A variable order wavelet method for the sparse representation of layer potentials in the non-standard form

Abstract

We discuss a variable order wavelet method for boundary integral formulations of elliptic boundary value problems. The wavelet basis functions are transformations of standard nodal basis functions and have a variable number of vanishing moments. For integral equations of the second kind we will show that the non-standard form can be compressed to contain only O(N) non-vanishing entries while retaining the asymptotic converge of the full Galerkin scheme, where N is the number of degrees of freedom in the discretization.