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Produktbild: Advanced Topics in Computational Partial Differential Equations
Band 33

Advanced Topics in Computational Partial Differential Equations Numerical Methods and Diffpack Programming

Aus der Reihe Lecture Notes in Computational Science and Engineering

49,99 €

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

29.10.2003

Abbildungen

XIX, 13 illus., schwarz-weiss Illustrationen

Herausgeber

Hans Petter Langtangen + weitere

Verlag

Springer Berlin

Seitenzahl

663

Maße (L/B/H)

23,5/15,5/3,7 cm

Gewicht

970 g

Auflage

2003

Sprache

Englisch

ISBN

978-3-540-01438-6

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

29.10.2003

Abbildungen

XIX, 13 illus., schwarz-weiss Illustrationen

Herausgeber

Verlag

Springer Berlin

Seitenzahl

663

Maße (L/B/H)

23,5/15,5/3,7 cm

Gewicht

970 g

Auflage

2003

Sprache

Englisch

ISBN

978-3-540-01438-6

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: GPSR Kontakt

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  • Produktbild: Advanced Topics in Computational Partial Differential Equations
  • 1 Parallel Computing.- 1.1 Introduction to Parallel Computing.- 1.2 A Different Performance Model.- 1.3 The First MPI Encounter.- 1.4 Basic Parallel Programming with Diffpack.- 1.5 Parallelizing Explicit FD Schemes.- 1.6 Parallelizing FE Computations on Unstructured Grids.- References.- Overlapping Domain Decomposition Methods.- 2.1 Introduction.- 2.2 The Mathematical Formulations.- 2.3 A 1D Example.- 2.4 Some Important Issues.- 2.5 Components of Overlapping DD Methods.- 2.6 A Generic Implementation Framework.- 2.7 Parallel Overlapping DD Methods.- 2.8 Two Application Examples.- References.- 3 Software Tools for Multigrid Methods.- 3.1 Introduction.- 3.2 Sketch of How Multilevel Methods are Implemented in Diffpack.- 3.3 Implementing Multigrid Methods.- 3.4 Setting up an Input File.- 3.5 Playing Around with Multigrid.- 3.6 Equipping the Poisson2 Solver with Multigrid.- 3.7 Systems of Equations, Linear Elasticity.- 3.8 Nonlinear Problems.- References.- 4 Mixed Finite Elements.- 4.1 Introduction.- 4.2 Model Problems.- 4.3 Mixed Formulation.- 4.4 Some Basic Concepts of a Finite Element.- 4.5 Some Code Examples.- 4.6 Programming with Mixed Finite Elements in a Simulator.- References.- 5 Systems of PDEs and Block Preconditioning.- 5.1 Introduction.- 5.2 Block Preconditioners in General.- 5.3 The Bidomain Equations.- 5.4 Two Saddle Point Problems.- References.- 6 Fully Implicit Methods for Systems of PDEs.- 6.1 Introduction.- 6.2 Implementation of Solvers for PDE Systems in Diffpack.- 6.3 Problem with the Gauss-Seidel Method, by Example.- 6.4 Fully Implicit Implementation.- 6.5 Applications.- 6.6 Conclusion.- References.- 7 Stochastic Partial Differential Equations.- 7.1 Introduction.- 7.2 Some Simple Examples.- 7.3 Solution Methods.- 7.4 Quick Overview of Diffpack Tools.- 7.5Tools for Random Variables.- 7.6 Diffpack Tools for Random Fields.- 7.7 Summary.- 7.A Transformation of Random Variables.- 7.B Implementing a New Distribution.- References.- 8 Using Diffpack from Python Scripts.- 8.1 Introduction.- 8.2 Developing Python Interfaces to C/C++ Functions.- 8.3 Compiling and Linking Wrapper Code with Diffpack.- 8.4 Converting Data between Diffpack and Python.- 8.5 Building an Interface to a More Advanced Simulator.- 8.6 Installing Python, SWIG etc.- 8.7 Concluding Remarks.- References.- 9 Performance Modeling of PDE Solvers.- 9.1 Introduction.- 9.2 Model Problems.- 9.3 Numerical Methods.- 9.4 Total CPU Time Consumption.- 9.5 Solution of Linear Systems.- 9.6 Construction of Linear Systems.- 9.7 Concluding Remarks.- References.- 10 Electrical Activity in the Human Heart.- 10.1 The Basic Physiology.- 10.2 Outline of a Mathematical Model.- 10.3 The Bidomain Model.- 10.4 A Complete Mathematical Model.- 10.5 Physiology of the Heart Muscle Tissue.- 10.6 The Numerical Method.- 10.7 Implementation.- 10.8 Optimization of the Simulator.- 10.9 Simulation Results.- 10.10 Concluding Remarks.- References.- 11 Mathematical Models of Financial Derivatives.- 11.1 Introduction.- 11.2 Basic Assumptions.- 11.3 Forwards and Futures.- 11.4 The Black-Scholes Analysis.- 11.5 European Call and Put Options.- 11.6 American Options.- 11.7 Exotic Options.- 11.8 Hedging.- 11.9 Remarks.- References.- 12 Numerical Methods for Financial Derivatives.- 12.1 Introduction.- 12.2 Model Summary.- 12.3 Monte-Carlo Methods.- 12.4 Lattice Methods.- 12.5 Finite Difference Methods.- 12.6 Finite Element Methods.- References.- 13 Finite Element Modeling of Elastic Structures.- 13.1 Introduction.- 13.2 An Introductory Example; Bar Elements.- 13.3 Another Example; Beam Elements.- 13.4 General Three-Dimensional Elasticity.- 13.5 Degrees of Freedom and Basis Functions.- 13.6 Material Types and Elasticity Matrices.- 13.7 Element Matrices in Local Coordinates.- 13.8 Element Load Vectors in Local Coordinates.- 13.9 Element Matrices and Vectors in Global Coordinates.- 13.10 Element Forces, Stresses, and Strains.- 13.11 Implementation of Structural Elements.- 13.12 Some Example Programs.- 13.13 Test Problems.- 13.14 Summary.- References.- 14 Simulation of Aluminum Extrusion.- 14.1 Introduction.- 14.2 Mathematical Formulation.- 14.3 Finite Element Implementation.- 14.4 Object-Oriented Implementation.- 14.5 Numerical Experiments.- 14.6 Concluding Remarks.- References.- 15 Simulation of Sedimentary Basins.- 15.1 Introduction.- 15.2 The Geomechanical and Mathematical Problem.- 15.3 Numerical Methods.- 15.4 Implementing a Solver for a System of PDEs.- 15.5 Verification.- 15.6 A Magmatic Sill Intrusion Case Study.- 15.7 Concluding Remarks.- References.