A Numerical Method Based on Daubechies Wavelet Basis and B-Spline Patches for Elasticity Problems

Yanan Liu,Keqin Din

doi:10.1155/2016/2549213

Abstract

The Daubechies (DB) wavelets are used for solving 2D plane elasticity problems. In order to improve the accuracy and stability in computation, the DB wavelet scaling functions in0,+∞)comprising boundary scaling functions are chosen as basis functions for approximation. The B-spline patches used in isogeometry analysis method are constructed to describe the problem domain. Through the isoparametric analysis approach, the function approximation and relevant computation based on DB wavelet functions are implemented on B-spline patches. This work makes an attempt to break the limitation that problems only can be discretized on uniform grids in the traditional wavelet numerical method. Numerical examples of 2D elasticity problems illustrate that this kind of analysis method is effective and stable.

Highlights

Wavelet is a powerful mathematical tool in solving many problems in science and engineering
Numerical examples of 2D elasticity problems illustrate that this kind of analysis method is effective and stable
Considering the similarity between wavelet basis functions and B-spline functions in framework, this paper introduces the B-spline patches to problems using wavelet numerical method

Summary

Introduction

Wavelet is a powerful mathematical tool in solving many problems in science and engineering. The isogeometry analysis method [22, 23] developed in recent years presented some new ideas in numerical simulation In this method, the B-spline functions or nonuniform rational B-spline functions are used to describe the problem geometry and the total solution domain can be divided into many B-spline patches which are similar to the elements in finite element method. It is reasonable to introduce the Bspline patches into the problems in which the traditional wavelet basis functions are used This is an attempt to break the limitation that the traditional wavelet-based numerical methods are only restricted on uniform grids. The function approximation based on DB wavelet basis functions and relevant computations are implemented on Bspline patches through the isoparametric analysis approach. Numerical examples for 2D elasticity problems are given to illustrate the effectiveness of the present method

The Function Approximation by DB Wavelet Scaling Function

Numerical Implementation

Numerical Examples

Figure 5

Conclusion