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Y. Ofir¹, D. Rabinovich² and D. Givoli²

¹Inter-departmental Program of Applied Mathematics, Technion, Israel Institute of Technology, Haifa, Israel
²Department of Aerospace Engineering, Technion, Israel Institute of Technology, Haifa, Israel

Keywords: coupling, 2D-1D, Panasenko, Dirichlet-to-Neumann, Nitsche, low dimension, high dimension, time-harmonic, elastodynamic, elastic waves, hybrid model, derivative-recovery..

Summary

The coupling of two-dimensional (2D) and one-dimensional (1D) models in time harmonic elasticity is considered. The hybrid 2D-1D model is justified for cases 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 2D-1D models are (a) the design of the hybrid model and its validation (with respect to the original problem), and (b) the way the 2D-1D coupling is done, and the coupling error generated. This paper focuses on the second issue. Three numerical methods are adapted to the 2D-1D 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 studied here. The accuracy of the 2D-1D coupling by the three methods is compared numerically for a specially designed benchmark problem, and conclusions are drawn on their relative performances.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 106 PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: Paper 68 Computational Coupling of One Dimensional and Two Dimensional Models for Elastic Structures Y. Ofir¹, D. Rabinovich² and D. Givoli² ¹Inter-departmental Program of Applied Mathematics, Technion, Israel Institute of Technology, Haifa, Israel ²Department of Aerospace Engineering, Technion, Israel Institute of Technology, Haifa, Israel doi:10.4203/ccp.106.68 purchase the full-text of this paper Full Bibliographic Reference for this paper Y. Ofir, D. Rabinovich, D. Givoli, "Computational Coupling of One Dimensional and Two Dimensional Models for Elastic Structures", in , (Editors), "Proceedings of the Twelfth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 68, 2014. doi:10.4203/ccp.106.68 Keywords: coupling, 2D-1D, Panasenko, Dirichlet-to-Neumann, Nitsche, low dimension, high dimension, time-harmonic, elastodynamic, elastic waves, hybrid model, derivative-recovery.. Summary The coupling of two-dimensional (2D) and one-dimensional (1D) models in time harmonic elasticity is considered. The hybrid 2D-1D model is justified for cases 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 2D-1D models are (a) the design of the hybrid model and its validation (with respect to the original problem), and (b) the way the 2D-1D coupling is done, and the coupling error generated. This paper focuses on the second issue. Three numerical methods are adapted to the 2D-1D 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 studied here. The accuracy of the 2D-1D coupling by the three methods is compared numerically for a specially designed benchmark problem, and conclusions are drawn on their relative performances. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £65 +P&P)
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