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An HR‐method of mesh refinement for boundary element method
Author(s) -
Ammons Bruce A.,
Vable Madhukar
Publication year - 1998
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19981130)43:6<979::aid-nme451>3.0.co;2-j
Subject(s) - boundary element method , boundary knot method , singular boundary method , mathematics , finite element method , quadratic equation , norm (philosophy) , mathematical optimization , algorithm , computer science , mathematical analysis , geometry , structural engineering , engineering , political science , law
This paper describes a mesh refinement technique for boundary element method in which the number of elements, the size of elements and the element end location are determined iteratively in order to obtain a user specified accuracy. The method uses L 1 norm as a measure of error in the density function and a grading function that ensures that error over each element is the same. The use of grading function along with L 1 norm makes the mesh refinement technique applicable to Direct and Indirect boundary element method formulation for a variety of boundary element method applications. Numerical problems in elastostatics, fracture mechanics, and bending of plate solved using Direct and Indirect method in which the density functions are approximated by Linear Lagrange, Quadratic Lagrange or Cubic Hermite polynomials validate the effectiveness of the proposed mesh refinement technique. © 1998 John Wiley & Sons, Ltd.