A Performance Comparison of Adaptive Operator-Customized Wavelet Basis and Adaptive H-refinement Methods for 2-D Finite Element Analysis

摘要

This paper compares the performance of the popular adaptive H-refinement (HR) technique for the Finite Element Method (FEM) with the Operator-Customized Wavelet Basis (OCWB) FEM in its adaptive version. The latter is somehow an evolution of the HR method with the use of second generation wavelet theory, which allows the solution to be decoupled between iterations, decreasing significantly the total number of degrees of freedom and consequently, the processing time. Conversely, this procedure increases the algorithm complexity, that being the reason why there are such few applications on the subject. Like the HR method, adaptive OCWB can be programmed with various strategies. Since the results are shown in terms of processing time on a regular PC, both algorithms have been developed with similar structures.