Finite element heterogeneous multiscale method for transient wave propagation

Abdulle Assyr, and Grote, Marcus J. and Stohrer, Christian. (2011) Finite element heterogeneous multiscale method for transient wave propagation. In: Proceedings of WAVES 2010, the 10th International conference on the mathematical and numerical aspects of waves. Vancouver, pp. 45-48.

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Official URL: http://edoc.unibas.ch/dok/A6070233

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A finite element heterogeneous multiscale method (FE-HMM) is proposed for the time dependent wave equation with highly oscillatory, albeit not necessarily periodic, coefficients. It is based on a finite element discretization of an effective wave equation at the macro scale, whose a-priori unknown effective coefficients are computed “on the fly” on sampling domains within each macro finite element at the micro scale ε < 0. Since the sampling domains scale in size with ε, which corresponds to the finest scales in the possibly highly heterogeneous medium, the computational work is independent of ε. In [1], we proved optimal error estimates in the energy norm and the L2-norm with respect to the micro and macro scale mesh parameters, h and H, and also convergence to the homogenized solution as ε → 0.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Numerik (Grote)
UniBasel Contributors:Grote, Marcus J. and Stohrer, Christian M.
Item Type:Conference or Workshop Item, refereed
Conference or workshop item Subtype:Conference Paper
Publisher:The Pacific Institute for the Mathematical Sciences
Note:Publication type according to Uni Basel Research Database: Conference paper
Last Modified:13 Sep 2013 07:59
Deposited On:13 Sep 2013 07:50

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