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Numerical methods for wave-type equations
1. Mathematical modeling of wave phenomena
1.1. Acoustic waves
1.2. Elastic waves
1.3. Electromagnetic waves
1.4. Time-harmonic waves
2. Basic numerical methods for time-domain waves
2.2. Space-time methods vs. the method of lines
2.3. A basic FE method for the acoustic wave equation
2.4. Exercises
3. Basic numerical methods for frequency domain wave problems
3.1. FEM for scattering problems
3.2. FEM for resonance problems
3.3. Exercises for time-harmonic waves
4. Time-integration
4.1. Time-integration for the second order systems
4.2. Mixed formulations for wave equations
4.3. Time-integration for the first order system
4.4. Exercises for time-stepping schemes
5. Explicit methods for time-domain waves
5.1. Discontinuous Galerkin methods for the wave equation
5.2. DG Operators in NGSolve
5.3. Mass lumping for the wave equation
5.4. Integration rules in NGSolve
5.5. Exercises for explicit methods
6. Perfectly Matched Layers
6.1. Perfectly Matched Layers in the Frequency Domain
6.2. Perfectly matched layers in NGSolve
6.3. Perfectly Matched Layers in the time domain
6.4. Cartesian time-domain PMLs in ngsolve
6.5. Exercises for perfectly matched layers
7. Eigenvalue Problems
7.1. Eigenvalue solvers in NGSolve
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Index
