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计算数学  2008 

MULTIGRID DYNAMIC ITERATION OF TIME-PERIODIC PARABOLIC PROBLEMS ON SPATIAL FINITE ELEMENT MESHES
抛物方程时间周期问题的有限元多格子动力学迭代

Keywords: Parabolic partial differential equation,time-periodic problem,finite element method,multigrid method,dynamic iteration,spectral set,Fourier series,parallel processing
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

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Abstract:

We study linear parabolic problems with known time period by multigrid dynamic it- eration 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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