LowLevelFEM

LowLevelFEM is a Julia package for finite element analysis with an engineering-first workflow, designed to assemble finite element operators explicitly at matrix and field level.
It exposes each phase of the workflow as simple functions (mesh → matrices → loads/BCs → solve → postprocess → visualize), so you can customize, combine, or inspect any step at matrix and field level.
Typical tasks such as strain energy or resultants are one-liners (for example, U = q' * K * q / 2). The package is suitable not only for classical structural mechanics problems, but also for rapid assembly of general linear PDEs expressed in weak form.

Requirements

• Julia 1.x
• Gmsh C API is bundled via gmsh_jll and re-exported as gmsh from this package; no separate Gmsh.jl installation is required.

Capabilities

• Geometry and meshing: integrates with gmsh for 2D/3D geometry, meshing, and physical groups.
• Problem types: 3D solids, 2D plane stress/plane strain, axisymmetric; 3D/2D heat conduction and axisymmetric heat conduction.
• Elements and order: standard line/triangle/quad/tetra/hex/pyramid/wedge with Lagrange order up to 10.
• Materials: linear elastic (Hooke) and hyperelastic materials given by their free energy function. Direct input of 6×6 constitutive matrix is also possible.
• Matrices: stiffness K, mass M (lumped or consistent), proportional damping C (Rayleigh/Caughey), heat conduction/capacity, latent heat, convection matrices/vectors, and generic Poisson-type operators for scalar and vector fields.
• Explicit matrices and fields: unlike many high-level FEM packages, LowLevelFEM keeps global matrices and finite element fields accessible throughout the workflow, making every stage of the analysis transparent and customizable.
• Operator-level programming: implement, inspect and modify PDE operators, constitutive laws and weak-form formulations directly at matrix and field level.
• Loads and constraints: nodal and distributed loads on physical groups; function-based loads and temperature BCs; elastic supports; initial displacement/velocity/temperature.
• Thermal–structural coupling: thermal expansion, thermal stresses, and heat generated by elastic deformation.
• Solvers: static (direct and iterative solvers with arbitrary preconditioners) and transient dynamics (central difference and HHT-α from the Newmark family).
• Eigenproblems: modal analysis (frequencies and mode shapes, optionally prestressed) and linear buckling (critical factors and modes).
• Field operators and results: gradient/divergence/curl; stress/strain and heat flux as element or nodal fields; smoothing at nodes with field jumps; user-defined scalar/vector/tensor FE fields.
• Visualization and plots: Gmsh-based views for displacements, stresses, strains, heat flux, with animation for dynamics; plot results along user-defined paths; show results on surfaces.
• Coordinate systems: rotate nodal DOFs with constant or function-defined local coordinate systems (incl. curvilinear).
• Truss structures (static, transient, modal analysis)
• Nonlinear solid mechanics (Total Lagrangian formulation) Energy-based hyperelasticity with consistent stress and tangent operators, including geometric stiffness and follower loads for large-deformation problems.

Installation

julia using Pkg Pkg.add("LowLevelFEM")

Quick Start

```julia using LowLevelFEM

structuredrectmesh() # uses Gmsh to create mesh

mat = Material("body", E=2e5, ν=0.3) prob = Problem([mat], type=:PlaneStrain) # :Solid, :PlaneStress, :AxiSymmetric, :HeatConduction, ...

bc = displacementConstraint("left", ux=0, uy=0) force = load("right", fy=-1)

u = solveDisplacement(prob, load=[force], support=[bc]) S = solveStress(u)

showDoFResults(u, visible=true) showDoFResults(u, :ux) showStressResults(S) showStressResults(S, :sxy, name="Shear stress")

openPostProcessor() ```

Note: physical group names in your geometry (created in Gmsh) must match the strings used above (e.g., "body", "left", "right").

An alternative solution (instead of u = ..., S = ...)

```julia K = stiffnessMatrix(prob) f = loadVector(prob, [force]) u = solveDisplacement(K, f, support=[bc])

E = mat.E ν = mat.ν

u = expandTo3D(u)

A = (u ∘ ∇ + ∇ ∘ u) / 2 I = TensorField(prob, "body", [1 0 0; 0 1 0; 0 0 1]) S = E / (1 + ν) * (A + ν / (1 - 2ν) * trace(A) * I) ```

For interactive work with custom geometries

Gmsh can be launched directly from Julia.

julia openGeometry("test.geo") openPreProcessor()

If test.geo already exists, it is opened for editing. Otherwise, openGeometry automatically creates a new geometry file, which can then be edited in Gmsh using openPreProcessor().

This workflow is recommended for custom geometries and more advanced finite element models.

More end-to-end examples, tutorials and application notebooks are available in the examples directory and the online documentation.

Documentation

• Latest docs: https://perebalazs.github.io/LowLevelFEM.jl/dev
• Stable docs: https://perebalazs.github.io/LowLevelFEM.jl/stable

Planned features

• Beam and shell elements (partially implemented using compound operators for weak-form assembly)
• Contact problems (penalty, Lagrange multiplier)
• Multithreading (partially implemented)

Any suggestions are welcome. In case of any issue, please send a bug report.

License

This project is licensed under the MIT License — see LICENSE for details.