在空间有限元离散上扩展一种新的两网格波形松弛方法
Extending a new two-grid waveform relaxation on a spatial finite element discretization
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中文总结 AI 辅助
将一种新的两网格波形松弛方法从椭圆方程推广到线性抛物型方程，采用有限元空间离散和直线法，并基于谱半径分析收敛性，通过二维热方程验证效率。
中文摘要 AI 辅助
本文中，针对椭圆偏微分方程提出的一种新的两网格方法被推广到时间依赖的线性抛物型偏微分方程。新的两网格波形松弛方法采用数值方法中的直线法，用离散公式替换任何空间导数，此处通过有限元方法获得。还发展了关于相应两网格波形松弛算子谱半径的收敛性分析。此外，通过应用二维热方程，测试了所提出方法及其分析的效率。
英文摘要
In this work, a new two-grid method presented for the elliptic partial differential equations is generalized to the time-dependent linear parabolic partial differential equations. The new two-grid waveform relaxation method uses the numerical method of lines, replacing any spatial derivative by a discrete formula, obtained here by the finite element method. A convergence analysis in terms of the spectral radius of the corresponding two-grid waveform relaxation operator is also developed. Moreover, the efficiency of the presented method and its analysis are tested, applying the two-dimensional heat equation.
发表机构
- Faculty of Applied Mathematics, Shahrood University Of Technology（沙鲁德理工大学应用数学学院）
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