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62 produkter
62 produkter
E-bok
PDF, Engelska, 2012712 kr
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This book presents the description of the state of the modern iterative techniques together with systematic analysis. It discusses classical methods, semi-iterative techniques, incomplete decompositions, conjugate gradient methods, multigrid methods and domain decomposition techniques. Every technique described is illustrated by a Pascal program.
Häftad, Engelska, 2011
727 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
1 524 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. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.
E-bok
PDF, Engelska, 20191 891 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. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.
Del 56 - Springer Series in Computational Mathematics
Tensor Spaces and Numerical Tensor Calculus
Häftad, Engelska, 2021
1 524 kr
Skickas inom 10-15 vardagar
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. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.
E-bok
PDF, Engelska, 20121 416 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 120 - International Series of Numerical Mathematics
Integral Equations
Theory and Numerical Treatment
Häftad, Engelska, 2011
1 091 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
549 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.
E-bok
PDF, Engelska, 2014712 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
1 091 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.
E-bok
PDF, Engelska, 20162 366 kr
Läs direkt efter köp
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
549 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
1 130 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.
E-bok
PDF, Tyska, 2019437 kr
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E-bok
PDF, Tyska, 2013570 kr
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E-bok
PDF, Engelska, 20131 416 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.
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
1 092 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.
E-bok
PDF, Engelska, 20131 416 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.
Häftad, Engelska, 2012
1 092 kr
Skickas inom 10-15 vardagar
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.
E-bok
PDF, Tyska, 2013449 kr
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Häftad, Tyska, 1986
464 kr
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Häftad, Tyska, 1989
514 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.
Häftad, Tyska, 1990
565 kr
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Häftad, Tyska, 1992
565 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
565 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.
Häftad, Tyska, 1995
565 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
565 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
565 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
717 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
565 kr
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