基于径向基函数无网格法的声学应用
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- 英文论文题名：Acoustic Application of Meshless Method Based on the Radial Basis Function
- 论文作者：朱小松 ; 冯乐喜 ; 张新玉 ; 孟祥慈
- 英文论文作者：ZHU Xiao-song ; FENG Le-xi ; ZHANG Xin-yu ; MENG Xiang-ci ; College of Power and Engineering ; Harbin Engineering University
- 年：2016
- 作者机构：哈尔滨工程大学动力与能源工程学院;
- 论文关键词：无网格法 ; 声学计算 ; 傅里叶级数
- 英文论文关键词：Meshless method ; acoustic simulation ; Fourier series
- 会议召开时间：2016-07-28
- 会议录名称：第二十七届全国振动与噪声应用学术会议论文集
- 语种：中文
- 分类号：O42;O241
- 学会代码：ZDZD
- 会议名称：第二十七届全国振动与噪声应用学术会议
- 会议地点：中国黑龙江哈尔滨
- 主办单位：中国振动工程学会振动与噪声控制专业委员会
- 学会名称：中国振动工程学会振动与噪声控制专业委员会
- 页数：7
- 文件大小：502k
- 原文格式：D
- 会议级别：全国
摘要
本文将基于径向基函数的无网格法引入到声学计算的领域当中,对比分析了直接配点型和Hermite型无网格法在计算域边界处理上的特点,针对含有导数边界声学问题的处理方式结合实例探讨。为了提高Hermite型无网格法的数值计算稳定性,添加傅里叶级数到数值解的表达形式里,并与解析解进行对比,得到较好的计算结果。
Meshless method based on the radial basis function was introduced into the acoustic numerical simulation in this paper. Comparative analyses on Direct Collocation meshless method and Hermite Collocation meshless method to handle with acoustic derivative boundary were studied. Combined with some instances, the processing mode of acoustic derivative boundary was discussed. In order to improve the numerical calculation's stability of Hermite Collocation meshless method, Fourier series were appended to the expression of numerical solutions. Furthermore, the result by meshless method is approximate to the analytical solution.
Meshless method based on the radial basis function was introduced into the acoustic numerical simulation in this paper. Comparative analyses on Direct Collocation meshless method and Hermite Collocation meshless method to handle with acoustic derivative boundary were studied. Combined with some instances, the processing mode of acoustic derivative boundary was discussed. In order to improve the numerical calculation's stability of Hermite Collocation meshless method, Fourier series were appended to the expression of numerical solutions. Furthermore, the result by meshless method is approximate to the analytical solution.
引文
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[5]吴宗敏.径向基函数、散乱数据拟合与无网格偏微分方程数值解[J].工程数学学报,2002,19(2):1–12.
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[2]Buhmann M.D.Radial Basis Functions:theory and implementations[J].New York:Cambridge University Press,2003.
[3]Fasshauer G.E.Meshfree approximation methods with Matlab[M].New Jersey:World Scientific,2007.
[4]Wendland H.Scattered data approximation[D].New York:Cambridge University Press,2005.
[5]吴宗敏.径向基函数、散乱数据拟合与无网格偏微分方程数值解[J].工程数学学报,2002,19(2):1–12.
[6]Franke R.Scattered data interpolation:test of some methods.Mathematics of Computation,1982,38:181-200
[7]Madych W.R.,Nelson S.A Multivariate interpolation and conditionally positive definite functions II.Mathematic of Computation,1990,54:211-230