ON THE CONDITIONING OF NUMERICAL BOUNDARY MEASURES IN WAVELET GALERKIN METHODS

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 doma in having regular geometry. One advantage of the domain embedding meth od is that the boundary conditions on the larger, regular domain can b e enforced in a straightforward manner, and the solution procedure can exploit the highly structured form of the resulting governing equatio ns. The defining characteristic of this method is that the calculation of integrals along the irregular boundary are carried out using recen tly derived numerical boundary measures. In addition, the coercive bil inear forms characterizing the boundary value problem of interest must be calculated when restricted to the actual domain. In the case of wa velet Galerkin formulations, this calculation is accomplished with the three term connection coefficients that characterize the numerical bo undary measure. The numerical stability and accuracy of the domain emb edding procedure is compared to a newly developed wavelet-based finite element formulation.