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Magiera, Jim

Jim Magiera

Dr. rer. nat.

Research assistant
Institute of Applied Analysis and Numerical Simulation
Chair of Applied Mathematics

Contact

+49 711 685 67646
Email

Pfaffenwaldring 57
70569 Stuttgart
Deutschland
Room: 7.161

Office Hours

Please contact me by E-Mail

Publications

2024
1. J. Magiera and C. Rohde, “A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate,” Communications on Applied Mathematics and Computation, 2024, doi: 10.1007/s42967-023-00349-8.
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  @article{magiera2023multiscale, archiveprefix = {arXiv}, author = {Magiera, Jim and Rohde, Christian}, doi = {10.1007/s42967-023-00349-8}, eprinttype = {arXiv}, journal = {Communications on Applied Mathematics and Computation}, title = {A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate}, year = 2024 }
2. M. Alkämper, J. Magiera, and C. Rohde, “An Interface-Preserving Moving Mesh in Multiple Space Dimensions,” ACM Trans. Math. Softw., vol. 50, no. 1, Art. no. 1, Mar. 2024, doi: 10.1145/3630000.
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  @article{10.1145/3630000, abstract = {An interface-preserving moving mesh algorithm in two or higher dimensions is presented. It resolves a moving (d-1)-dimensional manifold directly within the d-dimensional mesh, which means that the interface is represented by a subset of moving mesh cell-surfaces. The underlying mesh is a conforming simplicial partition that fulfills the Delaunay property. The local remeshing algorithms allow for strong interface deformations. We give a proof that the given algorithms preserve the interface after interface deformation and remeshing steps. Originating from various numerical methods, data is attached cell-wise to the mesh. After each remeshing operation, the interface-preserving moving mesh retains valid data by projecting the data to the new mesh cells.An open source implementation of the moving mesh algorithm is available at Reference [1].}, address = {New York, NY, USA}, articleno = {5}, author = {Alk\"{a}mper, Maria and Magiera, Jim and Rohde, Christian}, doi = {10.1145/3630000}, issn = {0098-3500}, issue_date = {March 2024}, journal = {ACM Trans. Math. Softw.}, month = {03}, number = 1, numpages = {28}, publisher = {Association for Computing Machinery}, title = {An Interface-Preserving Moving Mesh in Multiple Space Dimensions}, url = {https://doi.org/10.1145/3630000}, volume = 50, year = 2024 }
  Link
  https://doi.org/10.1145/3630000
2022
1. J. Magiera and C. Rohde, “Analysis and Numerics of Sharp and Diffuse Interface Models for Droplet Dynamics,” in Droplet Dynamics under Extreme Ambient Conditions, K. Schulte, C. Tropea, and B. Weigand, Eds., in Droplet Dynamics under Extreme Ambient Conditions. , Springer International Publishing, 2022. doi: 10.1007/978-3-031-09008-0_4.
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  @inbook{magiera.rohde:analysis:2021, abstract = {The modelling of liquid--vapour flow with phase transition poses many challenges, both on the theoretical level, as well as on the level of discretisation methods. Therefore, accurate mathematical models and efficient numerical methods are required. In that, we focus on two modelling approaches: the sharp-interface (SI) approach and the diffuse-interface (DI) approach. For the SI-approach, representing the phase boundary as a co-dimension-1 manifold, we develop and validate analytical Riemann solvers for basic isothermal two-phase flow scenarios. This ansatz becomes cumbersome for increasingly complex thermodynamical settings. A more versatile multiscale interface solver, that is based on molecular dynamics simulations, is able to accurately describe the evolution of phase boundaries in the temperature-dependent case. It is shown to be even applicable to two-phase flow of multiple components. Despite the successful developments for the SI approach, these models fail if the interface undergoes topological changes. To understand merging and splitting phenomena for droplet ensembles, we consider DI models of second gradient type. For these Navier--Stokes--Korteweg systems, that can be seen as a third order extension of the Navier--Stokes equations, we propose variants that are more accessible to standard numerical schemes. More precisely, we reformulate the capillarity operator to restore the hyperbolicity of the Euler operator in the full system.