This book presents the state-of-the-art in simulation on supercomputers. Leading researchers present results achieved on systems of the Gauss-Allianz, the association of High-Performance Computing centers in Germany. The reports cover all fields of computational science and engineering, ranging from CFD to Computational Physics and Biology to Computer Science, with a special emphasis on industrially relevant applications. Presenting results for large-scale parallel microprocessor-based systems and GPU and FPGA-supported systems, the book makes it possible to compare the performance levels and usability of various architectures. Its outstanding results in achieving the highest performance for production codes are of particular interest for both scientists and engineers. The book includes a wealth of color illustrations and tables.

This volume contains 20 contributions to the 1st GAMM-Seminar at ICA Stuttgart, which was held in Stuttgart, October 12 - 13, 1995. In the field of environmental sciences, numerical procedures for the simulation of ecological problems are growing increasingly topical. The solution of typical problems in environmental research is closely connected with numerical supercomputing. The main subject of the seminar was the modeling and numerical simulation of ground water and soil water. Further topics were multi-scale modeling, special discretization schemes, adaptivity, multi-grid methods, heterogenity, parameter identification, homogenization, density driven groundwater flow, and coupling of transport and chemistry.

Englischer Text: The volume contains 21 contributions to the 12th GAMM-Seminar (Kiel, January 1996), which was devoted to advanced algorithms in the field of boundary element methods. The topics were e. g. cubature techniques, multiscale methods, hp-discretisation, error estimation, domain decomposition, and programm design. Deutscher Text: Der Band enthalt die 21 Beitrage zum 12. GAMM-Seminar (Kiel, Jaunuar 1996), welches sich mit fortgeschrittenen Algorithmen auf dem Gebiet der Randwertprobleme befasste.

The coupling considered in this volume may be of physical or numerical nature. Examples of the first kind are the solid-fluid interactions, microelectronic systems, and the coupled modelling in groundwater flow. Examples of the latter kind are the domain or subspace decomposition, the local defect correction method, and the very important FEM-BEM coupling.

This book presents the state-of-the-art in simulation on supercomputers. Leading researchers present results achieved on systems of the Gauss-Allianz, the association of High-Performance Computing centers in Germany. The reports cover all fields of computational science and engineering, ranging from CFD to Computational Physics and Biology to Computer Science, with a special emphasis on industrially relevant applications. Presenting results for large-scale parallel microprocessor-based systems and GPU and FPGA-supported systems, the book makes it possible to compare the performance levels and usability of various architectures. Its outstanding results in achieving the highest performance for production codes are of particular interest for both scientists and engineers. The book includes a wealth of color illustrations and tables.

During the last decade essential progress has been achieved in the analysis and implementation of multilevel/rnultigrid and domain decomposition methods to explore a variety of real world applications. An important trend in mod ern numerical simulations is the quick improvement of computer technology that leads to the well known paradigm (see, e. g. , [78,179]): high-performance computers make it indispensable to use numerical methods of almost linear complexity in the problem size N, to maintain an adequate scaling between the computing time and improved computer facilities as N increases. In the h-version of the finite element method (FEM), the multigrid iteration real izes an O(N) solver for elliptic differential equations in a domain n c IRd d with N = O(h- ) , where h is the mesh parameter. In the boundary ele ment method (BEM) , the traditional panel clustering, fast multi-pole and wavelet based methods as well as the modern hierarchical matrix techniques are known to provide the data-sparse approximations to the arising fully populated stiffness matrices with almost linear cost O(Nr log?Nr), where 1 d Nr = O(h - ) is the number of degrees of freedom associated with the boundary. The aim of this book is to introduce a wider audience to the use of a new class of efficient numerical methods of almost linear complexity for solving elliptic partial differential equations (PDEs) based on their reduction to the interface.

This volume contains a selection from the papers presented at the Fifth European Multigrid Conference, held in Stuttgart, October 1-4, 1996. There were 88 registered participants from 14 different countries worldwide, and 65 lectures were given. Earlier European Multigrid Conferences were held in Cologne in 1981 and 1985, in Bonn in 1990, and in Amsterdam in 1993. The next European Conference is planned in 1999 in Gent. The European Multigrid Conference '96 was organized by the Institut fUr Computer- anwendungen (ICA) of Stuttgart University, in cooperation with the GAMM Com- mittee for "Scientific Computing", SFB 359 and 404 and the research network WiR Ba- Wii. The list of topics contained lectures on Multigrid Methods: robustness, adaptivity, wavelets, parallelization, application in computational fluid dynamics, porous media flow, optimisation and computational mechanics. A considerable part of the talks fo- cused on algebraic multigrid methods. The remaining contributions will be published by the Institut fUr Computeranwen- dungen (ICA) in Stuttgart in a special ICA report. Special thanks are due to Oktavia Klassen, who carefully compiled the contributions to this volume.

