NGSTrefftz Notebooks

We present the implementation of Trefftz discontinuous Galerkin (DG) methods.

Trefftz-DG methods

1. Notebook introduces the Trefftz space in NGSolve alongside a Trefftz-DG method using harmonic polynomials to solve the Laplace problem.

2. Notebook presents plane waves for the Helmholtz equation.

3. Notebook presents the space-time DG Trefftz method for the acoustic wave equation on meshes Cartesian in time.

4. Notebook presents the Trefftz method on unfitted geometries using ngsxfem.

Advanced Trefftz methods for the acoustic wave equation

5. Notebook presents quasi-Trefftz functions that are used for the wave equation with piecewise-smooth wavespeed.

6. Notebook shows how to use the Trefftz and quasi-Trefftz methods with tent-pitched meshes.

Embedded Trefftz methods

7. Notebook presents the embedded Trefftz method

8. Notebook for inhomogeneous problems

9. Notebook for the Helmholtz problem

10. Notebook for the acoustic wave equation

11. Notebook for advection

12. Notebook for the Stokes problem