Multiscale Algorithm for the Numerical Inversion of Elliptic Operators
Saiida Lazaar · 2013
This work develops an efficient and fast algorithm to invert elliptic operators associated to Lipschitz coefficients. The method is based on multiresolution analysis and uses localization properties of wavelets. The numerical inverse of the operator is defined through the coupling between a Galerkin approximation and a preconditioner based on wavelets. The inverse uses a standard residual correction method that may be applied to solve some partial differential equations. According to the algorithm the time derivation operators is approximated by a finite difference scheme. The work presents numerical simulations and provides comparisons with a standard Galerkin method. The results are quite reasonable when compared to the exact solution. Numerical examples show that the proposed method is efficient.