A new error estimation approach based on fuzzy logic system for H-R adaptive boundary element method

• Published in: Applied mathematics and computation Vol. 218; no. 5; pp. 2167 - 2177
• Main Authors: Chen, Yiming, Zhou, Zhiquan, Zhang, Jing, Li, Yulian, Wang, Xiaojuan
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.11.2011
• Subjects: Adaptive mesh refinement; Adaptive systems; Boundary element method; Elasticity problems; Error analysis; Error estimation; Errors; Fuzzy logic; Fuzzy logic system; H-R adaptive boundary element; Human; Mathematical analysis; Mathematical models; H-R adaptive boundary element; Adaptive mesh refinement; Elasticity problems; Error estimation; Fuzzy logic system
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2011.07.033

Conventional adaptive boundary element method cannot be universally applied to solve many more problems than the subject it discussed, and different error estimation formulas need to be designed for varied problems. This paper put forward a new error analysis method based on the fuzzy logic system, which is able to make error estimation effectively using human expert experience, and solve the two classical elasticity problems in conjunction with the H-R adaptive boundary element method. Numerical examples have illustrated the effectiveness, superiority and potential of a fuzzy logic approach in the adaptive boundary element method.