Wolfgang Hackbusch – författare
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35 produkter
35 produkter
708 kr
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C. F. GauS in a letter from Dec. 26, 1823 to Gerling: 3c~ empfe~le 3~nen biegen IDlobu9 aur 9tac~a~mung. ec~werlic~ werben eie ie wieber bi- reet eliminiren, wenigftens nic~t, wenn eie me~r als 2 Unbefannte ~aben. :Da9 inbirecte 93erfa~ren 109st sic~ ~alb im ec~lafe ausfii~ren, ober man fann wo~renb be9gelben an anbere :Dinge benfen. [CO F. GauS: Werke vol. 9, Gottingen, p. 280, 1903] What difference exists between solving large and small systems of equations? The standard methods well-known to any student oflinear algebra are appli- cable to all systems, whether large or small. The necessary amount of work, however, increases dramatically with the size, so one has to search for algo- rithms that most efficiently and accurately solve systems of 1000, 10,000, or even one million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretisation of partial differential equations. In this case, the matrices are sparse (i. e. , they contain mostly zeros) and well-suited to iterative algorithms.Because of the background in partial differential equa- tions, this book is closely connected with the author's Theory and Numerical Treatment of Elliptic Differential Equations, whose English translation has also been published by Springer-Verlag. This book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics.
Del 56 - Springer Series in Computational Mathematics
Tensor Spaces and Numerical Tensor Calculus
Inbunden, Engelska, 2020
1 496 kr
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Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd exceeds the computer memory by far. Since standard methods fail, a particular tensor calculus is needed to treat such problems.
Del 56 - Springer Series in Computational Mathematics
Tensor Spaces and Numerical Tensor Calculus
Häftad, Engelska, 2021
1 496 kr
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Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd exceeds the computer memory by far. Since standard methods fail, a particular tensor calculus is needed to treat such problems.
1 071 kr
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The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the «boundary integral equation method», which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of mathematics. The contents of the first six chapters correspond to an intensive lecture course of four hours per week for a semester. Readers of the book require background from analysis and the foundations of numeri cal mathematics. Knowledge of functional analysis is helpful, but to begin with some basic facts about Banach and Hilbert spaces are sufficient. The theoretical part of this book is reduced to a minimum; in Chapters 2, 4, and 5 more importance is attached to the numerical treatment of the integral equations than to their theory. Important parts of functional analysis (e. g. , the Riesz-Schauder theory) are presented without proof. We expect the reader either to be already familiar with functional analysis or to become motivated by the practical examples given here to read a book about this topic. We recall that also from a historical point of view, functional analysis was initially stimulated by the investigation of integral equations.
Del 102 - Lecture Notes in Computational Science and Engineering
Extraction of Quantifiable Information from Complex Systems
Inbunden, Engelska, 2014
539 kr
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In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 “Mathematical Methods for Extracting Quantifiable Information from Complex Systems.” This volume presents a comprehensive overview of the most important results obtained over the course of the program. Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance. Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges. Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program. The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics today. Since the problem of high-dimensionality appears in many fields of application, the above-mentioned synergy and cross-fertilization effects were expected to make a great impact. To be truly successful, the following issues had to be kept in mind: theoretical research and practical applications had to be developed hand in hand; moreover, it has proven necessary to combine different fields of mathematics, such as numerical analysis and computational stochastics. To keep the whole program sufficiently focused, we concentrated on specific but related fields of application that share common characteristics and as such, they allowed us to use closely related approaches.
Del 95 - Applied Mathematical Sciences
Iterative Solution of Large Sparse Systems of Equations
Inbunden, Engelska, 2016
1 101 kr
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In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature.The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms.The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.
Del 102 - Lecture Notes in Computational Science and Engineering
Extraction of Quantifiable Information from Complex Systems
Häftad, Engelska, 2016
539 kr
Skickas inom 10-15 vardagar
In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 “Mathematical Methods for Extracting Quantifiable Information from Complex Systems.” This volume presents a comprehensive overview of the most important results obtained over the course of the program. Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance. Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges. Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program. The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics today. Since the problem of high-dimensionality appears in many fields of application, the above-mentioned synergy and cross-fertilization effects were expected to make a great impact. To be truly successful, the following issues had to be kept in mind: theoretical research and practical applications had to be developed hand in hand; moreover, it has proven necessary to combine different fields of mathematics, such as numerical analysis and computational stochastics. To keep the whole program sufficiently focused, we concentrated on specific but related fields of application that share common characteristics and as such, they allowed us to use closely related approaches.
