Class of wavelet-based finite element methods for computational mechanics

This paper develops a class of finite elements for compactly supported, shift-invariant functions that satisfy a dyadic refinement equation. Commonly referred to as wavelets, these basis functions have been shown to be remarkably well-suited for operator compression, but somewhat difficult to employ for the representation of arbitrary boundary conditions. The current paper extends recent results for treating periodized partial differential equations on unbounded domains in Rn, and enables the solution of Neumann and Dirichlet variational boundary value problems on a class of bounded domains. Wavelet-based finite elements are constructed from the solution of an algebraic eigenvalue problem derived from the dyadic refinement equation characterizing the wavelet, and from normalization conditions arising from moment equations satisfied by the wavelet. The resulting finite elements can be viewed as generalizations of the connection coefficients employed in the wavelet expansion of periodic differential operators.

Class of wavelet-based finite element methods for computational mechanics Conference Paper