrapolation. We further show how these expansions can be translated to a new expansion of potentials calculated with the numerical solution of a boundary integral equation such as those treated before. Some numerical experiments, confirming our theoretical results, are given. This revised version was published online in August 2006 with corrections to the Cover Date.