Open AccessFast non-iterative methods for defect identification
Author(s) -
Marc Bonnet,
Bojan B. Guzina,
Nicolas Nemitz
Publication year - 2008
Publication title -
european journal of computational mechanics
Language(s) - English
Resource type - Journals
eISSN - 2642-2085
pISSN - 2642-2050
DOI - 10.13052/remn.17.571-582
Subject(s) - computation , identification (biology) , finite element method , multipole expansion , acceleration , topology (electrical circuits) , sensitivity (control systems) , numerical analysis , mathematics , computer science , algorithm , mathematical analysis , structural engineering , physics , engineering , electronic engineering , classical mechanics , botany , quantum mechanics , combinatorics , biology
This communication summarizes recent investigations on the identification of defects (cavities, inclusions) of unknown geometry and topology by means of the concept of topological sensitivity. This approach leads to the fast computation (equivalent to performing a few direct solutions), by means of ordinary numerical solution methods such as the BEM (used here), the FEM or the FDM, of defect indicator functions. Substantial further acceleration is obtained by using fast multipole accelerated BEMs. Possibilities afforded by this approach are demonstrated on numerical examples. The paper concludes with a discussion of further research on theoretical and numerical issues.