Numerical Methods and Software Tools in Industrial Mathematics, 1997

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 . . . . . . . . . .

I Numerical Software Tools.- 1 Object-Oriented Numerics.- 2 Basic Tools for Linear Algebra.- 3 Software Tools for Modelling Scattered Data.- 4 A Comprehensive Set of Tools for Solving Partial Differential Equations; Diffpack.- 5 On the Numerical Efficiency of C++ in Scientific Computing.- II Partial Differential Equations.- 6 Basic Equations in Eulerian Continuum Mechanics.- 7 A Mathematical Model of Macrosegregation Formation in Binary Alloy Solidification.- 8 Computation of Macrosegregation due to Solidification Shrink age.- 9 A Mathematical Model for the Melt Spinning of Polymer Fibers.- 10 Finite Element Methods for Two-Phase Flow in Heterogeneous Porous Media.- 11 Splines and Ocean Wave Modelling.- 12 Krylov Subspace Iterations for Sparse Linear Systems.- 13 Preconditioning Linear Saddle Point Problems.- III Geometric Modelling.- 14 Surface Modelling from Scattered Geological Data.- 15 Varioscale Surfaces in Geographic Information Systems.- 16 Surface Modelling from Biomedical Data.- 17 Data Reduction of Piecewise Linear Curves.- 18 Aspects of Algorithms for Manifold Intersection.- 19 Surface Editing.