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Numerical simulation of the Dynamic Beam Equation using the SBP-SAT method
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology.
2014 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

A stable boundary treatment of the dynamic beam equation (DBE) with two different sets of boundary conditions has been conducted using the summation-by-parts-simultaneous-approximation-term (SBP-SAT) method. As the DBE involves a fourth derivative in space the numerical boundary treatment is highly non-trivial. Using SBP-SAT operators together with suitable time integration schemes the DBE has been simulated and a convergence study has been made. The results show that the SBP-SAT method produces a stable discretistation that is accurate enough to capture the dispersive nature of the dynamic beam equation. In additions simulations were made presenting the importance of a stable boundary treatment showing that the numerical solutions diverge when the boundaries were not handled correctly.

Place, publisher, year, edition, pages
2014. , 39 p.
TVE, TVE 14 046 juni
Keyword [en]
Dynamic beam equation, finite difference methods, stability, boundary treatment
National Category
Computational Mathematics
URN: urn:nbn:se:uu:diva-227121OAI: oai:DiVA.org:uu-227121DiVA: diva2:728594
Educational program
Master Programme in Engineering Physics
Available from: 2014-08-13 Created: 2014-06-24 Last updated: 2014-08-13Bibliographically approved

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