メッシュフリー粒子法における差分公式の打ち切り誤差解析(理論)  [in Japanese] Truncation Error Analysis of Finite Difference Formulae in Meshfree Particle Methods(Theory)  [in Japanese]

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Abstract

MPS法やSPH法などのメッシュフリー粒子法は,煩雑なメッシュ生成が不要で領域形状の変化に柔軟に対応出来るため,近年非常に発展を遂げ,理工学の強力なツールとして確立されて来ている.その一方で,偏微分方程式の離散化手法として見たとき,その精度についての数学的な誤差解析はいくつかの限られた場合に得られているだけである.本論文では,重み関数を用いたメッシュフリー粒子法,特にMPS法において使われる勾配差分演算子の打ち切り誤差について,その数学的評価を試みる.

Meshfree particle methods such as MPS method and SPH method have been much developed in recent years and established as a powerful tool in the fields of science and engineering, since they require no troublesome mesh generation and have flexible adaptation to changing shape of domains. On the other hand, there are few mathematical error analysis on their accuracy as discretization methods for partial differential equations. In this paper, we investigate a mathematical analysis of the truncation error for a discrete gradient operator of meshfree particle methods with weight functions, particularly MPS method.

Journal

  • Transactions of the Japan Society for Industrial and Applied Mathematics

    Transactions of the Japan Society for Industrial and Applied Mathematics 20(3), 165-182, 2010

    The Japan Society for Industrial and Applied Mathematics

References:  15

Codes

  • NII Article ID (NAID)
    110007730733
  • NII NACSIS-CAT ID (NCID)
    AN10367166
  • Text Lang
    JPN
  • Article Type
    ART
  • ISSN
    09172246
  • NDL Article ID
    10853101
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z15-727
  • Data Source
    CJP  NDL  NII-ELS  J-STAGE 
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