Algebraic Multilevel Preconditioning for Helmholtz Equation

We propose efficient algebraic multilevel preconditioning for the Helmholtz equation with high wave numbers. Our method is mainly based on using new multilevel ILU techniques for symmetric indefinite systems. The method is mainly based on three major ingredients: 1. symmetric maximum weight matchings to increase the block di- agonal dominance of the system, 2. inverse-based pivoting to drive the coarsening process and finally 3. filtering techniques to handle frequencies near zero eigenvalues. We will illustrate the resulting multilevel method of this approach for selected numerical examples