FreeFem++, a tool to solve PDEs numerically

TL;DR

FreeFem++ is an open source software platform designed for solving partial differential equations using finite element methods, facilitating research and teaching with features like mesh adaptation and various solvers.

Contribution

It introduces a comprehensive, open source tool with advanced features for PDE simulation, including mesh adaptation and multiple solvers, tailored for research and education.

Findings

Includes an automatic mesh generator with adaptive capabilities

Supports various finite elements and iterative algorithms

Interfaces with fast solvers like UMFPACK and SuperLU

Abstract

FreeFem++ is an open source platform to solve partial differential equations numerically, based on finite element methods. It was developed at the Laboratoire Jacques-Louis Lions, Universit\'e Pierre et Marie Curie, Paris by Fr\'ed\'eric Hecht in collaboration with Olivier Pironneau, Jacques Morice, Antoine Le Hyaric and Kohji Ohtsuka. The FreeFem++ platform has been developed to facilitate teaching and basic research through prototyping. FreeFem++ has an advanced automatic mesh generator, capable of a posteriori mesh adaptation; it has a general purpose elliptic solver interfaced with fast algorithms such as the multi-frontal method UMFPACK, SuperLU . Hyperbolic and parabolic problems are solved by iterative algorithms prescribed by the user with the high level language of FreeFem++. It has several triangular finite elements, including discontinuous elements. For the moment this platform is restricted to the numerical simulations of problems which admit a variational formulation. We will give in the sequel an introduction to FreeFem++ which include the basic of this software. You may find more information throw this link http://www.freefem.org/ff++.