_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/
_/
_/ 流体力学セミナー ２００４ No. ４
_/
_/ 日 時 : ０４年 ６月 １４日 (月) １５：００〜１６：３０
_/
_/ 場 所 : 京大数理研 ００９号室
_/
_/ 講 師 : Bernie Shizgal 氏 （Department of Chemistry and
_/ Institute of Applied Mathematics
_/ University of British Columbia, Vancouver, CANADA）
_/
_/ 題 目 : Spectral Methods and the Resolution of the Gibbs Phenomenon
_/
_/ 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.
_/
_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/
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