Multiscale methods for solving wave equations on spatial networks
Journal article, 2023

We present and analyze a multiscale method for wave propagation problems, posed on spatial networks. By introducing a coarse scale, using a finite element space interpolated onto the network, we construct a discrete multiscale space using the localized orthogonal decomposition (LOD) methodology. The spatial discretization is then combined with an energy conserving temporal scheme to form the proposed method. Under the assumption of well-prepared initial data, we derive an a priori error bound of optimal order with respect to the space and time discretization. In the analysis, we combine the theory derived for stationary elliptic problems on spatial networks with classical finite element results for hyperbolic problems. Finally, we present numerical experiments that confirm our theoretical findings.

Wave equation

Localized orthogonal decomposition

Network model

Numerical homogenization

Author

Morgan Görtz

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Fraunhofer-Chalmers Centre

Per Ljung

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Axel Målqvist

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Computer Methods in Applied Mechanics and Engineering

0045-7825 (ISSN)

Vol. 410 116008

Subject Categories

Computational Mathematics

Mathematical Analysis

DOI

10.1016/j.cma.2023.116008

More information

Latest update

5/12/2023