Adaptive Wavelet Galerkin Solution of Some Elastostatics Problems on Irregularly Spaced Nodes

In this paper the second generation wavelets are applied as a basis in finite element method. The wavelet basis is constructed over typical nonequispaced nodes and on boundaries. In addition the wavelet bases are tailored to the Poisson's operator. The wavelet basis is lifted to enforce operator orthogonality, this eliminates coupling between coarse and detail parts of the stiffness matrix. The scale decoupled stiffness matrix permits optimal O(N) computation. The Lagrangian second order wavelets are chosen for demonstration purposes, and a Poisson equation is solved. The potential application of this method in simulating a heterogenous material is outlined.