Computational Partial Differential Equations : Numerical Methods and Diffpack Programming - Taschenbuch

EAN (ISBN-13): 9783642628115
ISBN (ISBN-10): 3642628117
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2012
Herausgeber: Springer Berlin

Buch in der Datenbank seit 2014-10-10T08:35:15+02:00 (Berlin)
Detailseite zuletzt geändert am 2023-02-28T19:14:03+01:00 (Berlin)
ISBN/EAN: 3642628117

ISBN - alternative Schreibweisen:
3-642-62811-7, 978-3-642-62811-5
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: hans lang, petter, langtangen, läng hans, computational partial differential equations
Titel des Buches: computational, partial differential equations, langtangen, method programming, numerical

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Daten vom Verlag:

Autor/in: Hans P. Langtangen
Titel: Texts in Computational Science and Engineering; Computational Partial Differential Equations - Numerical Methods and Diffpack Programming
Verlag: Springer; Springer Berlin
862 Seiten
Erscheinungsjahr: 2012-11-06
Berlin; Heidelberg; DE
Gedruckt / Hergestellt in Niederlande.
Sprache: Englisch
54,99 € (DE)

BC; Hardcover, Softcover / Informatik, EDV/Informatik; Theoretische Informatik; Verstehen; C++; computer; finite element method; fluid mechanics; mechanics; model; numerical methods; numerics; programming; Theory of Computation; Analysis; Software Engineering; Computational Mathematics and Numerical Analysis; Computational Intelligence; Theoretical, Mathematical and Computational Physics; Mathematische Analysis, allgemein; Software Engineering; Numerische Mathematik; Künstliche Intelligenz; Mathematische Physik; BC; BB; EA

