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  • 1
    Keywords: Forschungsbericht
    Description / Table of Contents: A direct discretization approach and an operator-splitting scheme are applied for the numerical simulation of a population balance system which models the synthesis of urea with a uni-variate population. The problem is formulated in axisymmetric form and the setup is chosen such that a steady state is reached. Both solvers are assessed with respect to the accuracy of the results, where experimental data are used for comparison, and the efficiency of the simulations. Depending on the goal of simulations, to track the evolution of the process accurately or to reach the steady state fast, recommendations for the choice of the solver are given.
    Type of Medium: Online Resource
    Pages: Online-Ressource (PDF-Datei: 24 S., 546 KB) , graph. Darst.
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik 2022
    Language: English
    Note: Systemvoraussetzungen: Acrobat reader.
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  • 2
    Online Resource
    Online Resource
    Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik Leibniz-Institut im Forschungsverbund Berlin e.V.
    Keywords: Forschungsbericht
    Description / Table of Contents: PARMOON is a program package for the numerical solution of elliptic and parabolic partial differential equations. It inherits the distinct features of its predecessor MOONMD [28]: strict decoupling of geometry and finite element spaces, implementation of mapped finite elements as their definition can be found in textbooks, and a geometric multigrid preconditioner with the option to use different finite element spaces on different levels of the multigrid hierarchy. After having presented some thoughts about in-house research codes, this paper focuses on aspects of the parallelization, which is the main novelty of PARMOON. Numerical studies, performed on compute servers, assess the efficiency of the parallelized geometric multigrid preconditioner in comparison with parallel solvers that are available in external libraries. The results of these studies give a first indication whether the cumbersome implementation of the parallelized geometric multigrid method was worthwhile or not.
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (25 Seiten, 1.145 kB) , Illustrationen, Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik No. 2316
    Language: English
    Note: Literaturverzeichnis: Seite 20-23
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  • 3
    Online Resource
    Online Resource
    Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V.
    Keywords: Forschungsbericht
    Description / Table of Contents: A simulation based method for the numerical solution of PDE with random coefficients is presented. By the Feynman-Kac formula, the solution can be represented as conditional expectation of a functional of a corresponding stochastic differential equation driven by independent noise. A time discretization of the SDE for a set of points in the domain and a subsequent Monte Carlo regression lead to an approximation of the global solution of the random PDE. We provide an initial error and complexity analysis of the proposed method along with numerical examples illustrating its behaviour.
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (33 Seiten, 1.753 kB) , Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik No. 2192
    Language: English
    Note: Literaturverzeichnis: Seite 29-31
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  • 4
    Online Resource
    Online Resource
    Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V.
    Keywords: Forschungsbericht
    Description / Table of Contents: A numerical method for the fully adaptive sampling and interpolation of PDE with random data is presented. It is based on the idea that the solution of the PDE with stochastic data can be represented as conditional expectation of a functional of a corresponding stochastic differential equation (SDE). The physical domain is decomposed subject to a non-uniform grid and a classical Euler scheme is employed to approximately solve the SDE at grid vertices. Interpolation with a conforming finite element basis is employed to reconstruct a global solution of the problem. An a posteriori error estimator is introduced which provides a measure of the different error contributions. This facilitates the formulation of an adaptive algorithm to control the overall error by either reducing the stochastic error by locally evaluating more samples, or the approximation error by locally refining the underlying mesh. Numerical examples illustrate the performance of the presented novel method.
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (21 Seiten, 1.261 kB) , Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik No. 2200
    Language: English
    Note: Literaturverzeichnis: Seite 18-19
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