Dietmar Kröner - Böcker
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This book systematically studies upwind methods for initial value problems for scalar conservation laws in one- and multidimensions. The mathematical theory of convergence theory and of a priori error estimates is presented in detail for structure (finite difference methods) as well as for unstructured grids (finite volume methods). Higher order schemes are also included. In the second part of the book the algorithms for scalar equations are generalized into systems of conversation laws in one- and multidimensions. The most powerful schemes for the discretization of systems are described and numerical examples are presented. In particular, local grid refinement has been taken into account. The initial boundary value problem is also considered for linear systems and nonlinear scalar conservation laws.
Del 5 - Lecture Notes in Computational Science and Engineering
Introduction to Recent Developments in Theory and Numerics for Conservation Laws
Proceedings of the International School on Theory and Numerics for Conservation Laws, Freiburg/Littenweiler, October 20–24, 1997
Häftad, Engelska, 1998
540 kr
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The importance of hyperbolic conservation laws for scientific and industrial applications has led to a growing amount of research activity in this field. A variety of physical phenomena in fluid mechanics, astrophysics, groundwa- ter flow, meteorology, reactive flow and several other areas can be effectively modeled by systems of conservation laws. In order to focus recent trends in theory and numerics in this research area and to stimulate further research in this field, we decided to organize the "International School on Theory and Numerics for Conservation Laws", which took place in FreiburgjLittenweiler, Germany, from 20 to 24 October 1997. The school was sponsored by the DFG-Graduiertenkolleg "Nichtlineare Dif- ferentialgleichungen, Modellierung, Theorie, Numerik, Visualisierung" at the University of Freiburg. It was attended by about 60 young international re- searchers. This volume contains the contributions of the five main lecturers of the school. Each article covers five hours of lectures on a specific new research area in the field of theory and numerics for conservation laws. Reviews of recent de- velopments are given, accompanied by new research results of the authors.The topics include a kinetic approach to conservation laws by Benoit Perthame, which can be used for the construction of approximate Riemann solvers for the full system of gas dynamics. Several ideas related to the stability and entropy analysis are discussed.
Del 115 - Notes on Numerical Fluid Mechanics and Multidisciplinary Design
Computational Science and High Performance Computing IV
The 4th Russian-German Advanced Research Workshop, Freiburg, Germany, October 12 to 16, 2009
Inbunden, Engelska, 2011
2 118 kr
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This volume contains 27 contributions to the Forth Russian-German Advanced Research Workshop on Computational Science and High Performance Computing presented in October 2009 in Freiburg, Germany. The workshop was organized jointly by the High Performance Computing Center Stuttgart (HLRS), the Institute of Computational Technologies of the Siberian Branch of the Russian Academy of Sciences (ICT SB RAS) and the Section of Applied Mathematics of the University of Freiburg (IAM Freiburg) The contributions range from computer science, mathematics and high performance computing to applications in mechanical and aerospace engineering. They show a wealth of theoretical work and simulation experience with a potential of bringing together theoretical mathematical modelling and usage of high performance computing systems presenting the state of the art of computational technologies.
Computational Science and High Performance Computing IV
The 4th Russian-German Advanced Research Workshop, Freiburg, Germany, October 12 to 16, 2009
Häftad, Engelska, 2014
2 118 kr
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This volume contains 27 contributions to the Forth Russian-German Advanced Research Workshop on Computational Science and High Performance Computing presented in October 2009 in Freiburg, Germany. The workshop was organized jointly by the High Performance Computing Center Stuttgart (HLRS), the Institute of Computational Technologies of the Siberian Branch of the Russian Academy of Sciences (ICT SB RAS) and the Section of Applied Mathematics of the University of Freiburg (IAM Freiburg) The contributions range from computer science, mathematics and high performance computing to applications in mechanical and aerospace engineering. They show a wealth of theoretical work and simulation experience with a potential of bringing together theoretical mathematical modelling and usage of high performance computing systems presenting the state of the art of computational technologies.
Die geheime Macht der Zahlen
Mathematik hinter Aschewolken, Verkehrsplanung, Steuerbetrug und Golfbällen
Häftad, Tyska, 2025
256 kr
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Dieses Buch zeigt die Schönheit, Möglichkeiten und Wirkungsmacht der Mathematik mit besonderem Fokus auf der Angewandten Mathematik. Die Simulation der Ausbreitung von Flugasche, des Abschmelzens von Gletschern, der Verkehrsplanung, von Überschwemmungen und Tsunamis, Crashtests, der Wettervorhersage, des Designs von Golfbällen und Segelbooten sind Herausforderungen für die Mathematik.In diesem Buch werden jeweils die Fragestellung des Problems und die Ergebnisse, sowie die persönlichen Erfahrungen, die der Autor bei der Bearbeitung einiger solcher Probleme gemacht hat, dargestellt. Während zur Bearbeitung dieser Probleme Höchstleistungscomputer notwendig sind, geht es im zweiten Teil des Buches um Probleme, die man auch mit Papier und Bleistift lösen kann. Interessante Begebenheiten aus dem Mathematischen Forschungsinstitut Oberwolfach sind Gegenstand eines weiteren Kapitels. Das Buch richtet sich an Leser ohne mathematisches Hintergrundwissen. Formeln werden weitgehend vermieden und kommen nur im Anhang vor.
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Henry Görtler hat nach dem zweiten Weltkrieg das Institut für Angewandte Mathematik an der Universität Freiburg gegründet. Er war einer der „profiliertesten Mathematiker“ an der Schnittstelle Angewandte Mathematik, Numerik und Strömungsmechanik. Er gehörte zu den Mitbegründern der Gesellschaft für mathematische Forschung des „Mathematischen Forschungsinstituts in Oberwolfach“, war Präsident der GAMM und von IUTAM.Vor dem Krieg war er Mitglied der NSDAP und der SA, Mitarbeiter von Ludwig Prandtl, hat als Wissenschaftler seine Karriere vor 1945 begonnen, war intensiv in die Arbeiten, auch kriegsrelevanten Arbeiten, des Kaiser-Wilhelm-Instituts (KWI) für Strömungsforschung in Göttingen involviert und hat 1936 einen NS-konformen Aufsatz veröffentlicht. Auszug: „Daseinsrecht hat insbesondere die Mathematik dann, wenn sie kraftvoller Ausdruck nordisch-deutschen Geistes ist. Daseinsrecht hat mathematisches Denken dann nicht, wenn es einer uns fremden und entgegengesetzten Geisteshaltung entspringt, … Was ist in der Mathematik in seiner Artgebundenheit Ausdruck rassischen Stils, was dagegen artunabhängig bloße Eigenschaft?“