Hierarchical solution procedure of combined finite element-wavelets methods

Abstract

A hierarchical solution procedure of finite element methods using the multi-resolution property of wavelets is proposed. The characteristics of the proposed procedure is that (1) an approximation with a coarse mesh is determined firstly, and (2) then the approximation is refined hierarchically without any requirement for remeshing. Therefore, the proposed method seems more attractive for problems involving greedy gradients in only a small sub-region such as thin skin effect study of iron materials in high frequency fields. Numerical example is designed to demonstrate the hierarchical nature of the proposed method.