The use of wavelet-like basis functions in the finite element analysis of heterogeneous one dimensional regions

The paper presents the use of wavelet-like basis functions in the finite element analysis of heterogeneous one dimensional regions. The construction of the wavelet-like basis functions (a multiresolution analysis procedure) for these type regions is discussed. The condition numbers of the resulting matrices, along with the number of steps required for convergence of the conjugate gradient solution are presented. For comparison, results obtained from a finite element algorithm employing traditional basis functions are presented.