Carina.jl is a finite element framework for coupling and multiphysics simulations, primarily in solid mechanics and heat conduction. As the spiritual successor to Norma.jl, Carina introduces GPU acceleration via KernelAbstractions.jl, targeting CPUs, NVIDIA GPUs, and AMD GPUs from a single code base.
A free 1 m × 50 mm × 50 mm neo-Hookean elastic bar is given an initial angular velocity field that launches torsion waves from every cross-section simultaneously. The waves superimpose, and the bar cycles through two complete twist-and-return sequences before the animation loops.
| Displacement magnitude | Velocity magnitude |
|---|---|
 |
 |
Neo-Hookean solid (E = 1 GPa, ν = 0.25, ρ = 1000 kg/m³). 160,000 hexahedral elements (~177,000 nodes). Explicit central difference, Δt = 500 ns, ~14,000 steps, 5.95 ms simulated. Wall time: 227 s on an AMD Radeon RX 7600 (ROCm). Left: displacement magnitude [0, 71 mm]. Right: velocity magnitude [0, 141 m/s]. Rainbow Uniform colormap; geometry warped by actual displacements.
A free unit neo-Hookean sphere is given an initial angular velocity field that twists the top and bottom hemispheres in opposite directions, launching torsional waves into the interior. The sphere undergoes large torsional deformation as wave energy accumulates, reaching peak displacements of ~2.1 m before the restoring force reverses the motion.
| Displacement magnitude | Velocity magnitude |
|---|---|
 |
 |
Neo-Hookean solid (E = 10 kPa, ν = 0.33, ρ = 1000 kg/m³). 864 hexahedral elements (997 nodes). Implicit Newmark-β (β = 0.49, γ = 0.9) with CG + Jacobi preconditioner, Δt = 10 ms, 400 steps, 4.0 s simulated. Left: displacement magnitude [0, 0.8 m]. Right: velocity magnitude [0, 4.5 m/s]. Rainbow Uniform colormap; geometry warped by actual displacements.
A 1 m linear elastic beam (1 mm × 1 mm cross section) clamped at both ends is given a Gaussian displacement pulse centered at the midpoint. The pulse splits into two counter-propagating waves that reflect off the clamped boundaries and return to form the mirror image of the initial condition at t = T = L/c = 1 ms. The computed solution (red) is overlaid on the closed-form analytical solution (black).
Linear elastic (E = 1 GPa, ν = 0, ρ = 1000 kg/m³); wave speed c = 1000 m/s. 1000 hexahedral elements (4004 nodes). Explicit central difference, Δt = 100 ns, 10,000 steps, 1 ms simulated. Top: z-displacement. Middle: z-velocity. Bottom: z-acceleration. Analytical solution: Mota, Tezaur & Phlipot, IJNME 123:5036–5071, 2022, eq. 28.
- GPU-accelerated kernels via
KernelAbstractions.jl— runs on CPU, NVIDIA, and AMD GPUs - Finite element framework powered by ReferenceFiniteElements.jl and FiniteElementContainers.jl
- Material models via ConstitutiveModels.jl (neo-Hookean, linear elastic, …)
- Time integrators: quasi-static Newton, implicit Newmark-β / HHT-α, explicit central difference, L-BFGS
- Exodus I/O: mesh input and field output compatible with ParaView
- YAML-driven problem setup — no recompilation needed
- Designed for extensibility toward coupling and multiphysics
Carina depends on
ConstitutiveModels.jl,
FiniteElementContainers.jl, and
ReferenceFiniteElements.jl,
tracking their main branches via relative paths in Project.toml.
Clone all four repos as siblings:
git clone git@github.com:Cthonios/ConstitutiveModels.jl.git
git clone git@github.com:Cthonios/FiniteElementContainers.jl.git
git clone git@github.com:Cthonios/ReferenceFiniteElements.jl.git
git clone git@github.com:Cthonios/Carina.jl.git
cd Carina.jl
julia --project=. -e 'using Pkg; Pkg.instantiate()'Changes to the sibling repos are picked up immediately after restarting Julia.
# Self-activating CLI wrapper (recommended)
bin/carina input.yaml
# With GPU
bin/carina input.yaml --device rocm
bin/carina input.yaml --device cuda
# Multi-threaded (CPU)
bin/carina input.yaml --threads 8
# Combined
bin/carina input.yaml --threads 8 --device rocm
# Or directly with julia
julia --project=. src/Carina.jl input.yaml
julia --project=. src/Carina.jl input.yaml --device rocmSelect the device in the YAML input or via --device:
device: cpu # default
device: cuda # NVIDIA
device: rocm # AMDSee docs/reference.md for full YAML input documentation: solver/preconditioner compatibility, material models, boundary conditions, time integrators, and output control.
julia --project=. test/runtests.jl # full suite
julia --project=. test/runtests.jl --quick # fast subset
julia --project=. test/runtests.jl --filter torsion
julia --project=. test/runtests.jl --list # show all tests
julia --project=. test/runtests.jl 1 3 5 # by index