MaxwellTrixi.jl

MaxwellTrixi implements three-dimensional Maxwell equations in Trixi.jl. The unknowns are the electric and magnetic fields. Optional state components carry material parameters, polarization currents and PML auxiliary fields.

The implementation follows Trixi's equations × mesh × solver structure. Trixi provides the DG operators, time integration interface, CFL control and adaptive mesh refinement. MaxwellTrixi adds electromagnetic fluxes, material models, excitation, boundary conditions, mesh import and diagnostics.

Reading the implementation

Topic	Mathematical role	Implementation
Equations and materials	Curl equations and constitutive models	`src/equations/`
DG discretization	Volume derivatives, interface fluxes, source projection	`src/solvers/`, `src/sources/projected.jl`
Sources and boundaries	Incident fields, TF/SF, conductors and PML	`src/sources/`, `src/equations/maxwell_3d.jl`
Meshes and output	Geometry maps, material groups, interpolation and VTK	`src/meshes/`, `src/visualization/`
Diagnostics and validation	Divergence, energy, Fourier transforms and references	`src/callbacks_step/`, `src/analytic/`, `test/`
Figures and videos	Field slices, probe comparisons and adaptive meshes	`utils/visualize/`, `utils/paraview/`

Running an example

Use Julia 1.13 or newer and Trixi.jl main. From the repository root:

julia --project=examples -e 'using Pkg; Pkg.instantiate()'
julia --project=examples

Then run an elixir:

using Trixi, MaxwellTrixi, OrdinaryDiffEqLowStorageRK
trixi_include(pkgdir(MaxwellTrixi, "examples", "dgmulti_3d",
                     "elixir_maxwell_3d_cavity.jl"))

Elixirs combine a mesh, equations, initial and boundary conditions, a DG solver, a semidiscretization and callbacks. Assignments such as polydeg or tspan can be overridden through trixi_include. Imported meshes are downloaded on first use; Gmsh meshes also require using Gmsh.

A useful presentation order is the cavity, Fresnel interface, TF/SF box, dipole, PML comparison and scattering examples, followed by the adaptive P4est mesh. The figures and videos show what each example measures.