A note on the convergence of discretized dynamic iteration

In this note we prove convergence results, including error estimates, for the dynamic iteration scheme where the forward Euler and backward Euler method are used to compute the iterates. The proofs are interesting in that they are exact analogues of the proof for the continuous case, using discrete versions of Gronwall's inequality.     

A comparison result for multisplittings and waveform relaxation methods

We show that certain multisplitting iterative methods based on overlapping blocks yield faster convergence than corresponding nonoverlapping block iterations, provided the coefficient matrix is an M-matrix. This result can be used to compare variants of the waveform relaxation algorithm for solving initial value problems. The methods under consideration use the same discretization technique, but are based on multisplittings with different overlaps. Numerical experiments on the Intel iPSC/860 hypercube are included.     

利用U-Net网络增强骨密度全波形反演

该文设计了一种使用U-Net网络解决骨密度全波形反演的初值依赖、多解、病态等问题的方法。首先使用逆时偏移成像，将其结果输入神经网络得到模型的预分布。将该分布作为全波形反演目标函数的约束，可以使反演的结果更接近最优值，还可以减小反演对初始值的依赖。该文进行了一些模拟实验，得出该文的方法可以改进全波形反演对初始值的依赖和容易陷入局部极值的问题。     

Overlapping Schwarz waveform relaxation method for the solution of the convection–diffusion equation

In this article we study the convergence of the overlapping Schwarz wave form relaxation method for solving the convection–diffusion equation over multi-overlapped subdomains. It is shown that the method converges linearly and superlinearly over long and short time intervals, and the convergence depends on the size of the overlap. Numerical results are presented from solving specific types of model problems to demonstrate the convergence and the role of the size of the overlap. Copyright © 2007 John Wiley & Sons, Ltd.     

一类求解反应扩散方程的Newton波形松弛方法

对反应扩散方程提出一种新型的Newton波形松弛方法,并给出此方法的误差估计式.通过与传统的波形松弛方法比较,这种Newton波形松弛方法有更快的收敛性,且收敛速度不随网格加密而减慢.这种方法可以保持传统波形松弛方法可并行的特点.最后通过数值算例验证这种方法的有效性.     

电容损耗对脉冲氙灯放电特性的影响

研究了储能电容自身损耗对氙灯放电特性的影响,对脉冲氙灯放电回路进行了分析与改进。在实际电容自身损耗不为零的情况下,将电容等效为理想电容与损耗阻抗的串联,给出了计算氙灯放电特性的改进公式,并详细计算和分析了电容自身损耗增大情况下的氙灯放电电流和放电功率变化情况,计算结果表明:损耗增大会导致氙灯放电电流、功率峰值下降,闪光时间缩短,显著影响激光泵浦效率;电容损耗增大还会导致LC放电回路出现电容反充电现象,影响氙灯正常工作并缩短灯的寿命。实际的储能电容充放电实验证明,电容损耗增大会导致氙灯闪光的波形峰值下降、闪光时间缩短和电极溅射加剧,验证了理论分析的合理性。另外,实验证明环境因素对储能电容自身损耗的增大具有非常显著的影响。     

ON THE CONVERGENCE OF WAVEFORM RELAXATION METHODS FOR LINEAR INITIAL VALUE PROBLEMS

We study a class of blockwise waveform relaxation methods,and investigate its con-vergence properties in both asymptotic and monotone senses.In addition,the monotoneconvergence rates between different pointwise/blockwise waveform relaxation methods re-sulted from different matrix splittings,and those between the pointwise and blockwisewaveform relaxation methods are discussed in depth.     

Observation and Interpretation for a Phenomenon Involved with the Self-mixing Interference in Semiconductor Laser

A phenomenon involved with self-mixing interference that the sign of the quasisawtooth waveform depends on whether the photodiode monitors the laser output from the front or the back facet in semiconductor laser is observed and explained. This explaination is different from the one given by previous researchers.     

非线性刚性微分-代数系统的波形松弛离散法

研究基于Runge-Kutta方法的波形松弛离散过程,得到新的刚性微分-代数系统的收敛理论,及该类系统解的存在性和惟一性,并用具体算例测试该理论的有效实用性.     

用调频正弦波形和示波器同步原理模拟纵波

基于示波器同步原理,用固定周期的调制电信号模拟机械简谐振动源,用调频波形模拟质点的稠密区和稀疏区,用不同步的左右移动波形模拟质点作简谐振动,实现了在示波器上模拟纵波.