Bøger udgivet af Friedrich Vieweg & Sohn Verlagsgesellschaft mbH

This volume contains the proceedings of the Ninth GAMM-Conference on Numerical Methods in Fluid Mechanics, held at the Ecole Polytechnique Federale de Lausanne, Switzerland, on September 25-27, 1991. This conference, as weil as the preceding eight ones, was organized by the GAMM Committee on Numerical Methods in Fluid Dynamics. 1t was probably also the last one in this successful series of conferences, since in the future, a bi-annual European meeting on Computational Fluid Dynamics will be organized by ECCOMAS, a new organization, representing all existing European professional societies working in this field. The conference was attended by about 100 registered participants coming from all corners of the world. These proceedings contain the written version of the 56 papers presented during the meeting. In order to eliminate all kinds of errors, omissions, spelling mistakes, etc. these papers have been reviewed by an ad hoc scientific committee. As a result of this work a good deal of the papers were sent back to the authors for correction. This procedure has somewhat delayed the publication of this volume. We feel, however, that this has been a worth while effort. The subjects treated during the meeting represent weil current interests in CFD. For instance, multigrid and multiblock techniques for viscous as weil as inviscid 3D flows were presented. Similarly, finite rate chemistry hypersonic flows still attracts many scientists due to the continuation of the Hermes Project.

This volume contains the Proceedings of the Eighth GAMM Conference on Numerical Methods in Fluid Mechanics, held in Delft, The Netherlands, September 27-29, 1989, at Delft University of Technology. This international conference is organized bi-annually at various locations in Europe by the Committee on Numerical Methods in Fluid Dynamics of the Gesellschaft fiir Angewandte Mathematik und Mechanik, chaired at present by W. Kordulla. At the moment, the organizing committee draws its-members from ten European countries. The conference attracted a worldwide attendance of about 140 registered partici­ pants. The book contains the written versions of the 61 papers that were presented and a report on the GAMM-Workshop "Numerical Simulation of Oscillatory Convec­ tion in Low-Pr Fluids" held in Marseille, October 12-14, 1988. The organizing committee had a difficult task in selecting the papers from 145 submitted abstracts. In view of the high quality of the abstracts it was decided to allow more papers than in previous conferences in this series. The contents of this volume reflect current trends in computational fluid dynamics. The renaissance of hypersonic aerodynamics manifests itself clearly, strongly stimulated in Europe by the Hermes project and plans for a later future. Notable advances are reported in adaptive and multigrid computing methods, visual­ ization and computing in three space dimensions. The local organization was taken care of by the Congress Office of Delft Universi­ ty of Technology, under the able directorship of Mrs. M.H.P. Komen-Zimmerman and Mrs. A. de Bruin.

Presents a comprehensive view of open distributed systems. The starting point is a small number of core concepts and basic principles, which are informally introduced and precisely defined using mathematical logic. The book is oriented towards the design and implementation of real systems.

"The book ...is a storehouse of useful information for the mathematicians interested in foliation theory." (John Cantwell, Mathematical Reviews 1992)

Spine title: System analysis of biological processes.

This work is a comparative study of nineteenth-century English-Canadian and French Canadian novel prefaces, a previously unexplored literary topic.

In dieser Einführung geht es vor allem um die geometrischen Aspekte der Invariantentheorie. Die hauptsächliche Motivation bildet das Studium von Klassifikations- und Normalformenproblemen, die auch historisch der Ausgangspunkt für invariantentheoretische Untersuchungen waren.

This book is a slightly augmented version of a set of lec­ tures on optimization which I held at the University of Got­ tingen in the winter semester 1983/84. The lectures were in­ tended to give an introduction to the foundations and an im­ pression of the applications of optimization theory. Since in­ finite dimensional problems were also to be treated and one could only assume a minimal knowledge of functional analysis, the necessary tools from functional analysis were almost com­ pletely developed during the course of the semester. The most important aspects of the course are the duality theory for convex programming and necessary optimality conditions for nonlinear optimization problems; here we strive to make the geometric background particularly clear. For lack of time and space we were not able to go into several important problems in optimization - e. g. vector optimization, geometric program­ ming and stability theory. I am very grateful to various people for their help in pro­ ducing this text. R. Schaback encouraged me to publish my lec­ tures and put me in touch with the Vieweg-Verlag. W. BrUbach and O. Herbst proofread the manuscript; the latter also pro­ duced the drawings and assembled the index. I am indebted to W. LUck for valuable suggestions for improvement. I am also particularly grateful to R. Switzer, who translated the German text into English. Finally I wish to thank Frau P. Trapp for her Gare and patience in typing the final version.

