@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 Many of these codes are based on inefficient and mathematically outdated algorithms.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} }