Space discretization and time integration methods for quasilinear wave equations

The following codes contain implementations of different time integration methods for spatially discretized quasilinear acoustic wave equations. For the space discretization continuous finite elements are used. The first code is about the discretization of the Westervelt equation with (fully/linearly) implicit midpoint rule and a modified leapfrog scheme for the time integration.

Information can be found in

• the paper Error analysis for space discretizations of quasilinear wave-type equations by Marlis Hochbruck and Bernhard Maier.
• the paper Error analysis for full discretizations of quasilinear wave-type equations with two variants of the implicit midpoint rule by Bernhard Maier.
• in the doctoral thesis Error analysis for space and time discretizations of quasilinear wave-type equations by Bernhard Maier.

The second code contains the implementation of exponential integrators for a quasilinearity of Kerr-type, see the paper Exponential integrators for quasilinear wave-type equations by Benajmin Dörich and Marlis Hochbruck or the doctoral thesis Error analysis of exponential integrators for nonlinear wave-type equations by Benajmin Dörich for further information.

Access to software

The codes for the Westervelt equation used in Error analysis for space discretizations of quasilinear wave-type equations can be downloaded here https://doi.org/10.5445/IR/1000128712.

The codes for the exponential integrators used in the paper Exponential integrators for quasilinear wave-type equations can be accessed here https://doi.org/10.5445/IR/1000143383 (Python3 with FEniCS version 2018.1.0).

Details about the programming language and requirements can be found in the corresponding Readme files.