Del 95 - Applied Mathematical Sciences
Iterative Solution of Large Sparse Systems of Equations
Häftad, Engelska, 2018
1 101 kr
Skickas inom 5-8 vardagar
In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature.The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms.The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.
Del 51 - Notes on Numerical Fluid Mechanics
Numerical Treatment of Coupled Systems
Proceedings of the Eleventh GAMM-Seminar, Kiel, January 20–22, 1995
Häftad, Engelska, 2012
1 071 kr
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The GAMM Committee for "Efficient Numerical Methods for Partial Differential Equations" organizes seminars and workshops on subjects concerning the algorithmic treatment of partial differential equations. The topics are discretisation methods like the finite element and the boundary element method for various type of applications in structural and fluid mechanics. Particular attention is devoted to the advanced solution methods. The series of such seminars was continued in 1995, January 20-22, with the 11th Kiel-Seminar on the special topic Numerical Treatment of Coupled Systems at the Christian-Albrechts-University of Kiel. The seminar was attended by 100 scientist from 9 countries. 23 lectures were given, including two survey lectures. Different kinds of couplings are considered in this volume. The coupling of different components may occur in the physical model. On the other hand, a coupling of subsystems can be generated by the numerical solution technique. General examples of the latter kind are the domain decomposition (see p. 128) or subspace decomposition (p. 117). The local defect correction method couples different discretizations of the same problem in order to improve the results, although the basic linear system to be solved remains unchanged (p. 47). In general, the aim of the numerical coupling is to make use of (efficient) subsystem solvers (p. 1). The combination of different discretization techniques is mentioned on page 59.
Boundary Elements: Implementation and Analysis of Advanced Algorithms
Proceedings of the Twelfth GAMM-Seminar Kiel, January 19–21, 1996
Häftad, Engelska, 2012
1 071 kr
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The GAMM Committee for "Efficient Numerical Methods for Partial Differential Equations" organizes seminars and workshops on subjects concerning the algorithmic treatment of partial differential equations. The topics are discretisation methods like the finite element and the boundary element method for various type of applications in struc tural and fluid mechanics. Particular attention is devoted to advanced solution method". The latest seminar in this series was the 12th Kiel-Seminar which took place on January 19-21, 1996 at Christian-Albrechts-University of Kiel and focussed on the topic Boundary Elements: Implementation and Analysis of Advanced Algorithms. The seminar was attended by 65 scientists from 10 countries. 23 lectures were given, including two survey lectures. In the last years, a remarkable progress in the numerical treatment of boundary de ment methods (BEM) has been obtained in Germany. This is, in particular, a res~I1t of a Schwerpunktverfahren supported by the DFG. Many aspects of the BEM are not ouly analysed but also implemented. Therefore, these proceedings present a number of papers on implementational aspects besides the analysis of advanced techniques.
454 kr
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504 kr
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Die Integralgleichungen stellen ein Gebiet dar. das für sich durchaus selbständig ist und auf einer interessanten Mischung von Analysis. Funktionentheorie und Funktionalanalysis beruht. Auf der anderen Seite gewinnen die Integralgleichungen ihr praktisches Interesse aus der «Integralgleichungsmethode». die es erlaubt, partielle Differential gleichungen in Integralgleichungen umzuformen. Das Buch ist aus Vorlesungen hervorgegangen, die der Autor an der Ruhr-Universität Bochum und der Christian-Albrechts-Universität Kiel gehalten hat. Der Umfang der Kapitel 1 bis 6 entspricht etwa einer intensiven vierstündigen Vorlesung. Das Studium der Integral gleichungen kann mit Vorkenntnissen der Analysis und den Grundlagen der Numerik aufgenommen werden. Kenntnisse aus der Funktional analysis sind hilfreich. aber nicht unabdingbar, wenn Grundbegriffe wie Banach-und Hilbert-Räume geläufig sind. Der Theorieteil dieses Buches ist so knapp wie möglich bemessen. da die Numerik in den Kapiteln 2. 4, 5 im Vordergrund stehen soll. Wichtige Teile der benötigten Funktionalanalysis wie etwa die Riesz-Schauder-Theorie werden ohne Herleitung wiedergegeben. Es wird dabei davon ausgegangen. daß dem Leser dieses Gebiet entweder aus einer Vorlesung über «Funktionalanalysis» bekannt ist oder daß e- mit gesteigerter Motivation durch praktische Beispiele - diese Kapitel durch Vorlesungen oder Lektüre nachholen wird. Es sei daran erinnert. daß auch historisch die Funktionalanalysis aus der Diskussion der Integralgleichungen hervorgegangen ist. Als Funktionenräume werden in dieser Darstellung vornehmlich die klassischen der stetigen oder Hölder-stetigen Funktionen verwendet. Die Sobolev-Räume werden weitgehend vermieden. was zum Beispiel zur Folge hat. daß dieIntegraloperatoren hier nicht in der erforderlichen Allgemeinheit als Pseudodifferentialoperatoren diskutiert werden können.
