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  • ddc:000  (7)
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  • ddc:000  (7)
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  • 1
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    Highly scalable parallel linearly-implicit extrapolation algorithms (1996)
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    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 2
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    Sensitivity analysis of linearly-implicit differential-algebraic systems by one-step extrapolation (2002)
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    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 3
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    Modelling and Simulation of Aerosol Formation by Heterogeneous Nucleation in Gas-Liquid Contact Devices (2001)
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    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 4
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    Parallel Extrapolation Methods and Their Application in Chemical Engineering (1997)
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    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 5
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    Massively Parallel Linearly-Implicit Extrapolation Algorithms as a Powerful Tool in Process Simulation. (1997)
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    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 6
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    GMERR - an Error Minimizing Variant of GMRES (1997)
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    Publication Date: 2014-02-26
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
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  • 7
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    Algorithmen- und Softwareoptimierung für die Satellitenbahn- und Schwerefeldmodellierung (2000)
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    Publication Date: 2014-02-26
    Description: 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.}
    Keywords: ddc:000
    Language: German
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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