2021/04/22 by Moritz Hauck, Daniel Peterseim, Hauck, Moritz +1 · 5 citations
Earth and Planetary Sciences · Engineering · #35J05 #65N12 #65N15 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Seismic Imaging and Inversion Techniques #Ultrasonics and Acoustic Wave Propagation
paper · pdf · doi:10.48550/arxiv.2104.11190
openalex publication_date 2021/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 the concepts of LOD and operator-adapted wavelets (gamblets) and proves its applicability for a class of complex-valued, non-hermitian and indefinite problems. It computes hierarchical bases that block-diagonalize the Helmholtz operator and thereby decouples the discretization scales. Sparsity is preserved by a novel localization strategy that improves stability properties even in the elliptic case. We present a rigorous stability and a-priori error analysis of the proposed method for homogeneous media. In addition, we investigate the fast solvability of the blocks by a standard iterative method. A sequence of numerical experiments illustrates the sharpness of the theoretical findings and demonstrates the applicability to scattering problems in heterogeneous media.