Helmholtz方程外问题的谱随机多尺度有限元法

J4 ›› 2011, Vol. 46 ›› Issue (6): 37-40.

Helmholtz方程外问题的谱随机多尺度有限元法

潘青飞1,单伟2*,吴建良3

1.三明大学土木建筑工程系，福建三明 365004； 2.济南大学理学院, 山东济南 250022;
3.山东大学数学学院, 山东济南 250100

收稿日期:2010-07-06 出版日期:2011-06-16 发布日期:2011-12-19
通讯作者: 单伟(1963- ),男,副教授,硕士,研究方向为图论及其应用等.Email:ss-shanw@ujn.edu.cn
作者简介:潘青飞(1962- )，男，副教授，研究方向为优化理论与方法. Email: pqf101@yahoo.com.cn
基金资助:
山东省自然科学基金资助项目(Y2008A20)

A spectral stochastic multi-scale finite element method for
the exterior problem of the Helmholtz equation

PAN Qingfei1, SHAN Wei2*, WU Jianliang3

1. Department of Civil Engineering and Architecture, Sanming University, Sanming 365004, Fujian, China;
2. School of Science, Jinan University, Jinan 250022, Shandong, China;
3. School of Mathematics, Shandong University, Jinan 250100, Shandong, China

Received:2010-07-06 Online:2011-06-16 Published:2011-12-19

摘要/Abstract

摘要：

研究了二维随机和多尺度求解声波与散射体相互作用的问题。基于变分原理和DtN映射方法,发展了数值求解这类声散射问题的一种谱随机多尺度有限元求解方法,提出了有效的数值实现手段。数值计算结果表明了所建立的有限元理论方法是有效和实用的,而且它的数值实现是快速的。

关键词: 声散射;多尺度有限元;谱随机

Abstract:

The interaction of acoustic waves with a scattering object in a stochastic and multi-scale media is studied. A spectral stochastic multi-scale finite-element method is developed to solve numerically the acoustic scattering problem based on the variation principle and the DtN mapping method. The results show that the proposed method is valid and its numerical implementation is very fast.

Key words: acoustic scattering; multi-scale finite-element; spectral stochastic

潘青飞1,单伟2*,吴建良3. Helmholtz方程外问题的谱随机多尺度有限元法[J]. J4, 2011, 46(6): 37-40.

PAN Qingfei1, SHAN Wei2*, WU Jianliang3. A spectral stochastic multi-scale finite element method for
the exterior problem of the Helmholtz equation[J]. J4, 2011, 46(6): 37-40.

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