JuliaFEM.jl/docs/src/index.md

[JuliaFEM.jl](@id home)

JuliaFEM.jl is an open-source finite element framework written in Julia. The package is 0.x; the repository is in the middle of a deliberate architectural reset toward a stable 1.0 with a type-stable, zero-allocation, GPU-friendly assembly pipeline.

Broader documentation (book, user/developer guides, examples) lives in the same repository under juliafem.github.io/ (Quarto). Start from juliafem.github.io/learning_path.md and juliafem.github.io/docs/documentation-map.md to see how this Documenter site relates to that material.

This page is a short, current-API quick start. The API Reference lists exported symbols.

For a maintainer-oriented summary of the current architecture and the non-negotiable invariants, see AGENTS.md in the repository root. For per-module developer notes, see the README.md files under src/<topic>/. For a logical layer diagram and an explicit dependency contract between those layers, see Architecture layers.

Installation

using Pkg
Pkg.add("JuliaFEM")

A modern minimal example

The following sets up a unit-cube linear-elasticity problem, builds an Element{K, P, S, N} template with a compile-time DOF layout, assembles the stiffness via the matrix-free-friendly DOF-based assembler, and extracts the assembled K and right-hand side f.

The listing is included verbatim from docs/src/snippets/minimal_elasticity_quickstart.jl. That file is executed in Pkg.test() (test/docs/runtests.jl) and in CI (scripts/verify_docs_quickstart.jl) so the example cannot drift from the package.

snippets/minimal_elasticity_quickstart.jl

Multi-field elements

@DOFSet accepts more than one field, and the rest of the pipeline is multi-field aware (see local_dof_layout and the thermo-elastic kernel in src/domains/thermo_elastic/). A longer walkthrough with a runnable block lives on [Thermo-elastic walkthrough](@ref thermo_elastic_walkthrough).

S = @DOFSet{T::DOF{Temperature, Vertex},
            u::DOF{Displacement{3}, Vertex}}

Matrix-free path

The same cache and kernel drive the matrix-free apply_K! / apply_M! operators in src/assemblers/:

• Dirichlet: PenaltyDirichlet, EliminatedDirichlet
• Linear MPC: LinearMPC
• Neumann loads: NodalForce, UniformBodyForce, SurfaceLoad
• Preconditioners: JacobiPreconditioner, BlockJacobiPreconditioner, ICholPreconditioner
• Generalized eigensolve: lowest_eigenpairs, solve_eigenproblem

matrix_free_op(cache, asm, kernel, mesh; dirichlet, mpc) returns a closure that wraps apply_K! with constraint hooks; it composes with any LinearOperator/Krylov stack.

Inspecting the compile-time DOF layout

local_dof_layout(::Type{Element{K,P,S,N}}) is a @generated function that returns an NTuple{N, DOFLayoutEntry} describing (field_idx, entity_local, component) for each local DOF. The compiler folds it into a constant at the call site, so DOF decoding is a tuple lookup with no runtime arithmetic.

S  = @DOFSet{u::DOF{Displacement{3}, Vertex}}
ET = Element{Hex8, Lagrange{1}, S, 24}
local_dof_layout(ET)

Where to look next

• Elements, DOFs, traits, mixed fields: [Elements and multiphysics](@ref elements_multiphysics_teaser)
• Coupled thermo-elasticity (multi-field): [Thermo-elastic walkthrough](@ref thermo_elastic_walkthrough)
• Assembler trade-offs: [Choosing an assembler](@ref assembler_choice)
• Legacy API (optional Legacy submodule): [Legacy module](@ref legacy_module)
• API reference: API Reference
• Repository layout: Repository layout (see also the pointer docs/repository_layout.md on GitHub).
• Changelog (0.x): docs/NEWS.md in the project root.
• Architecture: AGENTS.md in the project root, plus src/README.md for a per-module overview.
• Tests as documentation: test/assemblers/test_dof_based_*.jl, test/assemblers/test_eigensolve.jl, test/assemblers/test_linear_mpc.jl, test/assemblers/test_surface_load.jl, test/assemblers/test_ichol_preconditioner.jl.