}, author = {Magiera, Jim and Rohde, Christian}, booktitle = {Droplet Dynamics under Extreme Ambient Conditions}, doi = {10.1007/978-3-031-09008-0_4}, editor = {Schulte, Kathrin and Tropea, Cameron and Weigand, Bernhard}, isbn = {978-3-031-09008-0}, langid = {english}, publisher = {Springer International Publishing}, pubstate = {in review}, series = {Fluid Mechanics and its Application}, title = {Analysis and Numerics of Sharp and Diffuse Interface Models for Droplet Dynamics}, url = {https://doi.org/10.1007/978-3-031-09008-0_4}, year = 2022 }
  Link
  https://doi.org/10.1007/978-3-031-09008-0_4
2. J. Magiera and C. Rohde, “A molecular–continuum multiscale model for inviscid liquid–vapor flow with sharp interfaces,” J. Comput. Phys., p. 111551, 2022, doi: https://doi.org/10.1016/j.jcp.2022.111551.
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  @article{magiera.rohde:molecular:2022, abstract = {The dynamics of compressible liquid–vapor flow depends sensitively on the microscale behavior at the phase boundary. We consider a sharp-interface approach, and propose a multiscale model to describe liquid–vapor flow accurately, without imposing ad-hoc closure relations on the continuum scale. The multiscale model combines the Euler equations on the continuum scale with molecular-scale particle simulations that govern the interface motion. We rely on an interface-preserving moving mesh finite volume method to discretize the continuum-scale sharp-interface flow in a conservative manner. Computational efficiency, while preserving physical properties, is achieved by a surrogate solver for the interface dynamics based on constraint-aware neural networks. The multiscale model is presented in its general form, and applied to regimes of temperature-dependent liquid–vapor flow which have not been accessible before.}, author = {Magiera, J. and Rohde, C.}, doi = {https://doi.org/10.1016/j.jcp.2022.111551}, issn = {0021-9991}, journal = {J. Comput. Phys.}, pages = 111551, title = {A molecular–continuum multiscale model for inviscid liquid–vapor flow with sharp interfaces}, url = {https://www.sciencedirect.com/science/article/pii/S0021999122006131}, year = 2022 }
  Link
  https://www.sciencedirect.com/science/article/pii/S0021999122006131
2021
1. J. Magiera, “A Molecular--Continuum Multiscale Solver for Liquid--Vapor Flow,” in Small Collaboration: Advanced Numerical Methods for Nonlinear Hyperbolic Balance Laws and Their Applications (hybrid meeting), in Small Collaboration: Advanced Numerical Methods for Nonlinear Hyperbolic Balance Laws and Their Applications (hybrid meeting), vol. 41. 2021. doi: 10.14760/OWR-2021-41.
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  @inproceedings{magiera:oberwolfach:2021, author = {Magiera, Jim}, booktitle = {Small Collaboration: Advanced Numerical Methods for Nonlinear Hyperbolic Balance Laws and Their Applications (hybrid meeting)}, doi = {10.14760/OWR-2021-41}, fullseries = {Oberwolfach Reports}, langid = {english}, note = {Abstracts from the mini-workshop held 29 Aug -- 4 Sep 2021, Organized by Song Jiang, Jiequan Li, Maria Lukacova, Gerald Warnecke}, series = {Oberwolfach Rep.}, shortseries = {Oberwolfach Rep.}, title = {A Molecular--Continuum Multiscale Solver for Liquid--Vapor Flow}, url = {http://publications.mfo.de/handle/mfo/3891}, volume = 41, year = 2021 }
  Link
  http://publications.mfo.de/handle/mfo/3891
2. J. Magiera, “A Molecular--Continuum Multiscale Solver for Liquid--Vapor Flow: Modeling and Numerical Simulation,” Ph.D. Thesis, 2021. doi: 10.18419/opus-11797.
