Authors

Frédéric Hecht
Olivier Pironneau
Antoine Le Hyaric
Kohji Ohtsuka (Web master of this site(CoMFoS)) Examples

1 Introduction

Installation, How to use FreeFem++, Environment variables, and the init file, History

2 Getting Started

FEM by FreeFem++ : how does it work?, Some Features of FreeFem++, The Development Cycle,

3 Learning by Examples

Membranes, Heat Exchanger, Acoustics, Thermal Conduction, Irrotational Fan Blade Flow and Thermal effects, Pure Convection, A Projection Algorithm for the Navier-Stokes equations, The System of elasticity, The System of Stokes for Fluids, A Large Fluid Problem, An Example with Complex Numbers, Optimal Control, A Flow with Shocks, Classification of the equations

4 Syntax

Data Types, List of major types, Global Variables, System Commands, Arithmetic, One Variable Functions, Functions of Two Variables, Arrays, Loops, Input/Outpu, Exception handling,

5 Mesh Generation

Commands for Mesh Generation, Boundary FEM Spaces Built as Empty Meshes, Remeshing, Regular Triangulation: hTriangle, Adaptmesh, Trunc, Splitmesh, Meshing Examples, How to change the label, Mesh in 3d, Meshing Example (3d),

6 Finite Elements

Lagrange finite element, P1 Nonconforming Element, Other FE-space, Vector valued FE-function, A Fast Finite Element Interpolator, Keywords: Problem and Solve, Parameters affecting solve and problem, Problem definition, Numerical Integration, Variational Form, Sparse Matrix, PDE Data Vector, Interpolation matrix, Finite elements connectivity

7 Visualization

Plot, link with gnuplot, link with medit,

8 Algorithms

Conjugate Gradient/GMRES, Optimization

9 Mathematical Models

Static Problems, Elasticity, Nonlinear Static Problems, Eigenvalue Problems, Evolution Problems, Navier-Stokes Equation, Variational inequality, Domain decomposition, Schwarz Overlap Scheme, Fluid/Structures Coupled Problem, Transmission Problem, Free Boundary Problem, Nonlinear elasticity Compressible Neo-Hookean Materials: Computational Solutions

10 Parallel version experimental

Schwarz in parallel

11 Mesh Files

File mesh data structure, bb File type for Store Solutions, BB File Type for Store Solutions, Metric File, List of AM FMT, AMDBA Meshes

12 Add new finite element

Some notation, Which class of add

Appendix

A Table of Notations

Generalities, Sets, Mappings, Matrices, Vectors, Numbers, Differential Calculus, Meshes, Finite Element Spaces

B Grammar

The bison grammar, The Types of the languages, and cast, All the operators

C Dynamical link

A first example myfunction.cpp, Example Discrete Fast Fourier Transform, Load Module for Dervieux’ P0-P1 Finite Volume Method, Add a new finite element, Add a new sparse solver Keywords