EBOOK

Numerical Methods and Software Tools in Industrial Mathematics


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April 1997

Beschreibung

Beschreibung

13. 2 Abstract Saddle Point Problems . 282 13. 3 Preconditioned Iterative Methods . 283 13. 4 Examples of Saddle Point Problems 286 13. 5 Discretizations of Saddle Point Problems. 290 13. 6 Numerical Results . . . . . . . . . . . . . 295 III GEOMETRIC MODELLING 299 14 Surface Modelling from Scattered Geological Data 301 N. P. Fremming, @. Hjelle, C. Tarrou 14. 1 Introduction. . . . . . . . . . . 301 14. 2 Description of Geological Data 302 14. 3 Triangulations . . . . . . . . 304 14. 4 Regular Grid Models . . . . . 306 14. 5 A Composite Surface Model. 307 14. 6 Examples . . . . . . 312 14. 7 Concluding Remarks. . . . . 314 15 Varioscale Surfaces in Geographic Information Systems 317 G. Misund 15. 1 Introduction. . . . . . . . . . . . . . . 317 15. 2 Surfaces of Variable Resolution . . . . 318 15. 3 Surface Varioscaling by Normalization 320 15. 4 Examples . . . 323 15. 5 Final Remarks . . . . . . . . . . . . . 327 16 Surface Modelling from Biomedical Data 329 J. G. Bjaalie, M. Dtllhlen, T. V. Stensby 16. 1 Boundary Polygons. . . . . . . . . . . 332 16. 2 Curve Approximation . . . . . . . . . 333 16. 3 Reducing Twist in the Closed Surface 336 16. 4 Surface Approximation. 337 16. 5 Open Surfaces. . . . 339 16. 6 Examples . . . . . . 340 16. 7 Concluding Remarks 344 17 Data Reduction of Piecewise Linear Curves 347 E. Arge, M. Dtllhlen 17. 1 Introduction. . . . . . . . . . . 347 17. 2 Preliminaries . . . . . . . . . . 349 17. 3 The Intersecting Cones Method 351 17. 4 The Improved Douglas Method 353 17. 5 Numerical Examples . . . . . . 360 17. 6 Resolution Sorting . . . . . . . . . . . . . . . . . . 361 18 Aspects of Algorithms for Manifold Intersection 365 T. Dokken 18. 1 Introduction . . . . . . . . . . . . . . . 365 18. 2 Basic Concepts Used . . . . . . . . . .