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  @phdthesis{magiera:phdthesis:2021, author = {Magiera, Jim}, doi = {10.18419/opus-11797}, institution = {University of Stuttgart}, langid = {english}, title = {A Molecular--Continuum Multiscale Solver for Liquid--Vapor Flow: Modeling and Numerical Simulation}, type = {Ph.D. Thesis}, year = 2021 }
2020
1. J. Magiera, D. Ray, J. S. Hesthaven, and C. Rohde, “Constraint-aware neural networks for Riemann problems,” J. Comput. Phys., vol. 409, no. 109345, Art. no. 109345, 2020, doi: https://doi.org/10.1016/j.jcp.2020.109345.
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  @article{magiera2019constraintaware, abstract = {Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satisfied to obtain reliable results. However, standard machine learning algorithms are generally not tailored to respect such constraints. We propose two different strategies to generate constraint-aware neural networks. We test their performance in the context of front-capturing schemes for strongly nonlinear wave motion in compressible fluid flow. Precisely in this context so-called Riemann problems have to be solved as surrogates. Their solution describes the local dynamics of the captured wave front in numerical simulations. Three model problems are considered: a cubic flux model problem, an isothermal two-phase flow model, and the Euler equations. We observe, that constraint-aware neural networks do not only account for the constraint but lead to an improvement of the numerical accuracy of the overall fluid simulation.}, author = {Magiera, Jim and Ray, Deep and Hesthaven, Jan S. and Rohde, Christian}, doi = {https://doi.org/10.1016/j.jcp.2020.109345}, issn = {0021-9991}, journal = {J. Comput. Phys.}, number = 109345, title = {Constraint-aware neural networks for Riemann problems}, url = {https://doi.org/10.1016/j.jcp.2020.109345}, volume = 409, year = 2020 }
  Link
  https://doi.org/10.1016/j.jcp.2020.109345
2. D. Maier, “Construction of breather solutions for nonlinear Klein-Gordon equations on periodic metric graphs,” JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 268, no. 6, Art. no. 6, Mar. 2020, doi: 10.1016/j.jde.2019.09.035.
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  @article{WOS:000505986500001, abstract = {The purpose of this paper is to construct small-amplitude breather solutions for a nonlinear Klein-Gordon equation posed on a periodic metric graph via spatial dynamics and center manifold reduction. The major difficulty occurs from the irregularity of the solutions. The persistence of the approximately constructed pulse solutions under higher order perturbations is obtained by symmetry and reversibility arguments. (C) 2019 Elsevier Inc. All rights reserved.}, address = {525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA}, affiliation = {Maier, D (Corresponding Author), Univ Stuttgart, Inst Anal Dynam \& Modellierung, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Maier, Daniela, Univ Stuttgart, Inst Anal Dynam \& Modellierung, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.}, author = {Maier, Daniela}, author-email = {daniela.maier@mathematik.uni-stuttgart.de}, da = {2021-08-10}, doc-delivery-number = {KA7OB}, doi = {10.1016/j.jde.2019.09.035}, eissn = {1090-2732}, issn = {0022-0396}, journal = {JOURNAL OF DIFFERENTIAL EQUATIONS}, journal-iso = {J. Differ. Equ.}, language = {English}, month = {03}, number = 6, number-of-cited-references = {20}, oa = {Green Submitted}, pages = {2491-2509}, publisher = {ACADEMIC PRESS INC ELSEVIER SCIENCE}, research-areas = {Mathematics}, times-cited = {0}, title = {Construction of breather solutions for nonlinear Klein-Gordon equations on periodic metric graphs}, type = {Article}, unique-id = {WOS:000505986500001}, usage-count-last-180-days = {0}, usage-count-since-2013 = {6}, volume = 268, web-of-science-categories = {Mathematics}, year = 2020 }
3. D. Maier, “BREATHER SOLUTIONS ON DISCRETE NECKLACE GRAPHS,” OPERATORS AND MATRICES, vol. 14, no. 3, Art. no. 3, Sep. 2020, doi: 10.7153/oam-2020-14-48.
