FEniCSx (dolfinx)

Fast prototyping: you write the equation almost as on paper. Strong for fluid flow.

Install

conda create -n fenics -c conda-forge fenics-dolfinx

FEniCSx needs its own conda environment, not openPASO's .venv. openPASO finds environments whose name contains fenics or dolfinx by itself; otherwise set FENICS_PYTHON. Real and complex numbers are separate environments.

Then check that openPASO sees it:

python check_install.py

What openPASO knows for FEniCSx (dolfinx)

25 kinds of problem. Ask for any of them in plain words; the names below are what the model uses internally.

Physics	Description	Dimensions	Templates
biharmonic	Biharmonic equation (4th order) via interior penalty DG	2-D	2d
cahn_hilliard	Cahn-Hilliard phase separation: mixed (phi, mu) formulation, double-well potential	2-D	2d
contact	Contact / obstacle problem via smooth penalty method (Newton iteration)	2-D	2d
convection_diffusion	Convection-diffusion (SUPG stabilized)	2-D	2d
dg_methods	Discontinuous Galerkin for advection-dominated diffusion (upwind flux, interior penalty)	2-D	2d
eigenvalue	Eigenvalue problems (Laplace) via SLEPc	2-D	2d
fracture	Phase-field fracture mechanics. Coupled displacement / damage formulation with a diffuse crack representation (no remeshing). Extensions: PhaseFieldX library.	2-D, 3-D	2d
heat	Heat conduction (steady / transient)	2-D, 3-D	2d_steady, 2d_transient, rectangle
helmholtz	Helmholtz equation: -laplacian(u) - k^2*u = f. Acoustic / optical wave propagation. Indefinite system — GMRES or direct, NOT CG. May be complex-valued; needs PETSc compiled with --with-scalar-type=complex.	2-D, 3-D	2d
hyperelasticity	Nonlinear hyperelasticity (Neo-Hookean, large deformation)	3-D	3d
linear_elasticity	Linear elasticity (small strain)	2-D, 3-D	2d, 3d, plate_hole, thick_beam
magnetostatics	Magnetostatics: 2D scalar Az curl-curl formulation, spatially varying permeability	2-D	2d
matrix_free_poisson	Matrix-free conjugate-gradient Poisson solver. Builds A as a callable action_A(x, y) via ufl.action(a, ui) — no global sparse assembly. Mirrors dolfinx demo_poisson_matrix_free.py.	2-D	2d
maxwell	Maxwell's equations (curl-curl). Requires H(curl) (Nedelec / N1curl, basix.ElementFamily.N1E) elements for tangential continuity. Complex-valued forms need a complex-PETSc build.	2-D, 3-D	2d
mixed_poisson	Mixed Poisson / Darcy flow (Raviart-Thomas + DG pressure)	2-D	2d
multiphase	Two-phase flow via Allen-Cahn phase-field (interface tracking, transient)	2-D	2d
navier_stokes	Incompressible Navier-Stokes (cavity, channel with obstacle)	2-D, 3-D	2d, 3d, channel_cylinder
nearly_incompressible_elasticity	Nearly-incompressible elasticity (Poisson ratio approaching 0.5). Standard primal P1/P2 locks; needs mixed (u, p) Taylor-Hood / MINI or a displacement-pressure split with stable element pair (otherwise volumetric locking).	2-D, 3-D	2d
nonlinear_pde	General nonlinear PDE with Newton solver and UFL automatic differentiation	2-D	2d
poisson	Poisson equation / diffusion	2-D, 3-D	2d, 3d, l_domain, rectangle
reaction_diffusion	Two-species reaction-diffusion system (coupled, transient)	2-D	2d
stokes	Stokes flow with Taylor-Hood P2/P1 (lid-driven cavity)	2-D	2d
stokes_darcy	Coupled Stokes-Darcy for free fluid / porous medium interaction. Beavers-Joseph-Saffman interface conditions.	2-D, 3-D	2d
thermal_structural	Coupled thermal-structural (heat -> thermal expansion)	2-D	2d
time_dependent_heat	Transient heat equation with backward Euler, Robin convective BC, volumetric sources	2-D	2d