TY - GEN A1 - Ehrig, Rainald A1 - Nowak, Ulrich T1 - Algorithmen- und Softwareoptimierung für die Satellitenbahn- und Schwerefeldmodellierung N2 - Dieser Report enthält die Ergebnisse der Untersuchungen, die gemäss dem Forschungs-- und Entwicklungsvertrag Gravity zwischen dem GeoForschungsZentrum Potsdam und dem Konrad--Zuse--Zentrum Berlin vorgenommen wurden. Die damit vereinbarte wissenschaftliche Kooperation hat die folgenden Ziele: \item{die am GFZ vorhandenen Algorithmen und Softwaremodule auf ihre Effizienz hisichtlich Nutzung der Rechnerresourcen zu untersuchen und Lösungen für einen schnelleren Datendurchsatz zu entwickeln und zu implementieren,} \item{Methoden zur Regularisierung und Lösung schlecht konditionierter Normalgleichungssysteme (für Schwerefeldkoeffizienten) kritisch zu untersuchen und eine mathematisch objektive Strategie der Regularisierung zu entwickeln, und} \item{insbesondere im Hinblick auf die Anforderungen bei GRACE, verschiedene Bahnintegrationsverfahren hinsichtlich ihrer numerischen Genauigkeit und Einsatzmöglichkeiten zu untersuchen.} T3 - ZIB-Report - 00-01 KW - geodesy KW - gravity field models KW - regularization KW - ill-posed systems KW - orbit integration Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5694 ER - TY - GEN A1 - Schlegel, Martin A1 - Marquardt, Wolfgang A1 - Ehrig, Rainald A1 - Nowak, Ulrich T1 - Sensitivity analysis of linearly-implicit differential-algebraic systems by one-step extrapolation N2 - In this work we present an approach for the sensitivity analysis of linearly-implicit differential-algebraic equation systems. Solutions for both, states and sensitivities are obtained by applying an extrapolated linearly implicit Euler discretization scheme. This approach is compared to the widely used sensitivity extensions of multi-step BDF methods by means of case studies. Especially, we point out the benefit of this method in the context of dynamic optimization using the sequential approach. T3 - ZIB-Report - 02-38 KW - sensitivity evaluation KW - differential-algebraic systems KW - extrapolation methods KW - dynamic optimization KW - optimal control Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7052 ER - TY - GEN A1 - Ehrig, Rainald A1 - Ofenloch, Oliver A1 - Schaber, Karlheinz A1 - Deuflhard, Peter T1 - Modelling and Simulation of Aerosol Formation by Heterogeneous Nucleation in Gas-Liquid Contact Devices N2 - This paper describes a new simulation tool for the prediction of aerosol formation and behavior in gas--liquid contact devices such as absorbers, scrubbers, quench coolers, and condensers as well as multistage gas cleaning processes, respectively. Aerosol formation can impact severely the separation efficiency of gas cleaning processes. Aerosol or fog formation can arise by spontaneous condensation or desublimation in supersaturated gas phases. The rigorous description of the mass and energy transfer between the gas phase, the liquid phase, and the growing aerosol droplets leads to a system of partial differential and algebraic equations. For the solution of these systems we have developed the plant simulation tool AerCoDe. This program bases upon the linearly--implicit Euler discretisation, which in combination with extrapolation permits an adaptive step size and order control. Typical simulation results of a multistage industrial flue gas scrubbing process are presented. It is shown, that experimental data can be confirmed if the number concentration of condensation nuclei as an input parameter is roughly known. T3 - ZIB-Report - 01-15 KW - aerosols KW - heterogeneous nucleation KW - two-phase flow KW - balance equations KW - extrapolation methods Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6416 ER - TY - GEN A1 - Ehrig, Rainald A1 - Nowak, Ulrich A1 - Deuflhard, Peter T1 - Highly scalable parallel linearly-implicit extrapolation algorithms N2 - We present parallel formulations of the well established extrapolation algorithms EULSIM and LIMEX and its implementation on a distributed memory architecture. The discretization of partial differential equations by the method of lines yields large