Back to Search Start Over

SUPER-LOCALIZED ORTHOGONAL DECOMPOSITION FOR HIGH-FREQUENCY HELMHOLTZ PROBLEMS.

SUPER-LOCALIZED ORTHOGONAL DECOMPOSITION FOR HIGH-FREQUENCY HELMHOLTZ PROBLEMS.

Authors :
FREESE, PHILIP
HAUCK, MORITZ
PETERSEIM, DANIEL
Source :
SIAM Journal on Scientific Computing. 2024, Vol. 46 Issue 4, pA2377-A2397. 21p.
Publication Year :
2024

Abstract

We propose a novel variant of the Localized Orthogonal Decomposition (LOD) method for addressing time-harmonic scattering problems of Helmholtz type with high wavenumber k. This method operates on a coarse mesh of width HH and identifies local finite element source terms that produce rapidly decaying responses under the solution operator. These source terms can be constructed with high accuracy from independent local snapshot solutions on patches of width ℓH, and they are used as problem-adapted basis functions. Compared to classical LOD and other state-of-the-art multiscale methods, our approach demonstrates that the localization error decays super-exponentially as the oversampling parameter ℓ increases. This indicates that optimal convergence is achieved under a substantially relaxed oversampling condition of ℓ≳(log⁡κ/H)(d−1)/d, where d represents the spatial dimension. Numerical experiments highlight the significant improvements in both offline and online performance of the method, even in the presence of heterogeneous media and perfectly matched layers. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10648275
Volume :
46
Issue :
4
Database :
Academic Search Index
Journal :
SIAM Journal on Scientific Computing
Publication Type :
Academic Journal
Accession number :
179540878
Full Text :
https://doi.org/10.1137/21M1465950