Refine
Year of publication
Document Type
- Article (2178)
- ZIB-Report (1758)
- In Proceedings (1322)
- Master's Thesis (284)
- Book chapter (166)
- Doctoral Thesis (163)
- Other (99)
- Bachelor's Thesis (69)
- In Collection (66)
- Book (65)
Keywords
- integer programming (36)
- mixed integer programming (34)
- KOBV (33)
- optimal control (32)
- Annual Report (28)
- Kooperativer Bibliotheksverbund Berlin-Brandenburg (24)
- Mixed Integer Programming (21)
- Bibliotheksverbund (20)
- Integer Programming (19)
- mixed-integer programming (19)
Institute
- Numerical Mathematics (1502)
- Mathematical Optimization (1271)
- Visual and Data-centric Computing (1139)
- Visual Data Analysis (1017)
- ZIB Allgemein (951)
- Computational Nano Optics (496)
- Distributed Algorithms and Supercomputing (489)
- Modeling and Simulation of Complex Processes (398)
- Visual Data Analysis in Science and Engineering (378)
- Therapy Planning (315)
An Adaptive Finite Element Method for Convection-Diffusion Problems by Interpolation Techniques.
(1991)
For adaptive solution of convection- difussion problems with the streamline-diffusion finite element method, an error estimator based on interpolation techniques is developed. It can be shown that for correctness of this error estimator a restriction of the maximum angle is to be sufficient. Compared to usual methods, the adaptive process leads to more accurate solutions at much less computational cost. Numerical tests are enclosed. {\bf Keywords: } Adaptive finite elements, convection- diffusion equation, internal and boundary layers, streamline-diffusion. {\bf Subject Classifications:} AMS(MOS): 65N15, 65N30
A high resolution Godunov-type method is developed and applied to a two-dimensional version of the Burgers equation. On one-dimensional testproblems the scheme is second order accurate for smooth flow and resolves discontinuities sharply. On two-dimensional problems, however, large numerical oscillations are introduced when discontinuities traveling obliquely to the grid directions are present. These oscillations are caused by a Strang- type operator splitting, and cannot be eliminated using flux limiters or small timesteps. {\bf Keywords:} High resolution methods, Godunovs method, operator splitting, complex Burgers equation. {\bf AMS:} 35: A40, L45, L60, L65, L, 67. 65: M05, M10.
Mit zunehmender Dezentralisierung im Bereich des Wissenschaftlichen Rechnens steigt auch der Bedarf an Softwarequellen qualitativ hochwertiger mathematischer Algorithmen. Für den Software- und Informationsaustausch wird die Einrichtung öffentlicher, elektronischer Softwarebibliotheken vorgeschlagen. Am Beispiel der eLib des ZIB werden die notwendigen technischen Konzepte, die u.a. auch in den heutigen Gegebenheiten der technischen Kommunikation begründet sind, diskutiert. Die eLib ist fenster- und menüorientiert aufgebaut und folglich im Dialog sehr einfach zu benutzen. Sie kann aber auch mit ihrer Kommandosprache allein auf dem Wege über elektronische Post abgefragt werden. Über die eLib sind, nach dem Verbund mit den Netzbibliotheken NetLib und Reduce-NetLib jetzt etwa 6000 mathematische Programme und allgemeine Dokumente verfügbar. Das Dienstleistungsangebot der eLib setzt Beiträge aus einer aktiven Benutzergemeinschaft voraus. Es besteht die Hoffnung, daß durch den öffentlichen Softwareaustausch sich Entwickler und Anwender wechselseitig in ihrer Arbeit befruchten.
The C-implementation of KASKADE, an adaptive solver for linear elliptic differential equations in 2D, is object of a set of numerical experiments to analyze the use of resources (time and memory) with respect to numerical accuracy. We study the dependency of the reliability, robustness, and efficiency of the program from the parameters controlling the algorithm.
Part III of the paper is devoted to the construction of an adaptive FEM solver in two spatial dimensions, which is able to handle the singularly perturbed elliptic problems arising from discretization in time. The problems of error estimation and multilevel iterative solution of the linear systems - both uniformly well behaved with respect to the time step - can be solved simultaneously within the framework of preconditioning. A multilevel nodal basis preconditioner able to handle highly nonuniform meshes is derived. As a numerical example an application of the method to the bioheat-transfer equation is included. {\bf AMS CLASSIFICATION:} 65F10, 65F35, 65M50, 65M60, 65N30.
A variety of secant methods has been revisited in view of the construction of iterative solvers for large nonsymmetric linear systems $ Ax = b $ stemming from the discretization of convection diffusion equations. In the first section, we tried to approximate $ A ^{-1} $ directly. Since the sparsity structure of A- is not known, additional storage vectors are needed during the iteration. In the next section, an incomplete factorization $ LU $ of $ A $ is the starting point and we tried to improve this easy invertible approximation of $ A $. The update is constructed in such a way that the sparsity structure of $ L $ and $ U $ is maintained. Two different sparsity preserving updates are investigated from theoretical and practical point of view. Numerical experiments on discretized PDEs of convection diffusion type in 2- D with internal layers and on "arbitrary" matrices with symmetric sparsity structure are given. {\bf Key words:} nonsymmetric linear system, sparse secant method, Broyden's method, incomplete factorization.
The discrete Galerkin method developed by the authors has turned out to be an efficient tool for the computational treatment of very large scale ODE systems arising in polyreaction kinetics. Up to now, this approach has been worked out in detail for homogeneous polymer reactions. The present paper deals with one line of possible extensions of the method to the case of so-called heterogeneous processes, which may appear e. g. in smog reactions. The associated mathematical models involve reaction coefficients depending on the chain length of the reacting polymer. The herein suggested extension is worked out in some detail on the basis of the earlier paper. In addition, a numerical example describing polymer degradation is included.
This report presents the final realization and implementation of a global inexact Newton method proposed by Deuflhard. In order to create a complete piece of software, a recently developed iterative solver (program GBIT) due to Deuflhard, Freund, Walter is adapted and serves as the standard iterative linear solver. Alternative linear iterative solvers may be adapted as well, e.g. the widely distributed code GMRES. The new software package GIANT (Global Inexact Affine Invariant Newton Techniques) allows an efficient and robust numerical solution of very large scale highly nonlinear systems. Due to the user friendly interface and its modular design, the software package is open for an easy adaptation to specific problems. Numerical experiments for some selected problems illustrate performance and usage of the package.
We study the power-law type solutions of the fourth order field equations derived from a generic quadratic Lagrangian density in the case of multidimensional Bianchi I cosmological models. All the solutions of the system of algebraic equations have been found, using computer algebra, from a search of the Groebner bases associated to it. While, in space dimension $ d = 3 $ , the Einsteinian Kasner metric is still the most general power-law type solution, for $ d > 3 $ , no solution, other than the Minkowski space-time, is common to the three systems of equations associated with the three contributions to the Lagrangian density. In the case of a pure Riemann-squared contribution (suggested by a recent calculation of the effective action for the heterotic string), the possibility exists to realize a splitting of the $ d $-dimensional space into a ( $ d - 3 $)-dimensional internal space and a physical 3- dimensional space, the latter expanding in time as a power bigger than 2 (about 4.5 when $ d = 9 $).