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Numerical experiments to "Error analysis for space discretizations of quasilinear wave-type equations"

Maier, Bernhard

Abstract:
This code was used for the numerical experiments in the preprint (CRC Preprint 2021/2; URL: https://www.waves.kit.edu/downloads/CRC1173_Preprint_2021-2.pdf) and in the paper "Error analysis for space discretizations of quasilinear wave-type equations" by M. Hochbruck and B. Maier.

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Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsdaten
Publikationsdatum 25.01.2021
Erstellungsdatum 18.01.2021 - 18.01.2021
Identifikator DOI (KIT): 10.5445/IR/1000128712
KITopen-ID: 1000128712
Lizenz Creative Commons Namensnennung – Nicht kommerziell – Weitergabe unter gleichen Bedingungen 4.0 International
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Abstract/Volltext
Schlagwörter Westervelt equation, quasilinear wave equation, isoparametric finite elements, leapfrog, implicit midpoint rule
Liesmich

This program is intended to reproduce the results from the paper

"Error analysis for space discretizations of quasilinear wave-type equations"

It is an implementation of the full discretization of quasilinear wave equations, e.g., the Westervelt equation, following the method of lines.For the discretization in space, we apply a continuous Galerkin approach withisoparametric finite elements. For the subsequent discretization in time, two
variants of the implicit midpoint rule as well as the leapfrog scheme areimplemented.

The code is based on the open source finite element library MFEM (version 4.2). Further information can be found at https://mfem.org/ .


To use this code, MFEM (release 4.2) has to be installed supporting MPI, using Open MPI (release 4.1), Hypre (release 2.16.0), and Metis (release 5.1.0), cf. https://mfem.org/building/ .

In order to run the program, change the makefile such that MFEM_DIR and MFEM_BUILD_DIR point to the source and build directory of MFEM on your system. Then, open a terminal session, go to the directory of the makefile and call "make".

To reproduce the results shown in the paper, run the file "driver" to compute the results. These are then written to the file "res/results.txt" and can be displayed in a simple plot with the Matlab script "res/plot_results.m".

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