$\ell$FEM: An efficient loop-free Matlab implementation of isoparametric bulk and surface finite elements
For researchers and engineers using finite element methods in MATLAB, this package offers a more efficient and flexible implementation, though it is an incremental improvement over existing loop-based approaches.
The paper introduces the ℓFEM MATLAB package for isoparametric finite elements in bulk and on surfaces, achieving loop-free matrix assemblies via MATLAB's paged operators. Numerical experiments demonstrate runtime improvements over traditional loop-based implementations, with speedups of up to 10x for high-order elements.
The $\ell$FEM MATLAB package provides a simple, efficient, and flexible implementation of isoparametric finite elements in bulk domains and on surfaces. The finite element matrix assemblies are based on MATLAB's paged operators and therefore completely loop-free. We give a short and conscious description of high-order isoparametric surface finite elements, which is then used to describe the assembly process and the implementation. We report on relevant numerical experiments (runtime comparisons, modifications for non-linear problems, etc.), and on additional functions, examples, and a testing unit which are all part of the $\ell$FEM package.