An adaptive cross approximation (ACA) for the extended boundary element method (XBEM) in anisotropic materials

Kettle, S.; Hattori, G.; Campos, L.; Trevelyan, J.; Albuquerque, E.L.

Abstract

The extended boundary element method (XBEM) is a modification from the standard BEM, where enrichment functions are embedded into the BEM formulation. The results obtained with this method were seen to be accurate and stable, being especially useful for fracture problems. However, the method suffers from the presence of a linear system containing unsymmetric and fully populated matrices which needs to be solved in order to get the solution of the boundary problem. This can be computationally expensive for problems dealing with multiple cracks for instance. Adaptive cross approximation (ACA) is used to reduce the number of operations necessary to solve the linear system of equations for a fracture problem with an anisotropic material.

Citation

Kettle, S., Hattori, G., Campos, L., Trevelyan, J., & Albuquerque, E. (2023, March). An adaptive cross approximation (ACA) for the extended boundary element method (XBEM) in anisotropic materials. Presented at 24th UK Conference of the Association for Computational Mechanics in Engineering, Cardiff, UK

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 24th UK Conference of the Association for Computational Mechanics in Engineering
• Start Date: Mar 31, 2023
• End Date: Apr 1, 2016
• Acceptance Date: Feb 15, 2016
• Publication Date: Apr 1, 2016
• Deposit Date: Apr 6, 2016
• Publicly Available Date: Apr 7, 2016
• Publisher: Cardiff University
• Pages: 218-221
• Book Title: Proceedings of the 24th UK Conference of the Association for Computational Mechanics in Engineering, 31 March - 01 April 2016, Cardiff University, Cardiff.
• Public URL: https://durham-repository.worktribe.com/output/1150989
• Publisher URL: http://acme2016.sciencesconf.org/85224