Treatment of singularities in time-dependent problems using the boundary element method

✍ Scribed by D. Lesnic; L. Elliott; D.B. Ingham

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 545 KB
• Volume: 16
• Category: Article
• ISSN: 0955-7997
• DOI: 10.1016/0955-7997(95)00065-8

✦ Synopsis

Singularities which occur in the solution of a partial differential equation due to sharp corners in the boundary tend to produce inaccuracies near the singularity, which sometimes may also propagate into the solution domain, for any standard method of obtaining this solution. In this paper it is shown how this difficulty can be overcome in the case of the solution of the unsteady diffusion equation in both one and two dimensions by a time marching boundary element method (BEM) which takes account of the analytical form of the singularity. For typical examples, comparisons between the numerical results and the analytical solutions show that a significantly better accuracy in the vicinity of the singularity is achieved by the BEM based on the removal of the singularity than by the basic BEM which ignores the singularity.