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  @article{WOS:000576740400011, abstract = {We show the existence of breather solutions in a nonlinear Klein-Gordon system on a discrete graph with periodic junctions. The proof is based on the Theorem of Crandall-Rabinowitz.}, address = {R AUSTRIJE 11, 10000 ZAGREB, CROATIA}, affiliation = {Maier, D (Corresponding Author), Univ Stuttgart, Inst Anal Dynam \& Modellierung, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Maier, Daniela, Univ Stuttgart, Inst Anal Dynam \& Modellierung, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.}, author = {Maier, Daniela}, author-email = {daniela.maier@mathematik.uni-stuttgart.de}, da = {2021-08-10}, doc-delivery-number = {NY9WS}, doi = {10.7153/oam-2020-14-48}, issn = {1846-3886}, journal = {OPERATORS AND MATRICES}, journal-iso = {Oper. Matrices}, language = {English}, month = {09}, number = 3, number-of-cited-references = {13}, oa = {gold}, pages = {767-776}, publisher = {ELEMENT}, research-areas = {Mathematics}, times-cited = {0}, title = {BREATHER SOLUTIONS ON DISCRETE NECKLACE GRAPHS}, type = {Article}, unique-id = {WOS:000576740400011}, usage-count-last-180-days = {0}, usage-count-since-2013 = {0}, volume = 14, web-of-science-categories = {Mathematics}, year = 2020 }
2018
1. J. Magiera and C. Rohde, “A particle-based multiscale solver for compressible liquid-vapor flow,” Springer Proc. Math. Stat., pp. 291--304, 2018, doi: 10.1007/978-3-319-91548-7_23.
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  @article{magiera.rohde:particle:2018, abstract = {To describe complex flow systems accurately, it is in many cases important to account for the properties of fluid flows on a microscopic scale. In this work, we focus on the description of liquid--vapor flow with a sharp interface between the phases. The local phase dynamics at the interface can be interpreted as a Riemann problem for which we develop a multiscale solver in the spirit of the heterogeneous multiscale method (HMM) [7], using a particle-based microscale model to augment the macroscopic two-phase flow system. The application of a microscale model makes it possible to use the intrinsic properties of the fluid at the microscale, instead of formulating (ad hoc) constitutive relations.}, address = {Cham}, author = {Magiera, Jim and Rohde, Christian}, booktitle = {Theory, Numerics and Applications of Hyperbolic Problems II}, doi = {10.1007/978-3-319-91548-7_23}, editor = {Klingenberg, Christian and Westdickenberg, Michael}, isbn = {978-3-319-91548-7}, journal = {Springer Proc. Math. Stat.}, pages = {291--304}, publisher = {Springer International Publishing}, title = {A particle-based multiscale solver for compressible liquid-vapor flow}, url = {http://dx.doi.org/10.1007/978-3-319-91548-7_23}, year = 2018 }
  Link
  http://dx.doi.org/10.1007/978-3-319-91548-7_23
2. C. Chalons, J. Magiera, C. Rohde, and M. Wiebe, “A finite-volume tracking scheme for two-phase compressible flow,” Springer Proc. Math. Stat., pp. 309--322, 2018, doi: https://doi.org/10.1007/978-3-319-91545-6_25.
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  @article{chalons.magiera.ea:finite:2018, abstract = {We propose a finite-volume tracking method in multiple space dimensions to approximate weak solutions of the hydromechanical equations that allow two-phase behavior. The method relies on a moving mesh ansatz such that the phase boundary is represented as a sharp interface without any artificial smearing. At the interface, an approximate solver is applied, such that the exact Riemann solution is not required. From precedent work, it is known that the method is locally conservative and recovers planar traveling wave solutions exactly. To demonstrate the efficiency and reliability of the new scheme, we test it on various situations for liquid--vapor flow.}, address = {Cham}, author = {Chalons, Christophe and Magiera, Jim and Rohde, Christian and Wiebe, Maria}, booktitle = {Theory, Numerics and Applications of Hyperbolic Problems I}, doi = {https://doi.org/10.1007/978-3-319-91545-6_25}, editor = {Klingenberg, Christian and Westdickenberg, Michael}, isbn = {978-3-319-91545-6}, journal = {Springer Proc. Math. Stat.}, pages = {309--322}, publisher = {Springer International Publishing}, title = {A finite-volume tracking scheme for two-phase compressible flow}, url = {https://doi.org/10.1007/978-3-319-91545-6_25}, year = 2018 }