The GAMM Committee for "Efficient Numerical Methods for Partial Differential Equations" organises seminars on subjects concerning the algorithmic treatment of par tial differential equations. The topics are discretisation methods like the finite element and the boundary element method for various types of applications in structural and fluid mechanics. Particular attention is devoted to the advanced solution methods. The series of such seminars was continued in 1994, January 14-16, with the 10th Kiel-Seminar on the special topic Fast Solvers for Flow Problems at the Christian-Albrechts-University of Kiel. The seminar was attended by 100 scientist from 9 countries. 23 lectures were given, including two invited survey lectures. The central topic of most of the contributions are the Navier-Stokes equations. The authors discuss robust methods, parallel implementations, defect correction techniques, adaptive methods including error estimators, domain decompositions and FEM-BEM coupling. The invited lectures concern the hierarchical multigrid method for unstruc tured grids and structured adaptive finite-volume multigrid for compressible flows."

The Sonderforschungsbereich "Reactive Flow, Diffusion and Transport" (SFB 359) at Heidelberg University and the IBM Scientific Center Heidelberg have jointly organized a workshop on "Numerical Methods for the Navier-Stokes Equations." This workshop took place from October 25-28, 1993, at the IBM Scientific Center and was attended by 113 scientists from 13 countries. The scientific program consisted of 12 invited and 34 contributed lectures which dealt with various aspects of the numerical solution of the Navier Stokes equations describing compressible as well as incompressible flows. The main topics were stable and higher-order discretization schemes, discretizations based on non-standard variational formulations, operator splitting methods, multilevel and domain decomposition techniques, a posteriori error control and adaptivity, and implementation issues on parallel computers. These proceedings contain 29 of the contributions to the workshop in alphabetical order. The editors thank the Deutsche Forschungsgemeinschaft (DFG) for its financial support through the SFB 359. They also like to express their gratitude to all persons involved in the organization of the workshop and the preparation of these proceedings. F. K. Hebeker April1994 R. Rannacher G. Wittum v CONTENTS Page M. BERZINS, J. M. WARE: Reliable Finite Volume Methods for Navier-Stokes Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . S. BIKKER, H. GREZA, W. KOSCHEL: Parallel Computing and Multigrid Solution on Adaptive Unstructured Meshes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 . . . . . . . . . . . . . . . . X.-C. CAl, W. D. GROPP, D. E. KEYES, M.D. TIDRIRI: Newton-Krylov-Schwarz Methods in CFD........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . . . . . . . . . H. DANIELS, A. PETERS: PASTIS-3D - A Parallel Finite Element Projection Code for the Time-Dependent Incompressible Navier-Stokes Equations. . . . . . . . . . 31 . . ."

This volume contains 22 papers presented at the Kiel Seminar in 1992. The Kiel Seminars are well known, and cover special areas in numerical methods for partial differential equations, numerical linear algebra, numerical methods for integral equations and related areas. The papers cover a broad range of topics from mathematical theory to practical applications of incomplete decompositions as smoothers in multi-grid methods, as preconditioners for conjugate gradient-type methods and the use of ILU for systems of partial differential equations.

While information and communication technology has a vast influence on our lives, little is understood about its effects on the way we learn. In the Age of Information, students - consciously or not - are learning in diverse formal and informal environments from a broad variety of sources, with scientific knowledge competing against unfounded assertions, and misinformation and biased data spreading through social and mass media. The Positive Learning in the Age of Information (PLATO) program illustrated by the contributions in this book unites outstanding and highly innovative expertise on the fundamentals of information processing and human learning to investigate a new paradigm of positive learning as a vital, morally and ethically oriented approach, which is of existential importance to maintaining the civilization standards of a modern society in the digital age.

