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Dr. Marcel Arndt

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Research Interests

  • multiscale methods for continuum mechanics (upscaling techniques, quasi-continuum method)
  • partial differential equations
  • numerical methods

Publications

Articles:
[1] M. Arndt, M. Luskin: Goal-Oriented Adaptive Mesh Refinement for the Quasicontinuum Approximation of a Frenkel-Kontorova Model. Computer Methods in Applied Mechanics and Engineering 197(49-50):4298-4306, 2008. Also as arXiv:0711.1876. [pdf, 233 KiB] [ps, 878 KiB]
[2] M. Arndt, M. Luskin: Error Estimation and Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation of a Frenkel-Kontorova Model. Multiscale Modeling and Simulation 7(1):147-170, 2008. Also as arXiv:0704.1924. [pdf, 316 KiB] [ps, 793 KiB]
[3] M. Arndt, M. Luskin: Goal-oriented Atomistic-continuum Adaptivity for the Quasicontinuum Approximation. International Journal for Multiscale Computational Engineering 5(5):407-415, 2007. Also as arXiv:0708.0025. [pdf, 167 KiB] [ps, 280 KiB]
[4] M. Arndt, M. Griebel, V. Novák, T. Roubícek, P. Sittner: Martensitic transformation in NiMnGa single crystals: Numerical simulation and experiments. International Journal of Plasticity 22(10):1943-1961, 2006. [pdf, 489 KiB]
[5] M. Arndt, M. Griebel: Derivation of higher order gradient continuum models from atomistic models for crystalline solids. Multiscale Modeling and Simulation 4(2):531-562, 2005. [pdf, 1307 KiB]
[6] M. Arndt, M. Griebel, T. Roubícek: Modelling and numerical simulation of martensitic transformation in shape memory alloys. Continuum Mechanics and Thermodynamics 15(5):463-485, 2003. [pdf, 558 KiB] [ps.gz, 531 KiB]
Series- and conference contributions:
[7] M. Arndt: Upscaling technique for the atomistic-continuum simulation of shape memory alloys with the EAM potential. Proceedings of the Sixth World Congress on Computational Mechanics (WCCM VI), Beijing, China. Tsinghua University Press & Springer, 2004. [pdf, 1022 KiB] [ps.gz, 2087 KiB]
[8] M. Arndt and M. Griebel: Higher order gradient continuum description of atomistic models for crystalline solids. In P. Neittaanmäki et al. (editors), Proceedings of the Fourth European Congress on Computational Methods in Applied Sciences and Engineering, Jyväskylä, Finland, 2004. [pdf, 633 KiB] [ps.gz, 871 KiB]
[9] M. Arndt: Modelling and numerical simulation of martensitic transformation. In W. L. Wendland and M. Efendiev (editors), Analysis and Simulation of Multifield Problems, Lecture Notes in Applied and Computational Mechanics, volume 12, pages 59-65. Springer, 2003.
Theses:
[10] M. Arndt: Upscaling from Atomistic Models to Higher Order Gradient Continuum Models for Crystalline Solids. Dissertation, Institute for Numerical Simulation, University of Bonn, 2004. [pdf, 4816 KiB]
[11] M. Arndt: Über die Ausbreitung von Flammenfronten in unendlichen Zylindern. Diplomarbeit, Mathematisches Institut, Universität Bonn, Germany, 1999. [pdf, 519 KiB] [ps, 255 KiB] [Errata, pdf, 47 KiB] [Errata, ps, 17 KiB]
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