DUNE-fem¶

Discontinuous Galerkin methods and adaptive meshes.

Install¶

pip install dune-fem mpi4py

mpi4py is a hidden requirement (no dune-* package declares it) when DUNE was built against MPI, which happens when an MPI library is found while the dune-* packages are built. Without it the first import then stops with:

RuntimeError:
The Dune modules were configured using MPI. For the Python bindings to work,
the Python package 'mpi4py' is required.
Please run
    pip install mpi4py
before rerunning your Dune script.

A DUNE built without MPI imports without mpi4py.

Then check that openPASO sees it:

python check_install.py

What openPASO knows for DUNE-fem¶

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

Physics	Description	Dimensions	Templates
`adaptive_poisson`	h-adaptive Poisson with residual error estimator	2-D	`2d`
`dg_advection`	DG method for pure advection equation (upwind flux)	2-D	`2d`
`dg_advection_diffusion`	Steady advection-diffusion with upwind flux and SIPG diffusion on triangles	2-D	`2d`
`eigenvalue`	Eigenvalue problem -Δu = λu via shift-invert inverse iteration	2-D	`2d`
`heat`	Steady heat conduction (UFL)	2-D	`2d`
`helmholtz`	Helmholtz equation -Δu - k²u = f with MMS verification	2-D	`2d`
`hyperelasticity`	Neo-Hookean finite-strain hyperelasticity with automatic Newton via UFL	2-D	`2d`
`linear_elasticity`	Linear elasticity (UFL vector space)	2-D	`2d`
`maxwell`	Maxwell equations: 2-D TE-mode scalar Helmholtz proxy (-Δu - k²u = f); full H(curl) via NGSolve	2-D	`2d`
`mixed_methods`	Mixed Poisson with Raviart-Thomas RT0 flux and DG-P0 pressure (H(div) x L²)	2-D	`2d`
`navier_stokes`	Incompressible Navier-Stokes via Picard iteration (lid-driven cavity)	2-D	`2d`
`nonlinear`	Nonlinear PDE via Newton method (UFL)	2-D	`2d`
`poisson`	Poisson equation -Δu = f (UFL forms, DUNE backend)	2-D, 3-D	`2d`
`poisson_mms`	3D variable-coefficient Poisson manufactured-solution (MMS) convergence family — -div(kappa grad u) = f on [0,L]^3, affine kappa, exact Dirichlet data, uniform refinement with per-level L2/H1 error lines; theoretical L2 order k+1 / H1 order k	3-D	`3d_varcoeff`
`reaction_diffusion`	Reaction-diffusion (transient)	2-D	`2d`
`registry_survey`	Registry survey: builds every entry this dune-fem install declares across all 8 axes (spaces, schemes, solvers, storages, models, operators, functions, views) and checks each against something independent of the run. Also records the first-use JIT cost, which is 85-200s per new space and 0.1s once cached.	2-D	`default`
`stokes`	Stokes flow, Taylor-Hood P2/P1 on one composite space, one monolithic direct solve (UFL)	2-D	`2d`
`time_dependent_heat`	Transient heat du/dt - alpha*Δu = f via implicit Euler time-stepping	2-D	`2d`