Gallery
A visual showcase of simulations and results produced with Rodin.
Overview
This gallery showcases results from simulations built with the Rodin framework. Each entry links to the corresponding example or tutorial page where you can find the full source code and step-by-step explanations.
Partial Differential Equations
Poisson Equation
The Poisson equation example solves the classic scalar PDE on the unit square with homogeneous Dirichlet boundary conditions, using P1 finite elements and the CG solver.
Linear Elasticity
The elasticity example solves the linearized elasticity system with mixed Dirichlet/Neumann boundary conditions. It demonstrates vector-valued P1 spaces and the LinearElasticityIntegral bilinear form.
Helmholtz Equation
The Helmholtz equation example solves the complex-valued PDE using P1<Complex> finite element spaces. This demonstrates Rodin's support for complex-valued computations.
Navier–Stokes Equations
The Navier–Stokes tutorial covers the steady incompressible Navier–Stokes equations using Taylor–Hood elements (H1 order 2 for velocity, order 1 for pressure) with Picard iteration.
Periodic Poisson Equation
The periodic Poisson example demonstrates how to impose periodic boundary conditions using PeriodicBC and a DOF correspondence map. The solution on opposite edges of the domain is constrained to be equal, simulating a tiling pattern.
Reaction-Diffusion on a Surface
The surface mesh example solves a reaction-diffusion equation on a curved 3D manifold. It demonstrates that Rodin handles surface PDEs transparently — the same Integral(Grad(u), Grad(v)) syntax automatically computes the surface gradient.
Optimization
Shape Optimization: Cantilever
The simple cantilever example performs boundary-variation shape optimization of a cantilever beam, minimizing the compliance (structural stiffness) subject to a volume constraint. The shape gradient is computed and regularized via the Hilbert extension-regularization procedure, and the mesh is updated using the MMG remesher.
Level-Set Shape Optimization
The level-setcantilever" example combines body-fitted meshing with level-set
techniques. The optimizer advects a signed-distance function and recovers
the implicit domain at each iteration using the
@ref Rodin::External::MMG "MMG" level-set discretizer.
@subsection gallery-density-temp Density Optimization: Temperature
@image html SIMPTemperatureMinimization.png width=360px
The @ref examples-density_optimization-simp_temperature_minimization
"temperature minimization" example uses the SIMP (Solid Isotropic
Material with Penalization) approach to find an optimal material
distribution that minimizes the average temperature in a domain.
@section gallery-geometry Mesh Geometry and Utilities
Rodin provides a rich set of geometric operations for creating,
transforming, and querying meshes:
- <strong>UniformGrid</strong>: Generate structured meshes of triangles, quads,
tetrahedra, hexahedra, or wedges in any dimension. See
@ref examples-geometry-uniformgrid "UniformGrid example".
- <strong>Scale and displace</strong>: Transform mesh coordinates with
<tt>mesh.scale()</tt> and <tt>mesh.displace()</tt>.
- <strong>Trim</strong>: Remove cells by attribute to extract subdomains.
- <strong>Skin</strong>: Extract the boundary surface of a volumetric mesh.
- <strong>CCL</strong>: Connected component labeling for domain decomposition.
- <strong>Connectivity</strong>: Compute topological incidence relations between
mesh entities of any dimension. See
@ref examples-geometry-connectivity "Connectivity example".
@section gallery-io Visualization and I/O
Rodin supports exporting simulation data in the
@ref Rodin::IO::XDMF "XDMF" format, which can be opened directly in
<a href="https:/