1 Getting Started.- 1.1 The First Diffpack Encounter.- 1.2 Overview of Application Examples.- 1.3 Steady One-Dimensional Heat Conduction.- 1.5 Projects.- 1.6 About Programming with Objects.- 1.7 Coding the PDE Simulator as a Class.- 1.8 Projects.- 2 Introduction to Finite Element Discretization.- 2.1 Weighted Residual Methods.- 2.2 Time Dependent Problems.- 2.3 Finite Elements in One Space Dimension.- 2.4 Example: A ID Wave Equation.- 2.5 Naive Implementation.- 2.6 Projects.- 2.7 Higher-Dimensional Finite Elements.- 2.8 Calculation of Derivatives.- 2.9 Convection-Diffusion Equations.- 2.10 Analysis of the Finite Element Method.- 3 Programming of Finite Element Solvers.- 3.1 A Simple Program for the Poisson Equation.- 3.2 Increasing the Flexibility.- 3.3 Some Visualization Tools.- 3.4 Some Useful Diffpack Features.- 3.5 Introducing More Flexibility.- 3.6 Step-by-Step Development of a Diffpack Solver.- 3.7 Adaptive Grids.- 3.8 Projects.- 3.9 A Convection-Diffusion Solver.- 3.10 A Heat Equation Solver.- 3.11 A More Flexible Heat Equation Solver.- 3.12 Visualization of Time-Dependent Fields.- 3.13 A Transient Heat Transfer Application.- 3.14 Projects.- 3.15 Efficient Solution of the Wave Equation.- 4 Nonlinear Problems.- 4.1 Discretization and Solution of Nonlinear PDEs.- 4.2 Software Tools for Nonlinear Finite Element Problems.- 4.3 Projects.- 5 Solid Mechanics Applications.- 5.1 Linear Thermo-Elasticity.- 5.2 Elasto-Viscoplasticity.- 6 Fluid Mechanics Applications.- 6.1 Convection-Diffusion Equations.- 6.2 Shallow Water Equations.- 6.3 An Implicit Finite Element Navier-Stokes Solver.- 6.4 A Classical Finite Difference Navier-Stokes Solver.- 6.5 A Fast Finite Element Navier-Stokes Solver.- 6.6 Projects.- 7 Coupled Problems.- 7.1 Fluid-Structure Interaction; Squeeze-Film Damping.- 7.2 Fluid Flow and Heat Conduction in Pipes.- 7.3 Projects.- B.7 Optimizing Diffpack Codes.- A Mathematical Topics.- A.1 Scaling and Dimensionless Variables.- A.2 Indicial Notation.- A.3 Compact Notation for Difference Equations.- A.4 Stability and Accuracy of Difference Approximations.- A.4.1 Typical Solutions of Simple Prototype PDEs.- A.4.2 Physical Significance of Parameters in the Solution.- A.4.3 Analytical Dispersion Relations.- A.4.4 Solution of Discrete Equations.- A.4.5 Numerical Dispersion Relations.- A.4.6 Convergence.- A.4.7 Stability.- A.4.8 Accuracy.- A.4.9 Truncation Error.- A.4.10 Traditional von Neumann Stability Analysis.- A.4.11 Examples: Analysis of the Heat Equation.- A.5 Exploring the Nature of Some PDEs.- A.5.1 A Hyperbolic Equation.- A.5.2 An Elliptic Equation.- A.5.3 A Parabolic Equation.- A.5.4 The Laplace Equation Solved by a Wave Simulator.- A.5.5 Well-Posed Problems.- B Diffpack Topics.- B.1 Brief Overview of Important Diffpack Classes.- B.2 Diffpack-Related Operating System Interaction.- B.2.1 Unix.- B.2.2 Windows.- B.3 Combining Diffpack with Other Types of Software.- B.3.1 Calling Other Software Packages from Diffpack.- B.3.2 Calling Diffpack from Other Types of Software.- B.4. Basic Diffpack Features.- B.4.1 Diffpack Man Pages.- B.4.2 Standard Command-Line Options.- B.4.3 Generalized Input and Output.- B.4.4 Automatic Verification of a Code.- B.5 Visualization Support.- B.5.1 Curves.- B.5.2 Scalar and Vector Fields.- B.6 Details on Finite Element Programming.- B.6.1 Basic Functions for Finite Element Assembly.- B.6.2 Using Functors for the Integrands.- B.6.3 Integrating Quantities over the Grid or the Boundary.- B.6.4 Class Relations in the Finite Element Engine.- C Iterative Methods for Sparse Linear Systems.- C.1 Classical Iterative Methods.- C.1.1 A General Framework.- C.1.2 Jacobi, Gauss-Seidel, SOR, and SSOR Iteration.- C.2 Conjugate Gradient-Like Iterative Methods.- C.2.1 Galerkin and Least-Squares Methods.- C.2.2 Summary of the Algorithms.- C.2.3 A Framework Based on the Error.- C.3 Preconditioning.- C.3.1 Motivation and Basic Principles.- C.3.2 Classical Iterative Methods as Preconditioners.- C.3.3 Incomplete Factorization Preconditioners.- C.4 Multigrid and Domain Decomposition Methods.- C.4.1 Domain Decomposit ion.- C.4.2 Multigrid Methods.- D Software Tools for Solving Linear Systems.- D.1 Storing and Initializing Linear Systems.- D.1.1 Vector and Matrix Formats.- D.1.2 Detailed Matrix Examples.- D.1.3 Representation of Linear Systems.- D.2 Programming with Linear Solvers.- D.2.1 Gaussian Elimination.- D.2.2 A Simple Demo Program.- D.2.3 A 3D Poisson Equation Solver.- D.3 Classical Iterative Methods.- D.4 Conjugate Gradient-like Methods.- D.4.1 Symmetric Systems.- D.4.2 Nonsymmetric Systems.- D.5 Preconditioning Strategies.- D.6 Convergence History and Stopping Criteria.- D.7 Example: Implicit Methods for Transient Diffusion.- D.8 High-Level Stencil Programming of Finite Difference Schemes.- D.8.1 Finite Difference Stencils.- D.8.2 Basic Structure of a Stencil-Based Simulator.- D.8.3 Defining the Stencils.