TY - CHAP A1 - Ehrig, Rainald A1 - Nowak, Ulrich A1 - Oeverdieck, Lars A1 - Deuflhard, Peter ED - H.-J. Bungartz, F. T1 - Advanced Extrapolation Methods for Large Scale Differential Algebraic Problems T2 - High Performance Scientific and Engineering Computing Y1 - 1999 VL - 8 SP - 233 EP - 244 PB - Springer Verlag ER - TY - CHAP A1 - Ehrig, Rainald A1 - Nowak, Ulrich A1 - Deuflhard, Peter ED - Khoroshevsky, V. T1 - Massively Parallel Simulation in Chemical Engineering by Extrapolation Algorithms T2 - Procs. 16th International Workshop on Distributed Data Processing, Novosibirsk, Russia Y1 - 1998 SP - 1 EP - 6 ER - TY - CHAP A1 - Nowak, Ulrich A1 - Deuflhard, Peter T1 - Towards Parameter Identification for Large Chemical Reaction Systems T2 - Numerical Treatment of Inverse Problems in Differential and Integral Equations Y1 - 1983 VL - 2 SP - 13 EP - 26 PB - Boston: Birkhäuser ER - TY - JOUR A1 - Nowak, Ulrich A1 - Deuflhard, Peter T1 - Numerical Identification of Selected Rate Constants in Large Chemical Reaction Systems JF - Appl. Numer. Math. Y1 - 1985 VL - 1 SP - 59 EP - 75 ER - TY - GEN A1 - Deuflhard, Peter A1 - Lang, Jens A1 - Nowak, Ulrich T1 - Adaptive Algorithms in Dynamical Process Simulation N2 - 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. T3 - ZIB-Report - SC-95-16 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1823 ER - TY - GEN A1 - Deuflhard, Peter A1 - Nowak, Ulrich A1 - Weyer, J. T1 - Prognoserechnung zur AIDS-Ausbreitung in der Bundesrepublik Deutschland N2 - Die Autoren sind sich dar{ü}ber im klaren, daß zahlreiche Imponderabilien die Ergebnisse der vorgelegten Modellrechnungen beeinflussen k{ö}nnen. Immerhin repräsentiert 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 überschauen. Die Entwicklung neuer effizienter numerischer Methoden spielte eine Schlüsselrolle bei der tatsächlichen Simulation dieses umfangreichen realitätsnahen mathematischen Modells. T3 - ZIB-Report - SC-94-23 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1511 ER - TY - GEN A1 - Deuflhard, Peter A1 - Nowak, Ulrich A1 - Wulkow, Michael T1 - Recent Developments in Chemical Computing. N2 - 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. T3 - ZIB-Report - SC-90-07 Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-359 ER - TY - GEN A1 - Deuflhard, Peter A1 - Nowak, Ulrich T1 - Efficient Numerical Simulation and Identification of Large Chemical Reaction Systems. N2 - 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. T3 - ZIB-Report - SC-86-01 Y1 - 1986 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14 ER - TY - GEN A1 - Ehrig, Rainald A1 - Nowak, Ulrich A1 - Deuflhard, Peter T1 - Massively Parallel Linearly-Implicit Extrapolation Algorithms as a Powerful Tool in Process Simulation. N2 - We study the parallelization of linearly--implicit extrapolation codes for the solution of large scale PDE systems and differential algebraic equations on distributed memory machines. The main advantage of these algorithms is that they enable adapativity both in time and space. Additive Krylov--Schwarz methods yield high parallel perfomance for such extrapolation methods. Our approach combines a slightly overlapping domain decomposition together with a polynomial block Neumann preconditioner and a reduced system technique. Furthermore we get important advantages through the explicit computation of the matrix--products of the preconditioner and the matrix of the linear system. The parallel algorithms exhibit scalability up to 64 processors already for medium--sized test problems. We show that the codes are really efficient in large application systems for chemical engineering problems. T3 - ZIB-Report - SC-97-43 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3127 ER - TY - GEN A1 - Deuflhard, Peter A1 - Nowak, Ulrich A1 - Weiser, Martin T1 - Affine Invariant Adaptive Newton Codes for Discretized PDEs N2 - The paper deals with three different Newton algorithms that have recently been worked out in the general frame of affine invariance. Of particular interest is their performance in the numerical solution of discretized boundary value problems (BVPs) for nonlinear partial differential equations (PDEs). Exact Newton methods, where the arising linear systems are solved by direct elimination, and inexact Newton methods, where an inner iteration is used instead, are synoptically presented, both in affine invariant convergence theory and in numerical experiments. The three types of algorithms are: (a) affine covariant (formerly just called affine invariant) Newton algorithms, oriented toward the iterative errors, (b) affine contravariant Newton algorithms, based on iterative residual norms, and (c) affine conjugate Newton algorithms for convex optimization problems and discrete nonlinear elliptic PDEs. T3 - ZIB-Report - 02-33 KW - Affine invariant Newton methods KW - global Newton methods KW - inexact Newton methods KW - adaptive trust region methods KW - nonlinear partial differential equa Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7005 ER -