流体物理学ゼミナール2004/06/01

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_/ 流体力学セミナー 2004 No. 4
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_/ 日 時 : 04年 6月 14日 (月) 15:00〜16:30
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_/ 場 所 : 京大数理研 009号室
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_/ 講 師 : Bernie Shizgal 氏 (Department of Chemistry and
_/ Institute of Applied Mathematics
_/ University of British Columbia, Vancouver, CANADA)
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_/ 題 目 : Spectral Methods and the Resolution of the Gibbs Phenomenon
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_/ 内 容 :
_/ Spectral methods involve the expansion of the solution of some partial
_/ differential equation or integral equation in a set of basis functions.
_/ The usual basis functions chosen are the Fourier functions or Chebyshev
_/ polynomials. Recent work on the use of nonclassical basis functions will
_/ be briefly dicussed. It is well known that the expansion of an analytic
_/ nonperiodic function on a finite interval in a Fourier series leads to
_/ spurious oscillations at the interval boundaries. This result is known
_/ as the Gibbs phenomenon. The present talk describes a new method for the
_/ resolution of the Gibbs phenomenon (Shizgal and Jung, J. Comput. Appl.
_/ Math. 161 (2003) 41) which follows on the reconstruction method of
_/ Gottlieb and coworkers (SIAM Rev. 39 (1997) 644) based on Gegenbauer
_/ polynomials. We refer to their approach as the direct method and to the
_/ new methodology as the inverse method. The direct method requires that
_/ certain conditions are met concerning $¥lambda$ in the weight function
_/ $(1-x^2)^{¥lambda-1/2}$, the number of Fourier coefficients, $N$ and the
_/ number of Gegenbauer polynomials, $m$. We show that the new inverse
_/ method can give exact results for polynomials independent of $¥lambda$
_/ and with $m =3D N$. The paper presents several numerical examples
_/ applied to a single domain or to subdomains of the main domain so as to
_/ illustrate the superiority of the inverse method in comparison with the
_/ direct method.
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世話人:大木谷 耕司(京大数研)、藤 定義(京大理)、松本 剛(京大理)、
山田 道夫(京大数研)
アドバイザー:河原 源太(京大工)、小森 悟(京大工)、藤坂博一(京大情報学)、
船越 満明(京大情報学)、水島 二郎(同志社大工)、余田 成男(京大理)
連絡先:ohkitani@kurims.kyoto-u.ac.jp
メールリスト連絡先: semi-adm@kyoryu.scphys.kyoto-u.ac.jp