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Analysis of HMM for Long Time Multiscale Wave Propagation Problems in Locally-Periodic MediaPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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(English)Manuscript (preprint) (Other academic)
##### Abstract [en]

##### National Category

Computational Mathematics
##### Research subject

Applied and Computational Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-160121OAI: oai:DiVA.org:kth-160121DiVA, id: diva2:788656
#####

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##### Projects

Multiscale methods for wave propagation
##### Funder

Swedish e‐Science Research Center
##### Note

##### In thesis

Multiscale wave propagation problems are difficult to solve numerically due to the interaction of different scales inherent in the problem. Extracting information about the average behaviour of the system requires resolving small scales in the problem. This leads to a tremendous computational burden if the size of microscopic variations are much smaller than the size of scales of interest. Heterogeneous multiscale methods (HMM) is a tool to avoid resolving the small scales everywhere. Nevertheless, it approximates the average part of the solution by upscaling the microscopic information on a small part of the domain. This leads to a substantial improvement in the computational cost. In this article, we analyze an HMM-based numerical method which approximates the long time behaviour of multiscale wave equations. In particular, we consider theoretically challenging case of locally-periodic media where fast and slow variations are allowed at the same time. We are interested in the long time regime (T=O(e^{-1})), where e represents the wavelength of the fast variations in themedia. We first use asymptotic expansions to derive effective equations describing the long time effects of the multiscale waves in multi-dimensional locally-periodic media. We then show that HMM captures these non-trivial long time eects. All the theoretical statements are general in terms of dimension. Two dimensional numericale xamples are considered to support our theoretical arguments

QS 2015

Available from: 2015-02-16 Created: 2015-02-16 Last updated: 2015-02-17Bibliographically approved1. Analysis and Applications of Heterogeneous Multiscale Methods for Multiscale Partial Differential Equations$(function(){PrimeFaces.cw("OverlayPanel","overlay788665",{id:"formSmash:j_idt841:0:j_idt848",widgetVar:"overlay788665",target:"formSmash:j_idt841:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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