Titre :	Solving PDEs in Python : The FEniCS Tutorial I
Type de document :	texte imprimé
Auteurs :	Hans Petter Langtangen ; Anders Logg
Editeur :	Springer
Année de publication :	2016
Collection :	Simula SpringerBriefs on Computing num. 3
Importance :	1 vol (148 p.)
ISBN/ISSN/EAN :	978-3-319-52461-0
Note générale :	978-3-319-52461-0
Catégories :	Informatique
Mots-clés :	Python (langage de programmation informatique) Équations différentielles, Partielles - Traitement des données. Méthode par éléments finis - Processus de données
Index. décimale :	004 Informatique
Résumé :	Ce livre donne une introduction concise et douce à la programmation par éléments finis en Python basée sur la populaire bibliothèque logicielle FEniCS. A travers une série d'exemples incluant entre autres l'équation de Poisson, les équations d'élasticité linéaire, les équations de Navier-Stokes incompressibles et les systèmes d'équations non-linéaires advection-diffusion-réaction, le lecteur est guidé dans les étapes essentielles de la résolution rapide une PDE dans FEniCS, y compris comment définir un problème variationnel fini, comment définir des conditions aux limites, comment résoudre des systèmes linéaires et non linéaires, et comment visualiser des solutions et structurer des programmes Python à éléments finis. Ce document est également disponible en formats PDF et Sphinx
Note de contenu :	Sommaire Table of contents Preface Preliminaries The FEniCS Project What you will learn Working with this tutorial Obtaining the software Installation using Docker containers Installation using Ubuntu packages Testing your installation Obtaining the tutorial examples Background knowledge Programming in Python The finite element method Fundamentals: Solving the Poisson equation Mathematical problem formulation Finite element variational formulation Abstract finite element variational formulation Choosing a test problem FEniCS implementation The complete program Running the program Dissection of the program The important first line Generating simple meshes Defining the finite element function space Defining the trial and test functions Defining the boundary conditions Defining the source term Defining the variational problem Forming and solving the linear system Plotting the solution using the plot command Plotting the solution using ParaView Computing the error Examining degrees of freedom and vertex values Deflection of a membrane Scaling the equation Defining the mesh Defining the load Defining the variational problem Plotting the solution Making curve plots through the domain A Gallery of finite element solvers The heat equation PDE problem Variational formulation FEniCS implementation A nonlinear Poisson equation PDE problem Variational formulation FEniCS implementation The equations of linear elasticity PDE problem Variational formulation FEniCS implementation The Navier–Stokes equations PDE problem Variational formulation FEniCS implementation A system of advection–diffusion–reaction equations PDE problem Variational formulation FEniCS implementation Subdomains and boundary conditions Combining Dirichlet and Neumann conditions PDE problem Variational formulation FEniCS implementation Setting multiple Dirichlet conditions Defining subdomains for different materials Using expressions to define subdomains Using mesh functions to define subdomains Using C++ code snippets to define subdomains Setting multiple Dirichlet, Neumann, and Robin conditions Three types of boundary conditions PDE problem Variational formulation FEniCS implementation Test problem Debugging boundary conditions Generating meshes with subdomains PDE problem Variational formulation FEniCS implementation Extensions: Improving the Poisson solver Refactoring the Poisson solver A more general solver function Writing the solver as a Python module Verification and unit tests Parameterizing the number of space dimensions Working with linear solvers Choosing a linear solver and preconditioner Choosing a linear algebra backend Setting solver parameters An extended solver function A remark regarding unit tests List of linear solver methods and preconditioners High-level and low-level solver interfaces Linear variational problem and solver objects Explicit assembly and solve Examining matrix and vector values Degrees of freedom and function evaluation Examining the degrees of freedom Setting the degrees of freedom Function evaluation Postprocessing computations Test problem Flux computations Computing functionals Computing convergence rates Taking advantage of structured mesh da Taking the next step Bibliography
Côte titre :	Fs/19839

Solving PDEs in Python : The FEniCS Tutorial I [texte imprimé] / Hans Petter Langtangen ; Anders Logg . - [S.l.] : Springer, 2016 . - 1 vol (148 p.). - (Simula SpringerBriefs on Computing; 3) .
