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International Journal for Multiscale Computational Engineering

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ISSN Печать: 1543-1649

ISSN Онлайн: 1940-4352

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COMPARISON OF TWO-DIMENSIONAL-ONE-DIMENSIONAL COUPLING METHODS FOR TIME-HARMONIC ELASTICITY

Том 12, Выпуск 6, 2014, pp. 485-506
DOI: 10.1615/IntJMultCompEng.2014007923
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Краткое описание

The coupling of two-dimensional (2D) and one-dimensional (1D) models in time-harmonic elasticity is considered. The hybrid 2D1D model is justified in the case where some regions in the 2D computational domain behave approximately in a 1D way. This hybrid model, if designed properly, is much more efficient than the standard 2D model taken for the entire problem. Two important issues related to such hybrid 2D1D models are (a) the design of the hybrid model and its validation (with respect to the original problem), and (b) the way the 2D1D coupling is done, and the coupling error generated. The present paper focuses on the second issue. Three numerical methods are adapted to the 2D1D coupling scenario, for elastic time-harmonic waves: the Panasenko method, the Dirichlet-to-Neumann (DtN) method, and the Nitsche method. All three are existing methods that deal with interfaces; however, none of them has previously been adopted and applied to the type of problem under study here. The accuracy of the 2D1D coupling by the three methods is compared numerically for a specially designed benchmark problem, and conclusions are drawn on their relative performances.

ЦИТИРОВАНО В
  1. Ofir Yoav, Givoli Dan, DtN-based mixed-dimensional coupling using a Boundary Stress Recovery technique, Computer Methods in Applied Mechanics and Engineering, 287, 2015. Crossref

  2. Amosov Andrey, Panasenko Grigory, Partial dimension reduction for the heat equation in a domain containing thin tubes, Mathematical Methods in the Applied Sciences, 41, 18, 2018. Crossref

  3. Amar Hanan, Givoli Dan, Mixed-Dimensional Modeling of Time-Dependent Wave Problems Using the Panasenko Construction, Journal of Theoretical and Computational Acoustics, 26, 03, 2018. Crossref

  4. Amar Hanan, Givoli Dan, Mixed-dimensional coupling for time-dependent wave problems using the Nitsche method, Computer Methods in Applied Mechanics and Engineering, 349, 2019. Crossref

  5. Rabinovich Daniel, Givoli Dan, Elastodynamic 2D-1D coupling using the DtN method, Journal of Computational Physics, 448, 2022. Crossref

  6. Amosov A. A., Panasenko G. P., Partial Decomposition of a Domain Containing Thin Tubes for Solving the Diffusion Equation, Journal of Mathematical Sciences, 264, 5, 2022. Crossref

  7. Efrati Ron, Givoli Dan, Hybrid 3D-plane finite element modeling for elastodynamics, Finite Elements in Analysis and Design, 210, 2022. Crossref

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