计算抛物方程中乘积形式的Padé系数

详细信息    查看官网全文

• 英文论文题名：A novel method for computing padé coefficients of the product approximation formation for a parabolic equation
• 论文作者：李松 ; 岳皓
• 英文论文作者：LI Song ; YUE Hao ; Academy of Ocean Science and Engineering ; National University of Defense and Technology
• 年：2016
• 作者机构：国防科学技术大学海洋科学与工程研究院;
• 论文关键词：抛物方程(PE) ; Padé-PE ; 乘积形式
• 英文论文关键词：PE ; Padé-PE ; rational-linear product approximation
• 会议召开时间：2016-10-28
• 会议录名称：2016年全国声学学术会议论文集
• 语种：中文
• 分类号：P733.2
• 学会代码：OGSM
• 会议名称：2016年全国声学学术会议
• 会议地点：中国湖北武汉
• 主办单位：中国声学学会
• 学会名称：中国声学学会
• 页数：4
• 文件大小：387k
• 原文格式：D
• 会议级别：全国

摘要

抛物方程(PE)模型广泛应用于求解海洋中的声波传播问题。相较于标准抛物方程和其它广义抛物方程,以Padé级数形式展开的抛物方程(Padé-PE)能在大角度范围内为主传播方向上提供更高精度的值。理论上乘积形式的Padé级数在后续PE求解的FFT计算中更方便和更高效,本文将对乘积形式的Padé级数系数进行理论的推导和计算,以便于后续的抛物方程求解。
The parabolic equation(PE) method is useful for modeling sound propagation in the ocean. Compared to standard PE and some generalized PE of other formations, Padé-PE, which is based on a Padé approximation, can provide accurate solutions for wide-angle PE. Furtherly the rational-linear product approximations for Padé expansion are convenient for after FFT calculation. This article presents a novel method for calculating Padé coefficients for the product approximations from the theoretical foundation of Padé approximation.

引文

[1]Tappert F D.The parabolic approximation method in wave propagation in underwarter acoutics[A].New York:Spring-Velag[C],1977,224-287.
    [2]Davis J A,White D,Cavanagh R C.NORDA parabolic equation workshop[M].Naval Ocean Research and Development Activity,Stennis Space Center,1982.
    [3]Greene R R.The rational approximation to the acoustic wave equation with bottom interaction[J].J.Acoust.Soc.Am,1984,76:1764-1773.
    [4]Bamberger A,Engquist B,Halpern L,Joly P.Higher order parabolic wave approximations in heterogeneous media[J].SIAM J.Appl.Math,1988,48:129-154.
    [5]Collins M D.Applications and time-domain solution of higher-order parabolic equations in underwater acoustics[J].J.Acoust.Soc.Am,1989,86:1097-1102.
    [6]Halpern L,Trefethen L N.Wide-angle one-way wave equations[J].J.Acoust.Soc.Am,1988,84:1397-1404.
    [7]Collins M D.A split-step Padésolution for the parabolic equation method[J].J.Acoust.Soc.Am,1993,93:1736-1742.
    [8]李庆扬,王能超,易大义.数值分析(第5版)[M].北京:清华大学出版社,2008,80-82.Li Qingyang,Wang Nengchao,Yi Dayi.Numerical analysis(5thEdition)[M].Beijing:Tsinghua University Press,2008,80-82.
    [9]Jensen F B,Kuperman W A,M.B.Porter,et al..Computational ocean acoustic.Modern Acoustic and Signal Processing,2011,97:458-465.
    [10]Collins M D,Evans R B.A two-way parabolic equation for acoustic back scattering in the ocean[J].J.Acoust.Soc.Am,1992,91:1357-1368.
    [11]Collins M D.Higher-order Padéapproximations for accurate and stable elastic parabolic equations with application to interface wave propagation[J].J.Acoust,Soc.Am,1991,89:1050-1057.