fe-demo-cpp

A from-scratch C++ matrix-free finite-element basis library, built as a learning project mirroring libCEED's architecture (and, through it, Ratel). Long-term goal: a full CPU+MPI+CUDA matrix-free solid mechanics solver in 3D. Right now this covers the tensor-product basis layer — quadrature, Lagrange basis construction, and tensor-contraction-based basis evaluation — everything below the mesh/solver level.

PETSc is intended for the solver/preconditioner layer only, once that's reached; basis functions, element restriction, and (later) CUDA kernels are hand-written here rather than pulled in as a libCEED dependency.

What's implemented

• ** 1D quadrature rules: Fornberg's algorithm for Lagrange interpolation/derivative matrices
  • Tensor-product H1 Lagrange basis for dim = 1, 2, or 3, arbitrary node/quadrature order, num_comp fields, Gauss or GaussLobatto quadrature
• ** The single batched-contraction primitive (libCEED's CeedTensorContractApply)
  • tensor_basis_apply — dispatches the two above by EvalMode, mirroring CeedBasisApply

Not yet implemented: element restriction (local-to-global DOF mapping), mesh/geometry, MPI, CUDA, PETSc integration, any physics.

Requirements

• C++17 compiler
• CMake ≥ 3.20

(Catch2 is fetched automatically via CMake's FetchContent — no manual install needed.)

Build and test

cmake -S . -B build
cmake --build build -j
./build/fe_demo_test

Run a subset of tests by tag or name:

./build/fe_demo_test "[manufactured]"
./build/fe_demo_test "[transpose]"
./build/fe_demo_test --list-tests