A new method for numerical evaluation of nearly singular integrals over high-order geometry elements in 3D BEM

• Yaoming Zhang ^[1] ; Xiaochao Li ^[2] ; Vladimir Sladek ^[3] ; Jan Sladek ^[3] ; Xiaowei Gao ^[4]
  1. [1] Shandong University of Technology

     Shandong University of Technology

     China

     
  2. [2] Beijing Institute of Technology

     Beijing Institute of Technology

     China

     
  3. [3] Slovak Academy of Sciences

     Slovak Academy of Sciences

     Eslovaquia

     
  4. [4] Dalian University of Technology

     Dalian University of Technology

     China

     

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• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 277, Nº 1 (15 March 2015), 2015, págs. 57-72
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • This work presents a new method for numerical computation of the two-dimensional nearly singular integrals by using the eight-node second-order quadrilateral surface elements in 3D BEM. A new indirect regularized boundary element formulation excluding the CPV (Cauchy Principal Value) and HFP (Hadamard-Finite-Part) integrals is proposed. Based on this, a new approximation formula of the distance from the fixed calculation point to a generic point of the aforementioned surface geometry elements is developed firstly, and then the exponential transformation, which has been widely employed in 2D BEM, is extended to 3D BEM to remove the near singularities of integrands for considered integrals.

    Several numerical examples are given to verify the high efficiency and the stability of the proposed scheme.