Design of Adaptive Finite Element Software

The Finite Element Toolbox ALBERTA

Alfred Schmidt, Kunibert G. Siebert - Collection Lecture Notes in Computational Science and Engineering

316 pages, parution le 18/02/2005

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Résumé

During the last years, scientific computing has become an important research branch located between applied mathematics and applied sciences and engineering. Highly efficient numerical methods are based on adaptive methods, higher order discretizations, fast linear and non-linear iterative solvers, multi-level algorithms, etc. Such methods are integrated in the adaptive finite element software ALBERTA. It is a toolbox for the fast and flexible implementation of efficient software for real life applications, based on modern algorithms.

ALBERTA also serves as an environment for improving existent, or developing new numerical methods in an interplay with mathematical analysis and it allows the direct integration of such new or improved methods in existing simulation software. The book is accompanied by a full distribution of ALBERTA (Version 1.2) on a CD including an implementation of several model problems. System requirements for ALBERTA are a Unix/Linux environment with C and FORTRAN Compilers, OpenGL graphics and GNU make. These model implementations serve as a basis for students and researchers for the implementation of their own research projects within ALBERTA.

Sommaire

Introduction
Concepts and abstract algorithms
- Mesh refinement and coarsening
- The hierarchical mesh
- Degrees of freedom
- Finite element spaces and finite element discretization
- Adaptive Methods
Implementation of model problems
- Nonlinear reaction-diffusion equation
- Poisson equation
- Heat equation
- Installation of ALBERTA and file organization
- Data structures and implementation
- Basic types, utilities, and parameter handling
Data structures for the hierarchical mesh
- Administration of degrees of freedom.
- The refinement and coarsening implementation
- Implementation of basis functions
- Implementation of finite element spaces
- Routines for barycentric coordinates
- Data structures for numerical quadrature
- Functions for the evaluation of finite elements
- Calculation of norms for finite element functions
- Calculation of errors of finite element approximations
- Tools for the assemblage of linear systems
- Data structures and procedures for adaptive methods
- Implementation of error estimators
- Solver for linear and nonlinear systems
- Graphics output
References
Index
Data types, symbolic constants, functions, and macros
- Data types
- Symbolic constants
- Functions
- Macros

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	PAPIER
Éditeur(s)	Springer
Auteur(s)	Alfred Schmidt, Kunibert G. Siebert
Collection	Lecture Notes in Computational Science and Engineering
Parution	18/02/2005
Nb. de pages	316
Format	15,5 x 24
Couverture	Relié
Poids	646g
Intérieur	Noir et Blanc
EAN13	9783540228424