Matter may be divided into four phases or states: solid, liquid, gas and plasma (ionized gas). The termfluid has been used as a general name for the last three states: liquid, gas, and plasma because they may be deformed without applying any force, provided that the change of shape occurs very slowly. Furthermore, when a large number of small solid particles flow in a fluid, if the velocity of the fluid is sufficiently high, the behavior of such solids is similar to ordinary fluid. We may consider these solid particles as pseudofluid. Under proper conditions, we may treat fluid flow problems for solid (pseudofluid), liquid, gas and/or plasma. In ordinary fluid mechanics, we treat the flow problems of a fluid which is in one state only, i.e., liquid, gas, or plasma, and the solids in this fluid medium are assumed to be rigid bodies which may be considered as given boundary conditions of the flow problems.

The GAMM Committee for Efficient Numerical Methods for Par­ tial Differential Equations (GAMM-FachausschuB "Effiziente numerische Verfahren fUr partielle Differenzialgleichungen") organizes conferences and seminars on subjects concerning the algorithmic treatment of partial differential equation prob­ lems. The first seminar "Efficient Solution of Elliptic Systems" was followed by a second one held at the University of Kiel from January 17th to January 19th, 1986. The title was "Efficient Numerical Methods in Continuum Mechanics". The equations arising in continuum mechanics have many con­ nections to those of fluid mechanics, but are usually more complex. Therefore, much attention has to be paid to the ef­ ficient discretization, postprocessing and extrapolation. The seminar was attended by 66 scientists from 10 countries. Most of the 21 lectures presented at the seminar treated the discretization of equations in continuum mechanics by finite elements, methods for improving the accuracy of these approx­ imations and the use of boundary elements. Other contribu­ tions presented efficient methods for investigating bifurca­ tions which play an essential role in practical applications. These proceedings contain 11 contributions in alphabetical order. The editors and organizers of the seminar would like to thank the land Schleswig-Holstein and the DFG (Deutsche Forschungs­ gemeinschaft) for their support. Kiel, November 1986 W. Hackbusch K. Witsch v Contents Page K. ERIKSSON, C. JOHNSON, J. LENNBLAD: Optimal error estimates and adaptive time and space step control for linear parabolic problems ....................... .

Contains selected contributions to a workshop on "Numerical Methods for the Navier-Stokes Equations" held at the IBM Scientific Center, Heidelberg during October 25-28, 1993. The topics treated are advanced computational methods for the Navier-Stokes equations in fluid mechanics.

While the first two of us have worked mainly on algorithmic problems, the third has been concerned off and on with modelling and application problems of Euler methods. The problem which we soon faced, was that the field still is moving at a fast pace, for instance because hyper sonic computation problems became more and more important.

It is shown that other algorithms, such as finite difference and finite volume methods, can be derived using finite element principles. Some issues in the design and implementation of adaptive finite element algorithms on vector and parallel computers are discussed.

The contributions to this volume cover a wide spectrum of recent developments in geophysical data inversion, including basic mathematics and general theory, numerical methods, as well as computer implementation of algorithms. Most of the papers are motivated by problems arising from geophysical research and applications both on a global scale and with respect to local geophysical surveys, underlining the increasing importance of geophysical exploration methods in various fields, such as structural geology, prospecting for mineral and energy resources, hydro­ geology, geotechnology, environmental protection and archaeology. The first section of the book deals with basic mathematics and general theory underlying geophysical data inversion. Papers presented here are concerned with stabilization algorithms to solve ill-posed inverse problems, sensitivity of kernel function estimations to random data errors and reduction of errors in inverse modelling of response functions by linear constraints, numerical procedures for approximating the solution to boundary value problems, accuracy and stability of inverse ill-posed problems constituted by problems of moments, and fast Fourier transforms for solving potential field problems. The second section contains papers on gravity and magnetics, dealing with the solvability of the inverse gravimetric problem for sources represented by point masses and other elementary, solution of the inverse problem in cases of nonuniformly distributed data as obtained by palaeomagnetic studies, satellite observations, and surface projections of buried archaeological targets by inverse filtering of geomagnetic data.

