E-Book, Englisch, Band 42, 315 Seiten
Reihe: Lecture Notes in Computational Science and Engineering
Schmidt / Siebert Design of Adaptive Finite Element Software
1. Auflage 2006
ISBN: 978-3-540-27156-7
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark
The Finite Element Toolbox ALBERTA
E-Book, Englisch, Band 42, 315 Seiten
Reihe: Lecture Notes in Computational Science and Engineering
ISBN: 978-3-540-27156-7
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Autoren/Hrsg.
Weitere Infos & Material
1;Preface;5
2;Contents;8
3;Introduction;12
4;1 Concepts and abstract algorithms;20
4.1;1.1 Mesh refinement and coarsening;20
4.2;1.2 The hierarchical mesh;33
4.3;1.3 Degrees of freedom;35
4.4;1.4 Finite element spaces and finite element discretization;36
4.5;1.5 Adaptive Methods;53
5;2 Implementation of model problems;65
5.1;2.1 Poisson equation;66
5.2;2.2 Nonlinear reaction–diffusion equation;78
5.3;2.3 Heat equation;103
5.4;2.4 Installation of ALBERTA and file organization;121
6;3 Data structures and implementation;122
6.1;3.1 Basic types, utilities, and parameter handling;122
6.2;3.2 Data structures for the hierarchical mesh;137
6.3;3.3 Administration of degrees of freedom;170
6.4;3.4 The refinement and coarsening implementation;185
6.5;3.5 Implementation of basis functions;192
6.6;3.6 Implementation of finite element spaces;215
6.7;3.7 Routines for barycentric coordinates;217
6.8;3.8 Data structures for numerical quadrature;219
6.9;3.9 Functions for the evaluation of finite elements;225
6.10;3.10 Calculation of norms for finite element functions;230
6.11;3.11 Calculation of errors of finite element approximations;231
6.12;3.12 Tools for the assemblage of linear systems;233
6.13;3.13 Data structures and procedures for adaptive methods;258
6.14;3.14 Implementation of error estimators;272
6.15;3.15 Solver for linear and nonlinear systems;277
6.16;3.16 Graphics output;294
7;References;304
8;Index;309
9;Data types, symbolic constants, functions, and macros;319
9.1;Data types;319
9.2;Symbolic constants;319
9.3;Functions;320
9.4;Macros;323
