Wavelets in the solution of the volume integral equation: Application to eddy current modeling
| Autor: | John P. Basart, Bing Wang, John C. Moulder |
|---|---|
| Rok vydání: | 1997 |
| Předmět: | |
| Zdroj: | Journal of Applied Physics. 81:6397-6406 |
| ISSN: | 1089-7550 0021-8979 |
| Popis: | There is growing interest in the applications of wavelets as basis functions in solutions of integral equations, especially in the area of electromagnetic field problems. In this article we apply a wavelet expansion to the solution of the three-dimensional eddy current modeling problem based on the volume integral method. Although this method shows promise for eddy current modeling of three-dimensional flaws, it is restricted by the computing power required to solve a large linear system. In this article we show that applying a wavelet basis to the volume integral method can dramatically reduce the size of the linear system to be solved. In our approach, the unknown total field is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function that is often referred to as the mother wavelet. The wavelet expansion can adaptively fit itself to the total field distribution by distributing the localized functions near the flaw boundary, where the field change is large, and the more spatially diffused functions over the interior of the flaw where the total field tends to be smooth. The approach is thus best suited to modeling large three-dimensional flaws where the large number of elements used in the volume integral method requires extremely large memory space and computational capacity. The feasibility of the wavelet method is discussed in the context of the physical nature of eddy-current modeling problems. Numerical examples using both Haar wavelets and Daubechies compactly supported wavelets with periodic extension are given. The results of the wavelet method are also compared with experimental results from a cylindrical flat-bottom hole in an aluminum plate. These numerical examples and comparisons indicate that the wavelet method can greatly reduce the numerical complexity of the problem with negligible loss in accuracy. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|