Numerical Treatment of the Navier-Stokes Equations
Proceedings of the Fifth GAMM-Seminar, Kiel, January 20–22, 1989
Häftad, Tyska, 1990
554 kr
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Numerical Techniques for Boundary Element Methods
Proceedings of the Seventh GAMM-Seminar Kiel, January 25–27, 1991
Häftad, Tyska, 1992
554 kr
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Del 29 - Notes on Numerical Fluid Mechanics and Multidisciplinary Design
Incomplete Decomposition (ILU) — Algorithms, Theory, and Applications
Proceedings of the Eighth GAMM-Seminar, Kiel, January 24–26, 1992
Häftad, Tyska, 1993
554 kr
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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.
Fast Solvers for Flow Problems
Proceedings of the Tenth GAMM-Seminar Kiel, January 14–16, 1994
Häftad, Tyska, 1995
554 kr
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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. The Navier-Stokes equations are discussed with respect to anisotropically refined meshes, in combination with non-equilibrium chemistry and with respect to implicit time-discretizations and parallel solvers. Furthermore, robust multi-grid methods are described for this problem. Five papers are devoted to parallel algorithms, and a further one to domain decomposition techniques. The very important aspect of adaptive strategies is considered in several contributions, including a discussion of appropriate error estimators. Other subjects are the FEM-BEM coupling, convection-dominated systems, unstructured grid techniques and complex geometries in 3-D.
Del 10 - Notes on Numerical Fluid Mechanics and Multidisciplinary Design
Efficient Solutions of Elliptic Systems
Proceedings of a GAMM-Seminar Kiel, January 27 to 29, 1984
Häftad, Tyska, 1984
554 kr
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Del 11 - Notes on Numerical Fluid Mechanics and Multidisciplinary Design
Advances in Multi-Grid Methods
Proceedings of the conference held in Oberwolfach, December 8 to 13, 1984
Häftad, Tyska, 1985
554 kr
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Del 21 - Notes on Numerical Fluid Mechanics
Panel Methods in Fluid Mechanics with Emphasis on Aerodynamics
Proceedings of the Third GAMM-Seminar Kiel, January 16 to 18, 1987
Häftad, Tyska, 1988
703 kr
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Del 23 - Notes on Numerical Fluid Mechanics and Multidisciplinary Design
Robust Multi-Grid Methods
Proceedings of the Fourth GAMM-Seminar, Kiel, January 22 to 24,1988
Häftad, Tyska, 1989
554 kr
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Del 4 - Springer Series in Computational Mathematics
Multi-Grid Methods and Applications
Inbunden, Engelska, 1985
1 815 kr
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Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.).
Del 1228 - Lecture Notes in Mathematics
Multigrid Methods II
Proceedings of the 2nd European Conference on Multigrid Methods Held at Cologne, October 1-4, 1985
Häftad, Engelska, 1986
379 kr
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Del 28 - Lecture Notes in Computational Science and Engineering
Computational Electromagnetics
Proceedings of the GAMM Workshop on Computational Electromagnetics, Kiel, Germany, January 26–28, 2001
Häftad, Engelska, 2003
1 071 kr
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The contributions in this book by leading international experts in the field of electromagnetic field computation cover a wide area of contemporary research activities. They clearly underline the important role of modeling, analysis and numerical methods to provide powerful tools for the simulation of electromagnetic phenomena. The main topics range from the mathematical analysis of Maxwell's equations including its proper spatial discretizations (edge elements, boundary element methods, finite integration), and efficient iterative solution techniques (multigrid, domain decomposition) to multiscale aspects in micromagnetics. The reader will get acquainted with many facets of modern computational techniques and its applications to relevant problems in electromagnetism.
