H-R Fuzzy Logic Error Estimates And Fuzzy H-Adaptive Boundary Element Methods

Adaptive boundary element method is based on the traditional boundary elementmethod. It is combined with error estimation and adaptive mesh improvement techniques.And it uses computer to automatically determine and improve the accuracy of theboundary element solution. Practical engineering often encountered in a large number offuzzy uncertainty. With the emergence and development of fuzzy mathematics, itgradually formes a study of the trend uncertainty, and it is developed fuzzy adaptiveboundary element method.Fuzzy adaptive fuzzy boundary element method is combined with the high efficiencyand high reliability of fuzzy mathematics and the high automation of traditional adaptiveboundary element method. It can play an important role in solving problems with fuzzyuncertainty in the actual project, such as nonlinear problems.This paper shows fuzzy adaptive boundary element method which is based on fuzzytheory, and shows a new adaptive error estimation scheme for H-R boundary elementmethod. And it verifies the validity of these schemes.Firstly, the first two chapters of this paper describe the basic theoretical knowledgeneeded in later chapters. It compositely descripts the boundary element method, adaptiveboundary element method and fuzzy theory.Secondly, the paper presents a new error estimation method which is based H-Radaptive boundary element method, And it perpetrates the corresponding H-R adaptiveboundary element program based on the error estimation formula.Then it studies the H-fuzzy adaptive boundary element which is based on the theoryof the structure element, and proposes the method of solving the system equation based onfuzzy theory. It decrypts the data structure of the method is in detail. This method issimpler than the traditional method, and it has simpler structure and faster computingspeed. In addition, during the adaptive iteration, it uses the E-mode fuzzy numbers andE-distance marking the error.Finally, this paper uses H-R boundary element method and fuzzy error estimationmethod to calculate some specific elasticity models and fuzzy heat problem in squareclosed domain. At the same time, we discuss the results and make sure that the adaptiveboundary element method based on posteriori error estimates are completely feasible, which well validates the efficiency and superiority of them and their extensive applicationvalue in practical engineering.