@misc{MaasNowak1996, author = {Maas, Ulrich and Nowak, Ulrich}, title = {An adaptive method of lines for the simulation of complex laminar combustion processes}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2665}, number = {SC-96-56}, year = {1996}, abstract = {For the simulation of one-dimensional flame configurations reliabl e numerical tools are needed which have to be both highly efficient (large num ber of parametric calculations) and at the same time accurate (in order t o avoid numerical errors). This can only be accomplished using fully adapt ive discretization techniques both in space and time together with a c ontrol of the discretization error. We present a method which accomplishes this task. It is based on a n adative MOL (method of lines) treatment. Space discretization is done by means of finite difference approxi mations on non-uniform grids. Time is discretized by the linearly-implicit Euler method. In order to control the discretization errors an extrapolation pro cedure is used in space and time. Results are presented for simple laser-induced ignition processes. The method, however, can be applied to other combustion processes, too.}, language = {en} } @misc{DierkesWadeNowaketal.2011, author = {Dierkes, Thomas and Wade, Moritz and Nowak, Ulrich and R{\"o}blitz, Susanna}, title = {BioPARKIN - Biology-related Parameter Identification in Large Kinetic Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12706}, number = {11-15}, year = {2011}, abstract = {Modelling, parameter identification, and simulation play an important r{\^o}le in Systems Biology. In recent years, various software packages have been established for scientific use in both licencing types, open source as well as commercial. Many of these codes are based on inefficient and mathematically outdated algorithms. By introducing the package BioPARKIN recently developed at ZIB, we want to improve this situation significantly. The development of the software BioPARKIN involves long standing mathematical ideas that, however, have not yet entered the field of Systems Biology, as well as new ideas and tools that are particularly important for the analysis of the dynamics of biological networks. BioPARKIN originates from the package PARKIN, written by P.Deuflhard and U.Nowak, that has been applied successfully for parameter identification in physical chemistry for many years.}, language = {en} } @misc{NowakGrahSchreier2004, author = {Nowak, Ulrich and Grah, Aleksander and Schreier, Manfred}, title = {Parameter Estimation and Accuracy Matching Strategies for 2-D Reactor Models}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7749}, number = {03-52}, year = {2004}, abstract = {The mathematical modeling of a special modular catalytic reactor kit leads to a system of partial differential equation in two space dimensions. As customary, this model contains unconfident physical parameters, which may be adapted to fit experimental data. To solve this nonlinear least squares problem we apply a damped Gauss-Newton method. A method of lines approach is used to evaluate the associated model equations. By an a priori spatial discretization a large DAE system is derived and integrated with an adaptive, linearly-implicit extrapolation method. For sensitivity evaluation we apply an internal numerical differentiation technique, which reuses linear algebra information from the model integration. In order not to interfere the control of the Gauss-Newton iteration these computations are done usually very accurately and, therefore, very costly. To overcome this difficulty, we discuss several accuracy adaptation strategies, e.g., a master-slave mode. Finally, we present some numerical experiments.}, language = {en} } @incollection{EhrigNowakOeverdiecketal.1999, author = {Ehrig, Rainald and Nowak, Ulrich and Oeverdieck, Lars and Deuflhard, Peter}, title = {Advanced Extrapolation Methods for Large Scale Differential Algebraic Problems}, volume = {8}, booktitle = {High Performance Scientific and Engineering Computing}, editor = {H.-J. Bungartz, F.}, publisher = {Springer Verlag}, pages = {233 -- 244}, year = {1999}, language = {en} } @inproceedings{EhrigNowakDeuflhard1998, author = {Ehrig, Rainald and Nowak, Ulrich and Deuflhard, Peter}, title = {Massively Parallel Simulation in Chemical Engineering by Extrapolation Algorithms}, booktitle = {Procs. 16th International Workshop on Distributed Data Processing, Novosibirsk, Russia}, editor = {Khoroshevsky, V.}, pages = {1 -- 6}, year = {1998}, language = {en} } @inproceedings{NowakEhrigOeverdieck1998, author = {Nowak, Ulrich and Ehrig, Rainald and Oeverdieck, Lars}, title = {Parallel Extrapolation Methods and Their Application in Chemical Engineering}, volume = {1401}, booktitle = {High-Performance Computing and Networking}, editor = {Sloot, P. and Bubak, Marian and Hertzberger, B.}, publisher = {Springer}, pages = {419 -- 428}, year = {1998}, language = {en} } @inproceedings{NowakPoehleRoitzsch1996, author = {Nowak, Ulrich and P{\"o}hle, Uwe and Roitzsch, Rainer}, title = {Eine graphische Oberfl{\"a}che f{\"u}r numerische Programme}, booktitle = {Software Engineering im Scientific Computing}, editor = {Mackens, W. and Rump, S.}, publisher = {Vieweg}, pages = {264 -- 278}, year = {1996}, language = {en} } @inproceedings{NowakPoehleRoitzschetal.1996, author = {Nowak, Ulrich and P{\"o}hle, Uwe and Roitzsch, Rainer and Sukrow, B.