Pages

• Credits People and third-party software who make Rodin possible.
• Partial differential equations Showcases how to use Rodin to solve PDEs.
  • Solving the Poisson equation Resolution of the Poisson equation using Rodin.
  • Solving the elasticity equation Showcases the resolution of the elasticity system.
  • Solving the Helmholtz equation Resolution of the complex-valued Helmholtz equation using Rodin.
  • Solving the Navier-Stokes equations Steady incompressible Navier-Stokes with Picard iteration.
  • Poisson equation with periodic boundary conditions Solving the Poisson equation on a periodic domain.
  • Solving PDEs on surface meshes Reaction-diffusion equation on a 3D surface mesh.
• Examples and tutorials Examples utilizing the Rodin library.
  • Input/Output examples Examples demonstrating I/O capabilities.
    • XDMF time-evolution output Exporting time-dependent data with XDMF for visualization in ParaView.
    • MFEM format How to read and write meshes and grid functions in MFEM format.
    • MEDIT format How to load and convert MEDIT-format meshes.
  • Mesh geometry examples Examples demonstrating mesh creation and geometric operations.
    • Generating uniform grids Creating structured meshes with UniformGrid.
    • Computing mesh connectivity How to compute and use topological connectivity.
  • Working with MMG Showcases the usage of the Rodin::External::MMG module.
    • Simple input/output of MMG objects How to read and write MMG meshes in MFEM and MEDIT formats.
    • Optimizing the mesh How to optimize a mesh using the MMG remesher.
    • Adapting the mesh How to adapt a mesh based on a solution field.
    • Casting between MMG and Rodin How to convert from MMG to Rodin objects and vice-versa.
  • Density optimization examples Implementation of density optimization algorithms.
    • Temperature minimization Density-based topology optimization to minimize average temperature.
  • Shape optimization examples Implementation of shape optimization algorithms.
    • Shape optimization of a cantilever Shows how to optimize the shape of a cantilever.
    • Shape optimization of a cantilever via the level set method Body-fitted optimization of a cantilever via the level set method.
• Gallery A visual showcase of simulations and results produced with Rodin.
• General concepts General concepts and design of Rodin features.
  • Installation and Setup How to install and configure Rodin on your system.
  • First Steps with Rodin Understanding the basics and creating your first Rodin program.
  • Your First Problem: Solving the Poisson Equation A complete walkthrough of solving a PDE with Rodin.
  • Understanding Core Concepts Deep dive into meshes, finite elements, and variational formulations.
  • Meshes Comprehensive guide to working with meshes in Rodin.
    • Mesh Creation How to create and load meshes in Rodin.
    • Mesh Connectivity Understanding and computing connectivity relations.
    • Mesh Iteration Iterating over mesh entities.
    • Geometric Queries Querying mesh properties and measurements.
    • Mesh Input/Output Saving and loading meshes.
    • Advanced Utilities Advanced mesh operations and transformations.
  • Polytopes Understanding the geometric elements in Rodin.
  • Connectivity Understanding mesh connectivity in Rodin.
  • Ciarlet's definition of a finite element The mathematical foundation of finite elements.
  • Finite element spaces Overview of the finite element spaces available in Rodin.
  • Variational formulations in Rodin How to define, assemble, and solve variational problems.
  • Weak Formulations Understanding and implementing weak formulations in Rodin.
  • Boundary Conditions Guide to applying boundary conditions in Rodin.
  • Solvers Guide to linear and nonlinear solvers in Rodin.
  • I/O in Rodin Comprehensive guide to input and output in Rodin.
    • XDMF Format Using the XDMF format for visualization and time series data.
    • Grid Function I/O Saving and loading grid functions in Rodin.
    • Mesh File Formats MFEM and MEDIT mesh file formats.
• Notation Explanation of the notation used throughout the documentation.
• Bibliography