Michael Griebel Livres

The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is an extremely active research field, both in the mathematics and engineering communities. Meshfree methods are becoming increasingly mainstream in various applications. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the papers from the proceedings of the Fifth International Workshop on Meshfree Methods, held in Bonn in August 2009. The articles address the different meshfree methods and their use in applied mathematics, physics and engineering. The volume is intended to foster this highly active and exciting area of interdisciplinary research and to present recent advances and findings in this field.

The book integrates theoretical analysis, numerical simulation and modeling approaches for the treatment of singular phenomena. The projects covered focus on actual applied problems, and develop qualitatively new and mathematically challenging methods for various problems from the natural sciences. Ranging from stochastic and geometric analysis over nonlinear analysis and modelling to numerical analysis and scientific computation, the book is divided into the three sections: A) Scaling limits of diffusion processes and singular spaces, B) Multiple scales in mathematical models of materials science and biology and C) Numerics for multiscale models and singular phenomena. Each section addresses the key aspects of multiple scales and model hierarchies, singularities and degeneracies, and scaling laws and self-similarity.

Meshfree methods, particle methods, and generalized finite element methods have witnessed substantial development since the mid 1990s. The growing interest in these methods is due in part to the fact that they are extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity. Furthermore, meshfree methods offer a number of advantageous features which are especially attractive when dealing with multiscale phenomena: a priori knowledge about particular local behavior of the solution can easily be introduced in the meshfree approximation space, and coarse-scale approximations can be seamlessly refined with fine-scale information. This volume collects selected papers presented at the Seventh International Workshop on Meshfree Methods, held in Bonn, Germany in September 2013. They address various aspects of this highly dynamic research field and cover topics from applied mathematics, physics and engineering.

There have been substantial developments in meshfree methods, particle methods, and generalized finite element methods since the mid 1990s. The growing interest in these methods is in part due to the fact that they offer extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity. Furthermore, meshfree methods have a number of advantageous features that are especially attractive when dealing with multiscale phenomena: A-priori knowledge about the solution’s particular local behavior can easily be introduced into the meshfree approximation space, and coarse scale approximations can be seamlessly refined by adding fine scale information. However, the implementation of meshfree methods and their parallelization also requires special attention, for instance with respect to numerical integration.

Particle models play an important role in many applications in physics, chemistry and biology. They can be studied on the computer with the help of molecular dynamics simulations. This book presents in detail both the necessary numerical methods and techniques (linked-cell method, SPME-method, tree codes, multipole technique) and the theoretical background and foundations. It illustrates the aspects modelling, discretization, algorithms and their parallel implementation with MPI on computer systems with distributed memory. Furthermore, detailed explanations are given to the different steps of numerical simulation, and code examples are provided. With the description of the algorithms and the presentation of the results of various simulations from the areas material science, nanotechnology, biochemistry and astrophysics, the reader of this book will be able to write his own programs for molecular dynamics step by step and to run successful experiments.

Das Buch behandelt Methoden des wissenschaftlichen Rechnens in der Moleküldynamik, einem Bereich, der in vielen Anwendungen der Chemie, der Biowissenschaften, der Materialwissenschaften, insbesondere der Nanotechnologie, sowie der Astrophysik eine wichtige Rolle spielt. Es führt in die wichtigsten Simulationstechniken zur numerischen Behandlung der Newtonschen Bewegungsgleichungen ein. Der Schwerpunkt liegt hierbei auf der schnellen Auswertung kurz- und langreichweitiger Kräfte mittels Linked Cell-, P$/\3$M-, Baum- und Multipol-Verfahren, sowie deren paralleler Implementierung und Lastbalancierung auf Rechensystemen mit verteiltem Speicher. Die einzelnen Kapitel beinhalten darüberhinaus detailierte Hinweise, um die Verfahren Schritt für Schritt in ein Programmpaket umzusetzen. In zahlreichen farbigen Abbildungen werden Simulationsergebnisse für eine Reihe von Anwendungen präsentiert.

Die numerische Simulation stellt eine Verbindung zwischen dem praktischen Experiment und dem theoretischen Ansatz her und wird in Zukunft zu einer Schlüsseltechnologie heranwachsen. Eine entscheidende Rolle kommt hier der interdisziplinären Zusammenarbeit von Ingenieuren, Informatikern und Mathematikern zu. Dieses Buch gibt am Beispiel der Strömungsmechanik eine Einführung in die numerische Simulation und beleuchtet auf einfache Weise deren vielfältige Aspekte von der Modellbildung über Diskretisierung, Algorithmen und schnelle Löser, Parallelisierung bis hin zur Visualisierung. Neben der Beschreibung der einzelnen Schritte bei der numerischen Simulation werden auch detaillierte Hinweise zur Umsetzung in ein Computerprogramm gegeben. In zahlreichen Abbildungen werden Simulationsergebnisse präsentiert, die den Leser dazu animieren, ein Simulationsprogramm zu erstellen und es für eigene Berechnungen zu nutzen. Das Buch richtet sich an Studierende der Fachrichtungen Physik, Maschinenwesen, Informatik und Mathematik, sowie an Naturwissenschaftler und Ingenieure, die im Selbststudium erste Einblicke in die numerische Simulation von Strömungen erhalten wollen.

InhaltsverzeichnisOn the Necessity of Supporting Research.Parallel Computer Architectures for Numerical Simulation.Design Optimization of High Performance Satellites.Numerical Simulations of Dynamical Ginzburg-Landau Vortices in Superconductivity.High Performance Scientific Computing and its Application in Solving Engineering Problems.Computational Fluid Dynamics with FIRE on Massive Parallel Computers.Distributed Numerical Simulation on Workstation Networks.European Developments in High Performance Computing — A Comparison with Developments in Other OECD Countries.High-Performance Computing in Fluid Mechanics.Process Simulation for the Semiconductor Industry.Numerical Simulation of Crystal Growth Processes.Quantum Monte Carlo Simulations and Weak-Coupling Approximations for the Three-Band Hubbard Model.Dynamic Systems Visualization Applied to Flight Mechanics Problems.Efficient Methods and Parallel Computing in Numerical Fluid Mechanics.