In 1960 Wilhelm Stoll joined the University of Notre Dame faculty as Professor of Mathematics, and in October, 1984 the university acknowledged his many years of distinguished service by holding a conference in complex analysis in his honour.

"A publication of Deutsches Zentrum f'ur Entwicklungstechnologien-GATE in: Deutsche Gesellschaft f'ur Technische Zusammenarbeit (GTZ) GmbH."

Dieses Buch versteht sich als Einführung in die Theorie der Lie-Gruppen. Der Begriff der Lie-Gruppen wird ausgehend von den einfachsten Beispielen, den Matrizengruppen, entwickelt. Eine große Anzahl von Problemen für Lie-Gruppen kann man durch Übertragung auf die zugehörigen Lie-Algebren lösen. Dies ist der Leitgedanke des Buches. Vorausgesetzt werden Kenntnisse in der Linearen Algebra, der Differentialrechnung mehrerer Variablen und der elementaren Gruppentheorie.

In the present time, objects generated by computers are replacing models made from wood, wire, and plaster. It is interesting to see how computer graphics can help us to understand the geometry of surfaces and illustrate some recent results on representations of the real projective plane.

Since both the coments and the structure of the book appeared to be successful, only minor changes were made. As the world today has become so complex that humans apparently fail to manage it properly with their intellectual gifts, the realization of this dream might be regarded even as something like a necessity.

This book is based on a lecture course that I gave at the University of Regensburg. The purpose of these lectures was to explain the role of Kähler differential forms in ring theory, to prepare the road for their application in algebraic geometry, and to lead up to some research problems. The text discusses almost exclusively local questions and is therefore written in the language of commutative alge­ bra. The translation into the language of algebraic geometry is easy for the reader who is familiar with sheaf theory and the theory of schemes. The principal goals of the monograph are: To display the information contained in the algebra of Kähler differential forms (de Rham algebra) of a commutative algebra, to int- duce and discuss "differential invariants" of algebras, and to prove theorems about algebras with "differential methods". The most important object we study is the module of Kähler differentials n~/R of an algebra SIR. Like the differentials of analysis, differential modules "linearize" problems, i.e. reduce questions about algebras (non-linear problems) to questions of linear algebra. We are mainly interested in algebras of finite type.

This is a translation of "Auto ur du theoreme de Mordell-Weil", a course given by J . -P. Serre at the College de France in 1980 and 1981. These notes were originally written weekly by Michel Waldschmidt and have been reproduced by Publications Mathematiques de l'Universite de Paris VI, by photocopying the handwritten manuscript. The present translation follows roughly the French text, with many modi­ fications and rearrangements. We have not tried to give a detailed account of the new results due to Faltings, Raynaud, Gross-Zagier . . . ; we have just mentioned them in notes at the appropriate places, and given bibliographical references. Paris, Fall 1988 M. L. Brown J. -P. Serre VII CONTENTS 1. Summary. 1 1. 1. Heights. 3 1. 2. The Mordell-Weil theorem and Mordell's conjecture. 3 1. 3. Integral points on algebraic curves. Siegel's theorem. 4 1. 4. Balcer's method. 5 1. 5. Hilbert's irreducibility theorem. Sieves. 5 2. Heights. 7 2. 1. The product formula. 7 2. 2. Heights on Pm(K). 10 2. 3. Properties of heights. 13 2. 4. Northcott's finiteness theorem. 16 2. 5. Quantitative form of Northcott's theorem. 17 2. 6. Height associated to a morphism rj; : X -t P . 19 n 2. 7. The group Pic(X). 20 2. 8. Heights and line bundles. 22 2. 9. hc = 0(1) {:} c is of finite order (number fields). 24 2. 10. Positivity of the height. 24 2. 11. Divisors algebraically equivalent to zero.

