General concepts

Conceptual guides to understanding Rodin's design and features.

Getting started with Rodin

New to Rodin? Start here. These guides take you from installation to solving your first PDE:

Installation and Setup — Install Rodin and set up your development environment
First Steps with Rodin — Learn the basic Rodin classes (Mesh, P1, TrialFunction, TestFunction) and write your first program
Your First Problem: Solving the Poisson Equation — Solve a complete PDE (the Poisson equation) step by step
Understanding Core Concepts — Deeper dive into meshes, finite element spaces, operators, and variational formulations

Before starting, you should have:

Basic knowledge of C++17/C++20 (templates, lambdas, auto)
Some familiarity with calculus and linear algebra
Familiarity with finite element methods is helpful but not required — the guides introduce the necessary theory
A Linux or macOS system with a C++20 compatible compiler (GCC 12+)

The Geometry module handles meshes, polytopes, connectivity, and geometric transformations:

Meshes — Creating, loading, and querying meshes
Polytopes — Geometric elements (triangles, tetrahedra, etc.) and the reference element
Connectivity — Topological incidence relations between polytopes of different dimensions

Mathematical foundations and their realization in Rodin:

Ciarlet's definition of a finite element — Ciarlet's formal definition of a finite element: the triple
Finite element spaces — Available finite element spaces (P0, P0g, P1, H1), vector-valued and complex-valued variants, and the GridFunction class

From continuous PDEs to discrete linear systems:

Variational formulations in Rodin — Defining problems using bilinear forms, linear forms, and boundary conditions
Weak Formulations — Deriving weak formulations from strong-form PDEs (Poisson, elasticity)
Boundary Conditions — Dirichlet, Neumann, periodic, and mixed boundary conditions
Solvers — Direct solvers (SparseLU, UMFPack, CHOLMOD), iterative solvers (CG, GMRES, BiCGSTAB), and the Newton solver
Interfaces, traces, and discontinuous Galerkin — Facet integrals, traces, jump and average operators, interface tagging, and discontinuous Galerkin formulations

Higher-level functionality built on the variational core:

Shape and topology optimization — Shape derivatives, Hilbertian regularization (H1a), level-set evolution, redistancing, and the shape optimization loop
Solid mechanics — Finite-strain kinematics, hyperelastic constitutive laws, the internal virtual work residual/tangent pair, and active contraction

Reading and writing meshes, grid functions, and simulation data:

I/O in Rodin — Supported formats (MFEM, MEDIT, HDF5, XDMF), ParaView visualization, and time-series output

Using MPI and PETSc for large-scale problems:

MPI: Distributed Computing — Distributed mesh partitioning, sharding, and reconciliation with Context::MPI, Mesh<Context::MPI>, and Sharder
PETSc: Parallel Solvers and Distributed Linear Algebra — PETSc-backed variational forms, distributed linear algebra, KSP/SNES solvers, and multi-field problems
Thread safety and parallelism — The thread-safety model, the Threads utilities, and how parallel assembly scales

Check the GitHub repository for the latest code and issues
Browse the examples and tutorials for common use cases
Consult the notation reference for mathematical symbols used in the documentation