Finite element heterogeneous multiscale method for the wave equation: long-time effects

A new finite element heterogeneous multiscale method (FE-HMM) is proposed for the numerical solution of the wave equation over long times in a rapidly varying medium. Our new FE-HMM-L method captures not only the short-time behavior of the wave field, well described by classical homogenization theory, but also more subtle long-time dispersive effects, both at a computational cost independent of the microscale. Optimal error estimates in the energy norm and the L-2-norm are proved over finite time intervals, which imply convergence to the solution from classical homogenization theory when both the macro-and the microscale are refined simultaneously. Numerical experiments illustrate the usefulness of the FE-HMM-L method and corroborate the theory.


Published in:
Multiscale Modeling and Simulation, 12, 3, 1230-1257
Year:
2014
Publisher:
Philadelphia, Siam Publications
ISSN:
1540-3459
Keywords:
Laboratories:




 Record created 2013-10-23, last modified 2018-03-17

n/a:
Download fulltext
PDF

Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)