2026-10-10T08:30:54Zhttps://www.radar-service.eu/oai/OAIHandler10.35097/12702026-10-09T10:59:06Zradar4kit
https://dx.doi.org/10.35097/1270
Maier, Bernhard
Numerical experiments to "Error analysis for space discretizations of quasilinear wave-type equations"
Karlsruhe Institute of Technology
2023
Mathematics
dataset
Dataset
info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
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.
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/ .
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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".
Westervelt equation
quasilinear wave equation
isoparametric finite elements
leapfrog
implicit midpoint rule
10.5445/IR/1000128712
KITopen-DOI
application/x-tar