Inhaltsverzeichnis

I Numerical Software Tools.- 1 Object-Oriented Numerics.
- 1.1 Introduction.
- 1.2 A Motivating Example.
- 1.3 A Simple Matrix Class.
- 1.4 Flexible User Interfaces.
- 1.5 Abstraction and Top-Down Design.
- 1.6 Concluding Remarks.- 2 Basic Tools for Linear Algebra.
- 2.1 Introduction.
- 2.2 The Basic Building Blocks.
- 2.3 Representation of Linear Systems.
- 2.4 Solving Linear Systems.
- 2.5 Concluding Remarks.- 3 Software Tools for Modelling Scattered Data.
- 3.1 Introduction.
- 3.2 Scattered Data Characteristics.
- 3.3 Software Requirements.
- 3.4 Elements of Software Design.
- 3.5 Concluding Remarks.- 4 A Comprehensive Set of Tools for Solving Partial Differential Equations; Diffpack.
- 4.1 Introduction.
- 4.2 Current Applications.
- 4.3 The Need for Abstractions.
- 4.4 Overview.
- 4.5 General Representation of Fields.
- 4.6 Some Details on Finite Element Methods.
- 4.7 An Example.
- 4.8 Code Extension Based on OOP.
- 4.9 Controllers.
- 4.10 Combining Simulators.
- 4.11 Conclusions.- 5 On the Numerical Efficiency of C++ in Scientific Computing.
- 5.1 Introduction.
- 5.2 Optimizing C++ for Numerical Applications.
- 5.3 Low-level Linear Algebra Operations.
- 5.4 Finite Element Applications.
- 5.5 Concluding Remarks.- II Partial Differential Equations.- 6 Basic Equations in Eulerian Continuum Mechanics.
- 6.1 Introduction.
- 6.2 Mass, Momentum and Energy Balance.
- 6.3 Constitutive Laws.
- 6.4 Boundary Conditions.
- 6.5 Initial and Boundary Value Problems.
- 6.6 Numerical Solution Procedures.
- 6.7 Mixtures.
- 6.8 Concluding Remarks.- References.- 7 A Mathematical Model of Macrosegregation Formation in Binary Alloy Solidification.
- 7.1 Introduction.
- 7.2 Microscopic Conservation Equations.
- 7.3 Fundamentals of Volume Averaging.
- 7.4 Macroscopic Conservation Equations.
- 7.5 Macroscopic Constitutive Relations.
- 7.6 A Mixture Formulation of the Governing Equations.
- 7.7 Transformation to Dimensionless Form.
- 7.8 Dimensionless Mixture Equations.
- 7.9 Concluding Remarks.- 8 Computation of Macrosegregation due to Solidification Shrink age.
- 8.1 Introduction.
- 8.2 The Mathematical Model.
- 8.3 The Finite Element Method.
- 8.4 Implementation of the Finite Element Method in Diffpack..
- 8.5 Results and Discussion.
- 8.6 Conclusion.- 9 A Mathematical Model for the Melt Spinning of Polymer Fibers.
- 9.1 Introduction.
- 9.2 Model Description.
- 9.3 Additional Constitutive Relations.
- 9.4 Numerical Methods.
- 9.5 A Case Study.
- 9.6 Summary.- 10 Finite Element Methods for Two-Phase Flow in Heterogeneous Porous Media.
- 10.1 Introduction.
- 10.2 Mathematical Model.
- 10.3 Numerical Methods.
- 10.4 One-dimensional Flow.
- 10.5 Two-dimensional Flow.
- 10.6 Summary and Conclusion.- 11 Splines and Ocean Wave Modelling.
- 11.1 Introduction and Background.
- 11.2 Spline Functions Summary.
- 11.3 Splines and Ordinary Differential Equations: a Worked Example.
- 11.4 Splines and Partial Differential Equations: a Worked Example.
- 11.5 Splines in Water Wave Equations.
- 11.6 Nonlinear Waves in a Box: A Worked Example.- 12 Krylov Subspace Iterations for Sparse Linear Systems.
- 12.1 Introduction.
- 12.2 Krylov Subspace Methods.
- 12.3 Preconditioning Techniques.
- 12.4 Concluding Remarks.- 13 Preconditioning Linear Saddle Point Problems.
- 13.1 Introduction.
- 13.2 Abstract Saddle Point Problems.
- 13.3 Preconditioned Iterative Methods.
- 13.4 Examples of Saddle Point Problems.
- 13.5 Discretizations of Saddle Point Problems.
- 13.6 Numerical Results.- III Geometric Modelling.- 14 Surface Modelling from Scattered Geological Data.
- 14.1 Introduction.
- 14.2 Description of Geological Data.
- 14.3 Triangulations.
- 14.4 Regular Grid Models.
- 14.5 A Composite Surface Model.
- 14.6 Examples.
- 14.7 Concluding Remarks.- 15 Varioscale Surfaces in Geographic Information Systems.
- 15.1 Introduction.
- 15.2 Surfaces of Variable Resolution.
- 15.3 Surface Varioscaling by Normalization.
- 15.4 Examples.
- 15.5 Final Remarks.- 16 Surface Modelling from Biomedical Data.
- 16.1 Boundary Polygons.
- 16.2 Curve Approximation.
- 16.3 Reducing Twist in the Closed Surface.
- 16.4 Surface Approximation.
- 16.5 Open Surfaces.
- 16.6 Examples.
- 16.7 Concluding Remarks.- 17 Data Reduction of Piecewise Linear Curves.
- 17.1 Introduction.
- 17.2 Preliminaries.
- 17.3 The Intersecting Cones Method.
- 17.4 The Improved Douglas Method.
- 17.5 Numerical Examples.
- 17.6 Resolution Sorting.- 18 Aspects of Algorithms for Manifold Intersection.
- 18.1 Introduction.
- 18.2 Basic Concepts Used.
- 18.3 Geometric Tolerance and Intersection.
- 18.4 Representation of the ?-Intersection.
- 18.5 Finding all Intersection Occurrences.
- 18.6 Loop Elimination.- 19 Surface Editing.
- 19.1 Introduction.
- 19.2 Requirements for Surface Editing.
- 19.3 Surface Interrogation.
- 19.4 Surface Modification.
- 19.5 Boundary Conditions of the Surface.
- 19.6 Introducing New Degrees of Freedom.
- 19.7 Examples.
- 19.8 Conclusion.
EAN: 9780817639730
ISBN: 081763973X
Untertitel: Softcover reprint of the original 1st ed. 1997. Book. Sprache: Englisch.
Verlag: Birkhäuser
Erscheinungsdatum: April 1997
Seitenanzahl: 416 Seiten
Format: kartoniert
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