快速振荡系数抛物型方程的小波多尺度数值模拟
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摘要
分析了一种基于小波理论的多尺度计算方法——小波数值均匀化方法,并将该方法用于具有快速振荡系数的抛物型偏微分方程的数值求解。数值结果表明,与传统的有限差分法相比,小波数值均匀化方法不仅保持了较高的数值精度,而且大大提高了计算效率。小波数值均匀化方法能够对具有快速振荡系数的抛物型方程进行有效求解。
A kind of wavelet-based multi-scale method—wavelet-based numerical homogenization method is proposed for parabolic equa-tions with periodic coefficients.Compared to traditional finite difference method,numericalresult indicate that the wavelet-based nu-merical homogenization method keep better accuracy and further improve computational efficiency.
A kind of wavelet-based multi-scale method—wavelet-based numerical homogenization method is proposed for parabolic equa-tions with periodic coefficients.Compared to traditional finite difference method,numericalresult indicate that the wavelet-based nu-merical homogenization method keep better accuracy and further improve computational efficiency.
引文
[1]徐长发,李红.实用偏微分方程数值解法[M].2版.武汉:华中科技大学出版社,2003:328-349.
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[3]王自强,宋士仓,曹俊英.小周期复合材料热传导问题的双尺度渐近展开及收敛性分析[J].高校应用数学学报A辑,2008,23(2):145-152.
[4]薛禹群,叶淑君,谢春红,等.多尺度有限元法在地下水模拟中的应用[J].水利学报,2004(7):7-13.
[5]叶淑君,吴吉春,薛禹群.多尺度有限单元法求解多孔介质中的三维地下水流问题[J].地球科学进展,2004,19(3):437-442.
[6]马坚伟,朱亚平,杨慧珠.二维地震波形小波多尺度反演[J].工程数学学报,2004,21(1):109-113.
[7]马坚伟,杨慧珠.多尺度辛格式求解复杂介质波传问题[J].应用数学和力学,2004,25(5):3-8.
[8]Marcin Kaminski.Wavelet-based homogenization of unidirec-tional multiscale composites[J].Computional Materials Science,2003,27(6):446-460.
[9]Krishnan J,Runborg O,Keverkidis I G.Bifurcation analysis ofnonlinear reaction-diffusion problems using wavelet-based re-duction techniques[J].Computers and Chemical Engineering,2004,28(8):557-574.
[10]Mihai D,Bjorn E.Wavelet-based numerical homogenization[J].SIAM Journal on Numerical Analysis,1998,35(2):540-559.
[11]Mehraeen S,Juin-shyan C.Wavelet-based multiscale projectionmethod in homogenization of heterogeneous media[J].FiniteElements in Analysis and Design,2004,40(12):1665-1679.
[2]宋士仓,崔俊芝,刘宏生.复合材料稳态热传导问题多尺度计算的一个数学模型[J].应用数学,2005,18(4):560-566.
[3]王自强,宋士仓,曹俊英.小周期复合材料热传导问题的双尺度渐近展开及收敛性分析[J].高校应用数学学报A辑,2008,23(2):145-152.
[4]薛禹群,叶淑君,谢春红,等.多尺度有限元法在地下水模拟中的应用[J].水利学报,2004(7):7-13.
[5]叶淑君,吴吉春,薛禹群.多尺度有限单元法求解多孔介质中的三维地下水流问题[J].地球科学进展,2004,19(3):437-442.
[6]马坚伟,朱亚平,杨慧珠.二维地震波形小波多尺度反演[J].工程数学学报,2004,21(1):109-113.
[7]马坚伟,杨慧珠.多尺度辛格式求解复杂介质波传问题[J].应用数学和力学,2004,25(5):3-8.
[8]Marcin Kaminski.Wavelet-based homogenization of unidirec-tional multiscale composites[J].Computional Materials Science,2003,27(6):446-460.
[9]Krishnan J,Runborg O,Keverkidis I G.Bifurcation analysis ofnonlinear reaction-diffusion problems using wavelet-based re-duction techniques[J].Computers and Chemical Engineering,2004,28(8):557-574.
[10]Mihai D,Bjorn E.Wavelet-based numerical homogenization[J].SIAM Journal on Numerical Analysis,1998,35(2):540-559.
[11]Mehraeen S,Juin-shyan C.Wavelet-based multiscale projectionmethod in homogenization of heterogeneous media[J].FiniteElements in Analysis and Design,2004,40(12):1665-1679.
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