Wave equation with dynamic boundary conditions
The following codes contain implementations of wave equation with dynamic boundary conditions, written in the project A2. Space discretization is done with isoparametric finite elements. For semilinear problems (with kinetic boundary conditions) an IMEX scheme and exponential integrators are considered for the time integration.
More information can be found in
- the paper An implicit-explicit time discretization scheme for second-order semilinear wave equations with application to dynamic boundary conditions by Marlis Hochbruck and Jan Leibold.
- the paper Full discretization error analysis of exponential integrators for semilinear wave equations by Benjamin Dörich and Jan Leibold.
Further, nonlinear problems with kinetic and acoustic boundary conditions are implemented. Details can be found in
- the paper A unified error analysis for nonlinear wave-type equations with application to acoustic boundary conditions by Jan Leibold.
- in the doctoral thesis A unified error analysis for the numerical solution of nonlinear wave-type equations with application to kinetic boundary conditions by Jan Leibold.
Access to software
All codes are written in C++ with the finite element library deal.II. Further details of the implementation can be found in the corresponding README files.
- The codes used in the paper An implicit-explicit time discretization scheme for second-order semilinear wave equations with application to dynamic boundary conditions can be accessed here https://doi.org/10.5445/IR/1000127003.
- The codes used in the paper Full discretization error analysis of exponential integrators for semilinear wave equations can be accessed here https://doi.org/10.5445/IR/1000141073.
- The codes used in the paper A unified error analysis for nonlinear wave-type equations with application to acoustic boundary conditions can be accessed here https://doi.org/10.5445/IR/1000150159.
- The codes used in the thesis A unified error analysis for the numerical solution of nonlinear wave-type equations with application to kinetic boundary conditions can be accessed here https://doi.org/10.5445/IR/1000130223.