$\ell$FEM: An efficient loop-free Matlab implementation of isoparametric bulk and surface finite elements

TL;DR

The $\ ext{\ell}$FEM MATLAB package offers a fast, loop-free implementation of high-order isoparametric finite elements for bulk and surface domains, facilitating efficient finite element computations.

Contribution

It introduces a simple, flexible, loop-free MATLAB implementation of isoparametric finite elements with detailed assembly process and additional functionalities.

Findings

Loop-free matrix assembly improves computational efficiency.

Numerical experiments demonstrate performance benefits.

Package includes examples, tests, and extensions for nonlinear problems.

Abstract

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.