banded systems, which can be efficiently solved in parallel only by iterative methods. Polynomial preconditioning with a Neumann series expansion combined with an overlapping domain decomposition appears as a very efficient, robust and highly scalable preconditioner for different iterative solvers. A further advantage of this preconditioner is that all computation can be restricted to the overlap region as long as the subdomain problems are solved exactly. With this approach the iterative algorithms operate on very short vectors, the length of the vectors depends only on the number of gridpoints in the overlap region and the number of processors, but not on the size of the linear system. As the most reliable and fast iterative methods based on this preconditioning scheme appeared GMRES or FOM and BICGSTAB. To further reduce the number of iterations in GMRES or FOM we can reuse the Krylov-spaces constructed in preceeding extrapolation steps. The implementation of the method within the program LIMEX results in a highly parallel and scalable program for solving differential algebraic problems getting an almost linear speedup up to 64 processors even for medium size problems. Results are presented for a difficult application from chemical engineering simulating the formation of aerosols in industrial gas exhaust purification. T3 - ZIB-Report - TR-96-11 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5405 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 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - GMERR - an Error Minimizing Variant of GMRES N2 - The paper analyzes a recently proposed iterative error minimizing method for the solution of linear systems. Sufficient and necessary conditions for convergence are studied, which show that the method essentially requires normal matrices. An efficient implementation similar to GMRES has been worked out in detail. Numerical tests on general non--normal matrices, of course, indicate that this approach is not competitive with GMRES. Summarizing, if error minimizing is important, one should rather choose CGNE. A computational niche for GMERR might be problems, where normal but non--symmetric matrices occur, like dissipative quantum mechanics. T3 - ZIB-Report - SC-97-63 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3323 ER - TY - GEN A1 - Nowak, Ulrich A1 - Ehrig, Rainald A1 - Oeverdieck, Lars T1 - Parallel Extrapolation Methods and Their Application in Chemical Engineering N2 - We study the parallelization of linearly--implicit extrapolation methods for the solution of large scale systems of differential algebraic equations arising in a method of lines (MOL ) treatment of partial differential equations. In our approach we combine a slightly overlapping domain decomposi tion together with a polynomial block Neumann preconditioner. Through the explicit computation of the matrix products of the pre conditioner and the system matrix a significant gain in overall efficiency is achieved for medium--sized problems. The parallel algorithm exhibits a good scalability up to 32 proces sors on a Cray T3E. Preliminary results for computations on a workstation cluster are reported. T3 - ZIB-Report - SC-97-69 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3387 ER - TY - JOUR A1 - Bergmann, G. A1 - Graichen, F. A1 - Rohlmann, A. A1 - Bender, Alwina A1 - Ehrig, Rainald A1 - Westerhoff, P. A1 - Heinlein, B. T1 - Design and calibration of load sensing orthopaedic implants JF - Journal Biomech. Eng. Y1 - 2008 SP - 02109 EP - 1–02109–9 ER - TY - JOUR A1 - Schaber, Karlheinz A1 - Koerber, Jens A1 - Ofenloch, O. A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - Aerosol Formation in Gas-Liquid Contact Devices- Nucleation, Growth and Particle Dynamics JF - Chem.Eng.Sci. Y1 - 2002 VL - 57 SP - 4345 EP - 4356 ER - TY - CHAP A1 - Nowak, Ulrich A1 - Ehrig, Rainald A1 - Oeverdieck, Lars ED - Sloot, P. ED - Bubak, Marian ED - Hertzberger, B. T1 - Parallel Extrapolation Methods and Their Application in Chemical Engineering T2 - High-Performance Computing and Networking Y1 - 1998 VL - 1401 SP - 419 EP - 428 PB - Springer ER -