On the conditioning of numerical boundary measures in wavelet Galerkin methods

✍ Scribed by Ko, Jeonghwan ;Kurdila, Andrew J. ;Wells, Raymond O. ;Zhou, Xiaodong

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 795 KB
• Volume: 12
• Category: Article
• ISSN: 1069-8299
• DOI: 10.1002/(sici)1099-0887(199605)12:5<281::aid-cnm966>3.0.co;2-n

✦ Synopsis

The paper investigates the accuracy and numerical stability of a class of wavelet Galerkin formulations on irregular domains. The method of numerical boundary measures is based upon a domain embedding strategy in which the irregular domain of interest is embedded in a larger domain having regular geometry. One advantage of the domain embedding method is that the boundary conditions on the larger, regular domain can be enforced in a straightforward manner, and the solution procedure can exploit the highly structured form of the resulting governing equations. The defining characteristic of this method is that the calculation of integrals along the irregular boundary are carried out using recently derived numerical boundary measures. In addition, the coercive bilinear forms characterizing the boundary value problem of interest must be calculated when restricted to the actual domain. In the case of wavelet Galerkin formulations, this calculation is accomplished with the three term connection coefficients that characterize the numerical boundary measure. The numerical stability and accuracy of the domain embedding procedure is compared to a newly developed wavelet-based finite element formulation.