Del 3 - Lecture Notes in Computational Science and Engineering
Multigrid Methods V
Proceedings of the Fifth European Multigrid Conference held in Stuttgart, Germany, October 1–4, 1996
Häftad, Engelska, 1998
1 071 kr
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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.
703 kr
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Bei der Diskretisierung von Randwertaufgaben und Integralgleichungen entstehen große, eventuell auch voll besetzte Matrizen. Es wird eine neuartige Methode dargestellt, die es erstmals erlaubt, derartige Matrizen nicht nur effizient zu speichern, sondern auch alle Matrixoperationen einschließlich der Matrixinversion bzw. der Dreieckszerlegung approximative durchzuführen. Anwendungen findet diese Technik nicht nur bei der Lösung großer Gleichungssysteme, sondern auch bei Matrixgleichungen und der Berechnung von Matrixfunktionen.
Del 4 - Springer Series in Computational Mathematics
Multi-Grid Methods and Applications
Häftad, Engelska, 2010
1 555 kr
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Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. The reader finds here an elementary introduction to multi-grid algorithms as well as a comprehensive convergence analysis. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.). The book also contains a complete presentation of the multi-grid method of the second kind, which has important applications to integral equations (e.g. the "panel method") and to numerous other problems. Readers with a practical interest in multi-grid methods will benefit from this book as well as readers with a more theoretical interest.
2 017 kr
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Special numerical techniques are already needed to deal with nxn matrices for large n.Tensor data are of size nxnx...xn=n^d, where n^d exceeds the computer memory by far. Since standard methods fail, a particular tensor calculus is needed to treat such problems.
Del 45 - Springer Series in Computational Mathematics
Concept of Stability in Numerical Mathematics
Inbunden, Engelska, 2014
539 kr
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In this book, the author compares the meaning of stability in different subfields of numerical mathematics.Concept of Stability in numerical mathematics opens by examining the stability of finite algorithms. A more precise definition of stability holds for quadrature and interpolation methods, which the following chapters focus on. The discussion then progresses to the numerical treatment of ordinary differential equations (ODEs). While one-step methods for ODEs are always stable, this is not the case for hyperbolic or parabolic differential equations, which are investigated next. The final chapters discuss stability for discretisations of elliptic differential equations and integral equations.In comparison among the subfields we discuss the practical importance of stability and the possible conflict between higher consistency order and stability.
305 kr
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Das Verständnis der numerischen Behandlung elliptischer Differentialgleichungen erfordert notwendigerweise auch die Kenntnisse der Theorie der Differentialgleichungen. Deshalb behandelt das Buch beide parallel. Zunächst wird der klassische Zugang (starke Lösungen, Differenzenverfahren) beschrieben. Dem Maximum-Minimum-Prinzip auf der theoretischen Seite entsprechen beispielsweise die Eigenschaften der M-Matrizen, die sich bei der Diskretisierung ergeben. Nach einem Exkurs über die Funktionalanalysis werden die Variationsformulierung und die Finite-Element-Diskretisierungen behandelt. Weitere Themen sind die Analyse der Diskretisierungen von Eigenwertaufgaben und die Stokes-Gleichungen mit den inf-sup-Bedingungen für die Finite-Element-Diskretisierung. Auf der theoretischen Seite wird die Regularität der Lösungen näher untersucht.Gegenüber der zweiten Auflage enthält der vorliegende Text zahlreiche Aktualisierungen, vor allem im Bereich der Finiten Elemente sowie in den Literaturangaben. Außerdem wurden die vollständigen Lösungen der Übungsaufgaben hinzugefügt.
Del 49 - Springer Series in Computational Mathematics
Hierarchical Matrices: Algorithms and Analysis
Inbunden, Engelska, 2015
1 101 kr
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This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix.The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition.Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchicalmatrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.