ISBN : 978-3-319-52461-0
978-3-319-52461-0

Catégories :	Informatique
Mots-clés :	Python (langage de programmation informatique) Équations différentielles, Partielles - Traitement des données. Méthode par éléments finis - Processus de données
Index. décimale :	004 Informatique
Résumé :	Ce livre donne une introduction concise et douce à la programmation par éléments finis en Python basée sur la populaire bibliothèque logicielle FEniCS. A travers une série d'exemples incluant entre autres l'équation de Poisson, les équations d'élasticité linéaire, les équations de Navier-Stokes incompressibles et les systèmes d'équations non-linéaires advection-diffusion-réaction, le lecteur est guidé dans les étapes essentielles de la résolution rapide une PDE dans FEniCS, y compris comment définir un problème variationnel fini, comment définir des conditions aux limites, comment résoudre des systèmes linéaires et non linéaires, et comment visualiser des solutions et structurer des programmes Python à éléments finis. Ce document est également disponible en formats PDF et Sphinx
Note de contenu :	Sommaire Table of contents Preface Preliminaries The FEniCS Project What you will learn Working with this tutorial Obtaining the software Installation using Docker containers Installation using Ubuntu packages Testing your installation Obtaining the tutorial examples Background knowledge Programming in Python The finite element method Fundamentals: Solving the Poisson equation Mathematical problem formulation Finite element variational formulation Abstract finite element variational formulation Choosing a test problem FEniCS implementation The complete program Running the program Dissection of the program The important first line Generating simple meshes Defining the finite element function space Defining the trial and test functions Defining the boundary conditions Defining the source term Defining the variational problem Forming and solving the linear system Plotting the solution using the plot command Plotting the solution using ParaView Computing the error Examining degrees of freedom and vertex values Deflection of a membrane Scaling the equation Defining the mesh Defining the load Defining the variational problem Plotting the solution Making curve plots through the domain A Gallery of finite element solvers The heat equation PDE problem Variational formulation FEniCS implementation A nonlinear Poisson equation PDE problem Variational formulation FEniCS implementation The equations of linear elasticity PDE problem Variational formulation FEniCS implementation The Navier–Stokes equations PDE problem Variational formulation FEniCS implementation A system of advection–diffusion–reaction equations PDE problem Variational formulation FEniCS implementation Subdomains and boundary conditions Combining Dirichlet and Neumann conditions PDE problem Variational formulation FEniCS implementation Setting multiple Dirichlet conditions Defining subdomains for different materials Using expressions to define subdomains Using mesh functions to define subdomains Using C++ code snippets to define subdomains Setting multiple Dirichlet, Neumann, and Robin conditions Three types of boundary conditions PDE problem Variational formulation FEniCS implementation Test problem Debugging boundary conditions Generating meshes with subdomains PDE problem Variational formulation FEniCS implementation Extensions: Improving the Poisson solver Refactoring the Poisson solver A more general solver function Writing the solver as a Python module Verification and unit tests Parameterizing the number of space dimensions Working with linear solvers Choosing a linear solver and preconditioner Choosing a linear algebra backend Setting solver parameters An extended solver function A remark regarding unit tests List of linear solver methods and preconditioners High-level and low-level solver interfaces Linear variational problem and solver objects Explicit assembly and solve Examining matrix and vector values Degrees of freedom and function evaluation Examining the degrees of freedom Setting the degrees of freedom Function evaluation Postprocessing computations Test problem Flux computations Computing functionals Computing convergence rates Taking advantage of structured mesh da Taking the next step Bibliography
Côte titre :	Fs/19839