Multi-Resolution Localized Orthogonal Decomposition for Helmholtz Problems

We introduce a novel multi-resolution localized orthogonal decomposition (LOD) for time-harmonic acoustic scattering problems that can be modeled by the Helmholtz equation. The method merges concepts of LOD and operator-adapted wavelets (gamblets) proves its applicability class complex-valued, non-hermitian, indefinite problems. It computes hierarchical bases block-diagonalize operator thereby decouples discretization scales. Sparsity is preserved localization strategy improves stability properties even in elliptic case. present rigorous priori error analysis proposed homogeneous media. In addition, we investigate fast solvability blocks standard iterative method. A sequence numerical experiments illustrates sharpness theoretical findings demonstrates to heterogeneous