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抛物方程时间周期问题的有限元多格子动力学迭代
  • 期刊名称：计算数学, Vol. 30, No. 2, pp. 113- - 128, May 2008.
  • 时间：0
  • 分类：O414.22[理学—理论物理;理学—物理] TP311.52[自动化与计算机技术—计算机软件与理论;自动化与计算机技术—计算机科学与技术]
  • 作者机构：[1]西安交通大学理学院数学系,西安710049
  • 相关基金：本文得到国家自然科学基金（NSFC10171080,60472003）、国家863计划（2001AA111042）和国家973项目（2005CB321701）的资助.
  • 相关项目：大型复杂系统瞬态模拟的计算理论与并行实现
关键词： 抛物型方程, 周期问题, 有限元方法, 多重网格方法, 动力学迭代, 谱集, Fourier级数, 并行处理, Parabolic partial differential equation, time-periodic problem, finite element method, multigrid method, dynamic iteration, spectral set, Fourier series, parallel processing
中文摘要：

本文我们研究线性周期抛物方程的有限元多格子动力学迭代．多格子动力学迭代又称多重网格波形松弛，它是在函数空间中的一种迭代过程．对于由加速技术得到的多格子动力学迭代算子，我们通过计算周期函数的Fourier系数给出了新的谱表达式．从这些有用的表达式出发，我们推导了时间连续和离散格式的迭代收敛条件．数值实验进一步验证了本文的理论结果．

英文摘要：

We study linear parabolic problems with known time period by multigrid dynamic iteration or multigrid waveform relaxation on spatial finite element meshes. The multigrid acceleration of the paper is an iteration process in function space. For multigrid dynamic iteration operators arising from the accelerated technique new spectral expressions are es- tablished by calculating coefficients of Fourier series of periodic functions. The convergence conditions of continuous-time and discrete-time iterative processes are also deduced from the useful expressions. Numerical experiments are provided to further illustrate the new theoretical results of the paper.

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