The Resource Advanced Topics in Computational Partial Differential Equations : Numerical Methods and Diffpack Programming, edited by Hans Petter Langtangen, Aslak Tveito, (electronic resource)

Advanced Topics in Computational Partial Differential Equations : Numerical Methods and Diffpack Programming, edited by Hans Petter Langtangen, Aslak Tveito, (electronic resource)

Label
Advanced Topics in Computational Partial Differential Equations : Numerical Methods and Diffpack Programming
Title
Advanced Topics in Computational Partial Differential Equations
Title remainder
Numerical Methods and Diffpack Programming
Statement of responsibility
edited by Hans Petter Langtangen, Aslak Tveito
Contributor
Editor
Editor
Subject
Language
  • eng
  • eng
Summary
The book is suitable for readers with a background in basic finite element and finite difference methods for partial differential equations who wants gentle introductions to advanced topics like parallel computing, multigrid methods, and special methods for systems of PDEs. The goal of all chapters is to *compute* solutions to problems, hence algorithmic and software issues play a central role. All software examples use the Diffpack programming environment, so to take advantage of these examples some experience with Diffpack is required. There are also some chapters covering complete applications, i.e., the way from a model, expressed as systems of PDEs, through discretization methods, algorithms, software design, verification, and computational examples
Member of
Dewey number
518/.64
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsedt
  • o3g1vJr15CA
  • pychPFSa-Uw
Image bit depth
0
Language note
English
LC call number
QA299.6-433
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Langtangen, Hans Petter.
  • Tveito, Aslak.
Series statement
Lecture Notes in Computational Science and Engineering,
Series volume
33
http://library.link/vocab/subjectName
  • Global analysis (Mathematics)
  • Computer science
  • Differential equations, partial
  • Analysis
  • Computational Science and Engineering
  • Partial Differential Equations
Label
Advanced Topics in Computational Partial Differential Equations : Numerical Methods and Diffpack Programming, edited by Hans Petter Langtangen, Aslak Tveito, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references at the end of each chapters
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
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 -- 7.5 Tools 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
Dimensions
unknown
Edition
1st ed. 2003.
Extent
1 online resource (XIX, 663 p. 13 illus.)
File format
multiple file formats
Form of item
online
Isbn
9783642182372
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-642-18237-2
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000102531
  • (SSID)ssj0000805008
  • (PQKBManifestationID)11422619
  • (PQKBTitleCode)TC0000805008
  • (PQKBWorkID)10823294
  • (PQKB)10655038
  • (DE-He213)978-3-642-18237-2
  • (MiAaPQ)EBC3088897
  • (EXLCZ)993400000000102531
Label
Advanced Topics in Computational Partial Differential Equations : Numerical Methods and Diffpack Programming, edited by Hans Petter Langtangen, Aslak Tveito, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references at the end of each chapters
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
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 -- 7.5 Tools 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
Dimensions
unknown
Edition
1st ed. 2003.
Extent
1 online resource (XIX, 663 p. 13 illus.)
File format
multiple file formats
Form of item
online
Isbn
9783642182372
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-642-18237-2
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000102531
  • (SSID)ssj0000805008
  • (PQKBManifestationID)11422619
  • (PQKBTitleCode)TC0000805008
  • (PQKBWorkID)10823294
  • (PQKB)10655038
  • (DE-He213)978-3-642-18237-2
  • (MiAaPQ)EBC3088897
  • (EXLCZ)993400000000102531

Library Locations

  • Architecture LibraryBorrow it
    Gould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US
    35.205706 -97.445050
  • Bizzell Memorial LibraryBorrow it
    401 W. Brooks St., Norman, OK, 73019, US
    35.207487 -97.447906
  • Boorstin CollectionBorrow it
    401 W. Brooks St., Norman, OK, 73019, US
    35.207487 -97.447906
  • Chinese Literature Translation ArchiveBorrow it
    401 W. Brooks St., RM 414, Norman, OK, 73019, US
    35.207487 -97.447906
  • Engineering LibraryBorrow it
    Felgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US
    35.205706 -97.445050
  • Fine Arts LibraryBorrow it
    Catlett Music Center 500 West Boyd Street, Rm. 20, Norman, OK, 73019, US
    35.210371 -97.448244
  • Harry W. Bass Business History CollectionBorrow it
    401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • History of Science CollectionsBorrow it
    401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • John and Mary Nichols Rare Books and Special CollectionsBorrow it
    401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • Library Service CenterBorrow it
    2601 Technology Place, Norman, OK, 73019, US
    35.185561 -97.398361
  • Price College Digital LibraryBorrow it
    Adams Hall 102 307 West Brooks St., Norman, OK, 73019, US
    35.210371 -97.448244
  • Western History CollectionsBorrow it
    Monnet Hall 630 Parrington Oval, Rm. 300, Norman, OK, 73019, US
    35.209584 -97.445414
Processing Feedback ...