  Link
  https://doi.org/10.1007/978-3-319-91545-6_25
2016
1. J. Magiera, C. Rohde, and I. Rybak, “A hyperbolic-elliptic model problem for coupled surface-subsurface flow,” Transp. Porous Media, vol. 114, pp. 425–455, 2016, doi: 10.1007/S11242-015-0548-Z.
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  @article{magiera2016hyperbolicelliptic, author = {Magiera, J. and Rohde, C. and Rybak, I.}, doi = {10.1007/S11242-015-0548-Z}, journal = {Transp. Porous Media}, owner = {ingrid}, pages = {425-455}, title = {A hyperbolic-elliptic model problem for coupled surface-subsurface flow}, volume = 114, year = 2016 }
2. I. Rybak and J. Magiera, “Decoupled schemes for free flow and porous medium systems,” in Domain Decomposition Methods in Science and Engineering XXII, T. D. et al., Ed., in Domain Decomposition Methods in Science and Engineering XXII, vol. 104. Springer, 2016, pp. 613--621. doi: 10.1007/978-3-319-18827-0\_54.
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  @inproceedings{rybak2016decoupled, author = {Rybak, I. and Magiera, J.}, booktitle = {Domain Decomposition Methods in Science and Engineering XXII}, doi = {10.1007/978-3-319-18827-0\_54}, editor = {et al., T. Dickopf}, owner = {rybak}, pages = {613--621}, publisher = {Springer}, series = {Lecture Notes in Computational Science and Engineering}, title = {Decoupled schemes for free flow and porous medium systems}, volume = 104, year = 2016 }
2015
1. I. Rybak, J. Magiera, R. Helmig, and C. Rohde, “Multirate time integration for coupled saturated/unsaturated porous medium and free flow systems,” Comput. Geosci., vol. 19, pp. 299–309, Apr. 2015, doi: 10.1007/s10596-015-9469-8.
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  @article{rybak2015multirate, affiliation = {Rybak, I (Reprint Author), Univ Stuttgart, Inst Appl Anal \& Numer Simulat, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Rybak, Iryna; Magiera, Jim; Rohde, Christian, Univ Stuttgart, Inst Appl Anal \& Numer Simulat, D-70569 Stuttgart, Germany. Helmig, Rainer, Univ Stuttgart, Inst Modelling Hydraul \& Environm Syst, D-70569 Stuttgart, Germany.}, author = {Rybak, Iryna and Magiera, Jim and Helmig, Rainer and Rohde, Christian}, doi = {10.1007/s10596-015-9469-8}, eissn = {1573-1499}, issn = {1420-0597}, journal = {Comput. Geosci.}, language = {English}, month = {04}, pages = {299-309}, publisher = {SPRINGER}, research-areas = {Computer Science; Geology}, title = {Multirate time integration for coupled saturated/unsaturated porous medium and free flow systems}, type = {Article}, unique-id = {ISI:000355335100003}, volume = 19, year = 2015 }
2014
1. I. Rybak and J. Magiera, “A multiple-time-step technique for coupled free flow and porous medium systems,” J. Comput. Phys., vol. 272, pp. 327--342, 2014, doi: 10.1016/j.jcp.2014.04.036.
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  @article{rybak2014multipletimestep, author = {Rybak, I. and Magiera, J.}, doi = {10.1016/j.jcp.2014.04.036}, journal = {J. Comput. Phys.}, note = {accepted}, owner = {rybak}, pages = {327--342}, title = {A multiple-time-step technique for coupled free flow and porous medium systems}, volume = 272, year = 2014 }

Teaching

Summer term 2019:
Assistance to Numerische Grundlagen
Winter term 2017/18:
Assistance to Structures of Linear Algebra
Summer term 2017:
Assistance to Numerical Linear Algebra
Winter term 2016/17:
Assistance to Practical Course in Computer Sciences for Mathematicians
Summer term 2016:
Assistance to Mathematics for Engineers 2
Winter term 2015/16:
Assistance to Mathematics for Engineers 1

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Jim Magiera

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2024

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