The GAMM Committee for "Efficient Numerical Methods for Partial Differential Equations" organizes workshops on subjects concerning the algorithmical treat ment of partial differential equations. The topics are discretization methods like the finite element and finite volume method for various types of applications in structural and fluid mechanics. Particular attention is devoted to advanced solu tion techniques. th The series of such workshops was continued in 1993, January 22-24, with the 9 Kiel-Seminar on the special topic "Adaptive Methods Algorithms, Theory and Applications" at the Christian-Albrechts-University of Kiel. The seminar was attended by 76 scientists from 7 countries and 23 lectures were given. The list of topics contained general lectures on adaptivity, special discretization schemes, error estimators, space-time adaptivity, adaptive solvers, multi-grid me thods, wavelets, and parallelization. Special thanks are due to Michael Heisig, who carefully compiled the contribu tions to this volume. November 1993 Wolfgang Hackbusch Gabriel Wittum v Contents Page A. AUGE, G. LUBE, D. WEISS: Galerkin/Least-Squares-FEM and Ani- tropic Mesh Refinement. 1 P. BASTIAN, G. WmUM : Adaptive Multigrid Methods: The UG Concept. 17 R. BEINERT, D. KRONER: Finite Volume Methods with Local Mesh Alignment in 2-D. 38 T. BONK: A New Algorithm for Multi-Dimensional Adaptive Nume- cal Quadrature. 54 F.A. BORNEMANN: Adaptive Solution of One-Dimensional Scalar Conservation Laws with Convex Flux. 69 J. CANU, H. RITZDORF : Adaptive, Block-Structured Multigrid on Local Memory Machines. 84 S. DAHLKE, A. KUNaTH: Biorthogonal Wavelets and Multigrid. 99 B. ERDMANN, R.H.W. HOPPE, R.

In the recent decade, there has been a growing interest in the numerical treatment of high-dimensional problems. It is well known that classical numerical discretization schemes fail in more than three or four dimensions due to the curse of dimensionality. The technique of sparse grids helps overcome this problem to some extent under suitable regularity assumptions. This discretization approach is obtained from a multi-scale basis by a tensor product construction and subsequent truncation of the resulting multiresolution series expansion. This volume of LNCSE is a collection of the papers from the proceedings of the workshop on sparse grids and its applications held in Bonn in May 2011. The selected articles present recent advances in the mathematical understanding and analysis of sparse grid discretization. Aspects arising from applications are given particular attention.

This book contains the main results of the German project POPINDA. It surveys the state of the art of industrial aerodynamic design simulations on parallel systems. POPINDA is an acronym for Portable Parallelization of Industrial Aerodynamic Applications. This project started in late 1993. The research and development work invested in POPINDA corresponds to about 12 scientists working full-time for the three and a half years of the project. POPINDA was funded by the German Federal Ministry for Education, Science, Research and Technology (BMBF). The central goals of POPINDA were to unify and parallelize the block-structured aerodynamic flow codes of the German aircraft industry and to develop new algorithmic approaches to improve the efficiency and robustness of these programs. The philosophy behind these goals is that challenging and important numerical appli cations such as the prediction of the 3D viscous flow around full aircraft in aerodynamic design can only be carried out successfully if the benefits of modern fast numerical solvers and parallel high performance computers are combined. This combination is a "conditio sine qua non" if more complex applications such as aerodynamic design optimization or fluid structure interaction problems have to be solved. When being solved in a standard industrial aerodynamic design process, such more complex applications even require a substantial further reduction of computing times. Parallel and vector computers on the one side and innovative numerical algorithms such as multigrid on the other have enabled impressive improvements in scientific computing in the last 15 years.

Advanced numerical simulations that use adaptive mesh refinement (AMR) methods have now become routine in engineering and science. Originally developed for computational fluid dynamics applications these methods have propagated to fields as diverse as astrophysics, climate modeling, combustion, biophysics and many others. The underlying physical models and equations used in these disciplines are rather different, yet algorithmic and implementation issues facing practitioners are often remarkably similar. Unfortunately, there has been little effort to review the advances and outstanding issues of adaptive mesh refinement methods across such a variety of fields. This book attempts to bridge this gap. The book presents a collection of papers by experts in the field of AMR who analyze past advances in the field and evaluate the current state of adaptive mesh refinement methods in scientific computing.

