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.
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 f...
In full multigrid methods for elliptic difference equations one works on a sequence of meshes where a number of pre- and/or postsmoothing steps are performed on each level. As is well known these methods can converge very fast on problems with a smooth solution and a regular mesh, but the rate of convergence can be severely degraded for problems with unisotropy or discontinuous coefficients unless some form of robust smoother is used. Also problems can arise with the increasingly coarser meshes because for some types of discretization methods, coercivity may be lost on coarse meshes and on...
In full multigrid methods for elliptic difference equations one works on a sequence of meshes where a number of pre- and/or postsmoothing steps are pe...
Dieses Buch ist aus Vorlestmgen entstanden, die der Autor an der Ruhr-Universitiit Bochum und an der Christian-Albrechts-Universitiit Kiel fUr Studenten der Mathematik gehalten hat. Die vorliegende Abhandltmg beschriinkt sich auf partielle Differentialgleichtmgen yom ell i p tis c hen Typ, da andemfalls die Darstelltmg entweder zu oberfliichlich oder zu umfangreich geriete. Die folgende Skizze zeigt, welche Aufgaben sich bei elliptischen Differentialgleichungen ergeben. A: Theorie der B: Diskretisierungen C: Numerische Analyse: elliptischen (Differenzenverfahren, Konvergenz, Gleichtmgen...
Dieses Buch ist aus Vorlestmgen entstanden, die der Autor an der Ruhr-Universitiit Bochum und an der Christian-Albrechts-Universitiit Kiel fUr Student...
The GAMM Committee for Efficient Numerical Methods for Par- tial Differential Equations (GAMM-FachausschuB "Effiziente numerische Verfahren fUr partielle Differenzialgleichungen") organizes conferences and seminars on subjects concerning the algorithmic treatment of partial differential equation prob- lems. The first seminar "Efficient Solution of Elliptic Systems" was followed by a second one held at the University of Kiel from January 17th to January 19th, 1986. The title was "Efficient Numerical Methods in Continuum Mechanics." The equations arising in continuum mechanics have many con-...
The GAMM Committee for Efficient Numerical Methods for Par- tial Differential Equations (GAMM-FachausschuB "Effiziente numerische Verfahren fUr partie...
The GAMM Committee l'or Efficient Numerical l1ethods l'or Partial Differential Equations (GAMM FachausschuB "Effiziente Numerische Verf'ahren fiir Partielle Differentialgleichungen") organizes conferences and serninars on subjects concerning the algorit hmic treatment of partial differential equation problerns. The two flrst serninars "Efficient Solution of Elliptic Systems" 098S) and "Efficient Numerical Methods in Continuum Mechanics" (986) were followed by a third one, co-organized together with the GAMM Committee l'or Dlscre tizing Methods in Solid Mechanics and the special re search...
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...
This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but ...
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...
In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content descr...
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....
In this book, the author compares the meaning of stability in different subfields of numerical mathematics.
Das Verstandnis der numerischen Behandlung elliptischer Differentialgleichungen erfordert notwendigerweise auch die Kenntnisse der Theorie der Differentialgleichungen. Deshalb behandelt das Buch beide parallel. Zunachst wird der klassische Zugang (starke Losungen, 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 uber die Funktionalanalysis werden die Variationsformulierung und die Finite-Element-Diskretisierungen behandelt. Weitere...
Das Verstandnis der numerischen Behandlung elliptischer Differentialgleichungen erfordert notwendigerweise auch die Kenntnisse der Theorie der Differe...