}, title = {Formale Spezifikation des ZIB-GUI mit Hilfe von Graph-Grammatiken}, booktitle = {Software Engineering im Scientific Computing}, editor = {Mackens, W. and Rump, S.}, publisher = {Vieweg}, pages = {290 -- 296}, year = {1996}, language = {en} } @inproceedings{NowakDeuflhard1983, author = {Nowak, Ulrich and Deuflhard, Peter}, title = {Towards Parameter Identification for Large Chemical Reaction Systems}, volume = {2}, booktitle = {Numerical Treatment of Inverse Problems in Differential and Integral Equations}, publisher = {Boston: Birkh{\"a}user}, pages = {13 -- 26}, year = {1983}, language = {en} } @article{NowakDeuflhard1985, author = {Nowak, Ulrich and Deuflhard, Peter}, title = {Numerical Identification of Selected Rate Constants in Large Chemical Reaction Systems}, volume = {1}, journal = {Appl. Numer. Math.}, pages = {59 -- 75}, year = {1985}, language = {en} } @article{SchlegelMarquardtEhrigetal.2004, author = {Schlegel, Martin and Marquardt, Wolfgang and Ehrig, Rainald and Nowak, Ulrich}, title = {Sensitivity analysis of linearly-implicit differential-algebraic systems by one-step extrapolation}, journal = {Applied Numerical Mathematics}, number = {48}, pages = {83 -- 102}, year = {2004}, language = {en} } @misc{FrauhammerKleinEigenbergeretal.1996, author = {Frauhammer, J{\"o}rg and Klein, Harald and Eigenberger, Gerhart and Nowak, Ulrich}, title = {Solving moving boundary problems with an adaptive moving grid method: Rotary heat exchangers with condensation and evaporation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2679}, number = {SC-96-57}, year = {1996}, abstract = {A numerical method for the treatment of moving discontinuities in the model equations of chemical engineering systems is presented. The derived model describing the effects of condensation and evaporation in a regenerative air to air heat exchanger yields an illustrative example for these so called moving boundary problems. The presented adaptive moving grid method is based on the algorithm {\sc Pdex} for parabolic partial differential equations. It is shown that the method is suited for problems where the arising discontinuities cause low rates of convergence if the equations are solved with a static grid.}, language = {en} } @misc{NowakPoehleRoitzsch1996, author = {Nowak, Ulrich and P{\"o}hle, Uwe and Roitzsch, Rainer}, title = {Eine graphische Oberfl{\"a}che f{\"u}r numerische Programme}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2242}, number = {SC-96-13}, year = {1996}, abstract = {Der Entwurf und die Implementierung des auf Tcl/Tk basierenden Werkzeugkastens ZGUI wird beschrieben und an einigen Beispielen erl{\"a}utert. ZGUI unterst{\"u}tzt die Entwicklung einer graphischen Benutzeroberfl{\"a}che (GUI) f{\"u}r die am ZIB erstellte numerische Software. Es sollen folgende Ziele erreicht werden: \begin{itemize} \item einfaches Ausprobieren anhand vordefinierter Testprobleme,\vspace*{-2mm} \item Kennenlernen numerischer Steuergr{\"o}\ss en und Verfahrensvarianten,\vspace*{-2mm} \item einfache Eingabe neuer Probleme,\vspace*{-2mm} \item einfache Nutzung graphischer Ausgabem{\"o}glichkeiten und\vspace*{-2mm} \item einheitliche Darstellung gleicher oder {\"a}hnlicher Optionen. \end{itemize}}, language = {de} } @misc{Nowak1995, author = {Nowak, Ulrich}, title = {A Fully Adaptive MOL-Treatment of Parabolic 1D-Problems with Extrapolation Techniques}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1913}, number = {SC-95-25}, year = {1995}, abstract = {A fully adaptive method is presented for the numerical solution of highly nonlinear, coupled systems of parabolic differential equations in one space dimension. Time discretization is by means of the linearly--implicit Euler discretization. Space discretization is by finite differences on non--uniform grids. Both basic discretizations are combined with extrapolation. Based on local error estimates for both the time and the space discretization error, the accuracy of the numerical approximation is controlled and the discretization stepsizes are adapted automatically and simultaneously. The algorithm is implemented in a user friendly software package, PDEX1M. To be a powerful tool for users coming from applications the package has been equipped with some additional useful devices.}, language = {en} } @misc{DeuflhardLangNowak1995, author = {Deuflhard, Peter and Lang, Jens and Nowak, Ulrich}, title = {Adaptive Algorithms in Dynamical Process Simulation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1823}, number = {SC-95-16}, year = {1995}, abstract = {Dynamical simulation of industrially relevant processes strongly advises the use of algorithms, which are {\em adaptive} both in time and in space discretization. The paper presents two alternatives: (a) a fully adaptive method of lines approach, which is based on finite difference methods and essentially applicable to 1D problems; (b) a fully adaptive Rothe method, which is based on a fast multilevel finite element method and applicable to 1D up to 3D.}, language = {en} } @misc{DeuflhardNowakWeyer1994, author = {Deuflhard, Peter and Nowak, Ulrich and Weyer, J.