The book concerns theoretical and numerical aspects of systems of conservation laws, which can be considered as a mathematical model for the flows of inviscid compressible fluids. Five leading specialists in this area give an overview of the recent results, which include: kinetic methods, non-classical shock waves, viscosity and relaxation methods, a-posteriori error estimates, numerical schemes of higher order on unstructured grids in 3-D, preconditioning and symmetrization of the Euler and Navier-Stokes equations. This book will prove to be very useful for scientists working in mathematics, computational fluid mechanics, aerodynamics and astrophysics, as well as for graduate students, who want to learn about new developments in this area.

Suitable either as a reference for practising engineers or as a text for a graduate course in adaptive control systems, this is a self-contained compendium of readily implementable adaptive control algorithms. These algorithms have been developed and applied by the authors for over fifteen years to a wide variety of engineering problems including flexible structure control, blood pressure control, and robotics. As such, they are suitable for a wide variety of multiple input-output control systems with uncertainty and external disturbances. The text is intended to enable anyone with knowledge of basic linear multivariable systems to adapt the algorithms to problems in a wide variety of disciplines. Thus, in addition to developing the theoretical details of the algorithms presented, the text gives considerable emphasis to designing algorithms and to representative applications in flight control, flexible structure control, robotics, and drug-infusion control. This second edition makes good use of MATLAB programs for the illustrative examples; these programs are described in the text and can be obtained from the MathWorks file server.

Sparse grids have gained increasing interest in recent years for the numerical treatment of high-dimensional problems. Whereas classical numerical discretization schemes fail in more than three or four dimensions, sparse grids make it possible to overcome the “curse” of dimensionality to some degree, extending the number of dimensions that can be dealt with. This volume of LNCSE collects the papers from the proceedings of the second workshop on sparse grids and applications, demonstrating once again the importance of this numerical discretization scheme. The selected articles present recent advances on the numerical analysis of sparse grids as well as efficient data structures, and the range of applications extends to uncertainty quantification settings and clustering, to name but a few examples.

The 7th Annual European Symposium on Algorithms (ESA ’99) is held in Prague, Czech Republic, July 16-18, 1999. This continued the tradition of the meetings which were held in – 1993 Bad Honnef (Germany) – 1994 Utrecht (Netherlands) – 1995 Corfu (Greece) – 1996 Barcelona (Spain) – 1997 Graz (Austria) – 1998 Venice (Italy) (The proceedingsof previousESA meetings were publishedas Springer LNCS v- umes 726, 855, 979, 1136, 1284, 1461.) In the short time of its history ESA (like its sister meeting SODA) has become a popular and respected meeting. The call for papers stated that the “Symposium covers research in the use, design, and analysis of ef?cient algorithms and data structures as it is carried out in c- puter science, discrete applied mathematics and mathematical programming. Papers are solicited describing original results in all areas of algorithmic research, including but not limited to: Approximation Algorithms; Combinatorial Optimization; Compu- tional Biology; Computational Geometry; Databases and Information Retrieval; Graph and Network Algorithms; Machine Learning; Number Theory and Computer Algebra; On-line Algorithms; Pattern Matching and Data Compression; Symbolic Computation.

This volume contains a selection from the papers presented at the Fifth European Multigrid Conference, held in Stuttgart, October 1996. All contributions were carefully refereed. The conference was organized by the Institute for Computer Applications (ICA) of the University of Stuttgart, in cooperation with the GAMM Committee for Scientific Computing, SFB 359 and 404 and the research network WiR Ba-Wü. 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 focused on algebraic multigrid methods.

This book constitutes the refereed proceedings of the 8th International Conference on High-Performance Computing and Networking, HPCN Europe 2000, held in Amsterdam, The Netherlands, in May 2000. The 52 revised full papers presented together with 34 revised posters were carefully reviewed for inclusion in the book. The papers are organized in sections on problem solving environments, metacomputing, load balancing, numerical parallel algorithms, virtual enterprises and virtual laboratories, cooperation coordination, Web-based tools for tele-working, monitoring and performance, low-level algorithms, Java in HPCN, cluster computing, data analysis, and applications in a variety of fields.