Das schnelle Losen grosser, schwachbesetzter linearer und nichtlinearer Glei chungssysteme ist in den letzten Jahren immer mehr in den Brennpunkt des Interes ses geruckt. Der Grund hierfur ist vor allem in der wachsenden Verflechtung von Numerischer Mathematik und Anwendungsbereichen zu suchen. So sind etwa die Probleme in der Numerischen Stromungsmechanik auch bei Verwendung der mod ernsten Computertechnologie kaum noch mit bisher oft ublichen Hau-Ruck-Metho den zu losen. Inzwischen existieren verschiedene Klassen schneller und moderner Verfahren zur Losung der hierbei auftretenden grossen Gleichungssysteme. Zu nen nen sind insbesondere Mehrgittertechniken und die Familie der Verfahren der kon jugierten Gradienten. Beide Verfahrenstypen lassen sich jedoch nicht ohne substan tiellen Effizienzverlust auf singular gestorte Systeme anwenden. Daher ist es ein wichtiges Anliegen der gegenwartigen Forschung, robuste Verfahren zu konstruie ren, mit denen ein moglichst grosser Anwendungsbereich effizient behandelt werden kann. In diesem Buch wird nun mit den filternden Zerlegungen eine neue Klasse von Verfahren fur grosse Gleichungssysteme vorgestellt. Filternde Zerlegungen lassen sich in Kombination mit klassischen Methoden, also etwa als Glatter in Mehrgitter verfahren oder als Vorkonditionieret fur cg-artige Verfahren einsetzen, sie dienen aber auch als Grundlage fur ein eigenstandiges Verfahren (Glatter-Korrektor-Ver fahren) zum Losen grosser Gleichungssysteme. Dieses Glatter-Korrektor-Verfahren ist dem Mehrgitterverfahren nachempfunden, ist jedoch rein algebraisch konstruiert und braucht daher nur ein Gitter. Das so entstandene Verfahren ist von nahezu opti maler Effizienz, die bei Problemen mittlerer Grosse mit derjenigen eines entspre chenden Mehrgitterverfahrens vergleichbar ist. Ferner ist es sehr vielseitig und hat gute Robustheitseigenschaften, wie entsprechende Tests zeigen."

Dieser Sammelband enthalt die ausgearbeiteten Fassungen einiger Beitrage zu einem Workshop uber "Numerische Algorithmen auf Transputer-Systemen", welcher im Rahmen der Aktivitaten zweier GAMM-Fachausschusse am 31. 5. - 1. 6. 1991 in Heidelberg stattfand. Die etwa 120 Teilnehmer aus Mathematik, Physik, Informatik und den Ingenieurwissenschaften diskutierten theoretische und praktische Aspekte des Entwurfs und der Realisierung von numerischen Al gorithmen vornehmlich auf Transputer-basierten Parallelrechnern. Die starke Rolle der Transputer-Systeme spiegelte deren grosse Verbreitung an Hochschul instituten wieder. Seit Anfang 1990 wurden in der Bundesrepublik mehrere groessere Parallelrechner dieser Art mit bis zu 320 Prozessoren installiert. Dazu kommen noch eine Vielzahl kleiner Entwicklungssysteme bis hinunter zu ein zelnen Transputer-Boards in Tischrechnern. Dies hat zu einem weitverbreite ten Interesse an den mit der Transputer-Technologie verbundenen Hard- und Software-Fragen gefuhrt. Die Prasenz der anderen Parallelrechnertypen vor nehmlich US-amerikanischer Herkunft blieb dagegen auf relativ wenige Instal lationen in groesseren Instituten und Rechenzentren beschrankt. Im Zuge der breiteren Verfugbarkeit von Parallelrechnern aller Groessenordnun gen befasst sich eine zunehmende Zahl von Arbeitsgruppen an Universitaten und in ausseruniversitaren Forschungseinrichtungen mit der Entwicklung von parallelen Algorithmen und deren Anwendung fur wissenschaftliche und tech nische Problemstellungen. Diese Entwicklung folgt dem internationalen Trend im wissenschaftlichen Rechnen hin zur Nutzung von Mehrprozessorsystemen zur Steigerung der numerischen Rechenleistung. Da abzusehen ist, dass die kommenden Hochleistungsrechner wohl durchgehend parallele Architekturen haben werden, ist es wichtig, bereits fruhzeitig moeglichst viele Erfahrungen mit der Parallelisierung von Algorithmen und ihrer Implementierung zu sammeln.