The object of this monograph is to present some optimal design methods in a certain sense for obtaining linear multivariable feedback systems such that they become insensitive or robust properties. The treatment is mainly confined to linear time­ invariant discrete systems with the exception of the sections 3.1 and 3.3 in which it was used linear time-invariant conti­ nuous systems. Sensitivity and robust methods for multivariable feedback systems have been extensively studied about the last decade and the successful development has led to a much better under­ standing of the performance of insensitive and robust proce­ dures. The contribution of this monograph is an improved beha­ viour of the feedback systems under the influence of distur­ bance, parameter variations and/or nonlinear effects with new design methods. Furthermore, in chapter 3 the reader finds improved necessary and sufficient conditions for robust stabi­ lity of the closed-loop system. The authors would like to express their thanks to Mrs. Regina Hade, who typed with great patience our manuscript and Mrs. Monika Thieke who drew the figures and symbols very careful.

In full multigrid methods for elliptic difference equations one works on a sequence of meshes where a number of pre- and/or postsmoothing steps are performed on each level. As is well known these methods can converge very fast on problems with a smooth solution and a regular mesh, but the rate of convergence can be severely degraded for problems with unisotropy or discontinuous coefficients unless some form of robust smoother is used. Also problems can arise with the increasingly coarser meshes because for some types of discretization methods, coercivity may be lost on coarse meshes and on massively parallel computers the computation cost of transporting information between computer processors devoted to work on various levels of the mesh can dominate the whole computing time. For discussions about some of these problems, see (11). Here we propose a method that uses only two levels of meshes, the fine and the coarse level, respec­ tively, and where the corrector on the coarse level is equal to a new type of preconditioner which uses an algebraic substructuring of the stiffness matrix. It is based on the block matrix tridiagonal structure one gets when the domain is subdivided into strips. This block-tridiagonal form is used to compute an approximate factorization whereby the Schur complements which arise in the recursive factorization are approximated in an indirect way, i. e.

The Dutch Association for Numerical Fluid Mechanics (Kontaktgroep Numerieke Stromingsleer, KNSL) was founded in The Netherlands in November 1974. Since then, the Association has organized meetings twice a year. The present volume contains the proceedings of the 25th meeting, held on October 20, 1986, at Delft University of Technology. The purpose of the KNSL is to provide an opportunity for researchers in numerical fluid mechanics to meet regularly and to inform each other about their research in an informal atmosphere. Presentations preferably describe work in progress, and discussion of unsolved problems and unresolved difficulties is encouraged. The working language is Dutch. Nevertheless, science and technology are worldwide activities, and therefore it was decided to publish the proceedings of the 25th meeting in English. The nine contributions to the 25th meeting were selected by profs. A.I. van de Vooren, C.B. Vreugdenhil and the editor. These works are far from covering completely all activity in this field in this country, but they are typical of what is going on. A wide range of subjects is discussed, including fundamental aspects of spectral methods, solution methods for the Euler equations and aeronautical applications, viscous ship hydrodynamics, shallow water equations, viscous flows with capillary and non-Newtonian effects, and turbulent heat transfer with industrial applications. The 25th meeting of the KNSL was supported financially by ECN (Netherlands Energy Research Foundation), MARIN (Maritime Research Institute Netherlands), NLR (National Aerospace Laboratory), WL (Delft Hydraulics Laboratory), VEG Gasinstituut, Delft University of Technology and University of Twente.

The GAMM Committee for Numerical Methods in Fluid Mechanics organizes workshops which should bring together experts of a narrow field of computational fluid dynamics (CFD) to exchange ideas and experiences in order to speed-up the development in this field.

This volume contains 23 contributions to the 10th GAMM-Seminar, which was held in Kiel on the 14-16 of January 1994. The central topics are advanced numerical techniques for solving flow problems. Five papers are devoted to parallel algorithms, a further one to domain decomposition techniques.

This volume contains 18 papers presented at the Kiel Seminar in 1993. 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.