Numerical Methods and Software Tools in Industrial Mathematics

✍ Scribed by Erlend Arge, Are Magnus Bruaset, Hans Petter Langtangen (auth.), Morten Dæhlen, Aslak Tveito (eds.)

• Publisher: Birkhäuser Basel
• Year: 1997
• Tongue: English
• Leaves: 403
• Edition: 1
• Category: Library

✦ Synopsis

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 . . . . . . . . . .

✦ Table of Contents

Front Matter....Pages i-4
Front Matter....Pages 5-5
Object-Oriented Numerics....Pages 7-26
Basic Tools for Linear Algebra....Pages 27-44
Software Tools for Modelling Scattered Data....Pages 45-60
A Comprehensive Set of Tools for Solving Partial Differential Equations; Diffpack....Pages 61-90
On the Numerical Efficiency of C++ in Scientific Computing....Pages 91-118
Front Matter....Pages 119-119
Basic Equations in Eulerian Continuum Mechanics....Pages 121-156
A Mathematical Model of Macrosegregation Formation in Binary Alloy Solidification....Pages 157-176
Computation of Macrosegregation due to Solidification Shrinkage....Pages 177-194
A Mathematical Model for the Melt Spinning of Polymer Fibers....Pages 195-212
Finite Element Methods for Two-Phase Flow in Heterogeneous Porous Media....Pages 213-234
Splines and Ocean Wave Modelling....Pages 235-253
Krylov Subspace Iterations for Sparse Linear Systems....Pages 255-280
Preconditioning Linear Saddle Point Problems....Pages 281-298
Front Matter....Pages 299-299
Surface Modelling from Scattered Geological Data....Pages 301-315
Varioscale Surfaces in Geographic Information Systems....Pages 317-328
Surface Modelling from Biomedical Data....Pages 329-346
Data Reduction of Piecewise Linear Curves....Pages 347-364
Aspects of Algorithms for Manifold Intersection....Pages 365-380
Surface Editing....Pages 381-396
Back Matter....Pages 397-400

✦ Subjects

Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics; Computational Science and Engineering; Numerical Analysis; Applications of Mathematics