}, title = {Prognoserechnung zur AIDS-Ausbreitung in der Bundesrepublik Deutschland}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1511}, number = {SC-94-23}, year = {1994}, abstract = {Die Autoren sind sich dar{{\"u}}ber im klaren, daß zahlreiche Imponderabilien die Ergebnisse der vorgelegten Modellrechnungen beeinflussen k{{\"o}}nnen. Immerhin repr{\"a}sentiert jedoch das vorgelegte mathematische Modell die Summe unserer derzeitigen Kenntnisse zur Fragestellung AIDS--Epidemie; neu hinzukommende Erkenntnisse lassen sich rasch einarbeiten und in ihren Konsequenzen {\"u}berschauen. Die Entwicklung neuer effizienter numerischer Methoden spielte eine Schl{\"u}sselrolle bei der tats{\"a}chlichen Simulation dieses umfangreichen realit{\"a}tsnahen mathematischen Modells.}, language = {de} } @misc{LubichNowakPoehleetal.1992, author = {Lubich, Christian and Nowak, Ulrich and P{\"o}hle, Uwe and Engstler, Ch.}, title = {MEXX - Numerical Software for the Integration of Constrained Mechanical Systems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-823}, number = {SC-92-12}, year = {1992}, abstract = {MEXX (short for MEXanical systems eXtrapolation integrator) is a Fortran code for time integration of constrained mechanical systems. MEXX is suited for direct integration of the equations of motion in descriptor form. It is based on extrapolation of a time stepping method that is explicit in the differential equations and linearly implicit in the nonlinear constraints. It only requires the solution of well--structured systems of linear equations which can be solved with a computational work growing linearly with the number of bodies, in the case of multibody systems with few closed kinematic loops. Position and velocity constraints are enforced throughout the integration interval, whereas acceleration constraints need not be formulated. MEXX has options for time--continuous solution representation (useful for graphics) and for the location of events such as impacts. The present article describes MEXX and its underlying concepts.}, language = {en} } @misc{Nowak1992, author = {Nowak, Ulrich}, title = {Dynamic Sparsing in Stiff Extrapolation Methods.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-911}, number = {SC-92-21}, year = {1992}, abstract = {Based on a simple stability analysis for the semi--implicit Euler discretization a new dynamic sparsing procedure is derived. This procedure automatically eliminates ``small'' elements of the Jacobian matrix. As a consequence, the amount of work needed to handle the linear algebra within a semi--implicit extrapolation integrator can be reduced drastically. Within the course of integration the sparsing criterion, which decides what ``small'' means, is dynamically adapted to ensure stability of the discretization scheme. Thus, stepsize restrictions due to instability can be avoided. Numerical experiments for quite different problems show robustness and efficiency of this dynamic sparsing technique. The techniques developed here in the context of stiff extrapolation integrators can, in principle, be applied to W--methods, where exact Jacobians may be replaced by ``sufficiently good'' approximations. {\bf Keywords:} Large scale integration, extrapolation methods, stiff ODEs, W--methods, sparse matrix techniques.}, language = {en} } @misc{DeuflhardNowakWulkow1990, author = {Deuflhard, Peter and Nowak, Ulrich and Wulkow, Michael}, title = {Recent Developments in Chemical Computing.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-359}, number = {SC-90-07}, year = {1990}, abstract = {The paper surveys three aspects of chemical computing, which seem to play a role in recent developments. First, extrapolation methods for the numerical treatment of differential- algebraic equations are introduced. The associated extrapolation code LIMEX has reached a certain level of sophistication, which makes it a real competitor to the elsewhere widely used multi-step code DASSL of Petzold. Second, adaptive methods of lines for partial differential equations such as those arising in combustion problems are treated. Both static and dynamic regridding techniques are discussed in some detail. Finally, some new ideas about the treatment of the kinetic equations arising from polymer reactions are presented. The new feature of the suggested approach is the application of a Galerkin procedure using sets of orthogonal polynomials over a discrete variable (which, of course, in the case of polymer reactions is the polymer degree). The new approach may open the door to a new reliable low dimensional treatment of complex polymer reactions.}, language = {en} } @misc{DeuflhardNowak1986, author = {Deuflhard, Peter and Nowak, Ulrich}, title = {Efficient Numerical Simulation and Identification of Large Chemical Reaction Systems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14}, number = {SC-86-01}, year = {1986}, abstract = {New, highly efficient techniques for the numerical simulation and parameter identification of large chemical reaction systems are surveyed. The survey particularly addresses to chemists, which are understood to be potential users of the distributed software packages. These packages are written in the form of interactive dialogue systems - thus enabling chemists to concentrate on the chemistry of their problem. Large scale examples from chemical research environments are included.}, language = {en} }