Large Scale Scientific Computing

In this book, the new and rapidly expanding field of scientific computing is understood in a double sense: as computing for scientific and engineering problems and as the science of doing such computations. Thus scientific computing touches at one side mathematical modelling (in the various fields of applications) and at the other side computer science. As soon as the mathematical models de­ scribe the features of real life processes in sufficient detail, the associated computations tend to be large scale. As a consequence, interest more and more focusses on such numerical methods that can be expected to cope with large scale computational problems. Moreover, given the algorithms which are known to be efficient on a tradi tional computer, the question of implementation on modern supercomputers may get crucial. The present book is the proceedings of a meeting on "Large Scale Scientific Computing" , that was held a t the Oberwolfach Mathematical Institute (July 14-19, 1985) under the auspices of the Sonderforschungsbereich 123 of the University of Heidelberg. Participants included applied scientists with computational interests, numerical analysts, and experts on modern parallel computers. 'l'he purpose of the meeting was to establish a common under­ standing of recent issues in scientific computing, especially in view of large scale problems. Fields of applications, which have been covered, included semi-conductor design, chemical combustion, flow through porous media, climatology, seismology, fluid dynami. cs, tomography, rheology, hydro power plant optimization, subwil. y control, space technology.

Contenu

I: Initial Value Problems for Ode's and Parabolic Pde's.- 1. Algorithms for Semiconductor Device Simulation.- 2. Hierarchical Bases in the Numerical Solution of Parabolic Problems.- 3. Extrapolation Integrators for Quasilinear Implicit ODE's.- 4. Numerical Problems Arising from the Simulation of Combustion Phenomena.- 5. Numerical Computation of Stiff Systems for Nonequilibrium.- 6. Finite Element Simulation of Saturated-Unsaturated Flow Through Porous Media.- II: Boundary Value Problems for ODE's and Elliptic PDE's.- 7. Numerical Pathfollowing Beyond Critical Points in ODE Models.- 8. Computing Bifurcation Diagrams for Large Nonlinear Variational Problems.- 9. Extinction Limits for Premixed Laminar Flames in a Stagnation Point Flow.- 10. A Numerical Method for Calculating Complete Theoretical Seismograms in Vertically Varying Media.- 11. On a New Boundary Element Spectral Method.- III: Hyperbolic PDE's.- 12. A High Order Non-Oscillatory Shock Capturing Method.- 13. Vortex Dynamics Studied by Large-Scale Solutions to the Euler Equations.- IV: Inverse Problems.- 14. Numerical Backprojection in the Inverse 3D Radon Transform.- 15. A Direct Algebraic Algorithm in Computerized Tomography.- 16. A Two-Grid Approach to Identification and Control Problems for Partial Differential Equations.- V: Optimization and Optimal Control Problems.- 17. Solving Large-Scale Integer Optimization Problems.- 18. Numerical Treatment of State & Control Constraints in the Computation of Feedback Laws for Nonlinear Control Problems.- 19. Optimal Production Scheme for the Gosau Hydro Power Plant System.- VI: Algorithm Adaptation on Supercomputers.- 20. The Use of Vector and Parallel Computers in the Solution of Large Sparse Linear Equations.- 21. Local Uniform Mesh Refinement on Vector and Parallel Processors.- 22. Using Supercomputer to Model Heat Transfer in Biomedical Applications.- Speakers.