Advanced Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Three-Dimensional Local Structural Analysis

This paper is devoted to advanced wavelet-based discrete-continual finite element method of local structural analysis. Structures with regular (in particular, constant or piecewise constant) physical and geometrical parameters along so-called "basic" direction are under consideration. High-accuracy solution of the corresponding problems at all points of the model is not required normally, it is necessary to find only the most accurate solution in some pre-known local domains. Wavelet analysis is a powerful and effective tool for corresponding researches. Initial continual and discrete-continual formulations of multipoint boundary problem of three-dimensional structural analysis are presented. The last formulation is transformed to corresponding localized one by using the discrete Haar wavelet basis and finally, with the use of averaging and reduction algorithms, the localized and reduced governing equations are obtained. Special algorithm of localization with respect to each degree of freedom is presented.