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.

Quasi-Trefftz methods

  1. Notebook presents the quasi-Trefftz DG method for the diffusion-advection-reaction equation with piecewise-smooth coefficients and right-hand side.

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

Embedded Trefftz methods

  1. Notebook presents the embedded Trefftz method

  2. Notebook for inhomogeneous problems

  3. Notebook for the Helmholtz problem

  4. Notebook for the acoustic wave equation

  5. Notebook for advection

  6. Notebook for the Stokes problem

Trefftz methods and …

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

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