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An equation-free approach for second order multiscale hyperbolic problems in non-divergence form
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. École Polytechniques Fédérale de Lausanne, Switzerland. (MAM)ORCID iD: 0000-0003-4481-0964
Uppsala University, Uppsala, Sweden.
2018 (English)In: Communications in Mathematical Sciences, ISSN 1539-6746, E-ISSN 1945-0796, Vol. 16, no 8, p. 2317-2343Article in journal (Refereed) Published
Abstract [en]

The present study concerns the numerical homogenization of second order hyperbolic equations in non-divergence form, where the model problem includes a rapidly oscillating coefficient function. These small scales influence the large scale behavior, hence their effects should be accurately modelled in a numerical simulation. A direct numerical simulation is prohibitively expensive since a minimum of two points per wavelength are needed to resolve the small scales. A multiscale method, under the equation-free methodology, is proposed to approximate the coarse scale behaviour of the exact solution at a cost independent of the small scales in the problem. We prove convergence rates for the upscaled quantities in one as well as in multi-dimensional periodic settings. Moreover, numerical results in one and two dimensions are provided to support the theory.

Place, publisher, year, edition, pages
2018. Vol. 16, no 8, p. 2317-2343
National Category
Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-45331DOI: 10.4310/CMS.2018.v16.n8.a11OAI: oai:DiVA.org:mdh-45331DiVA, id: diva2:1355425
Available from: 2019-09-28 Created: 2019-09-28 Last updated: 2019-10-12Bibliographically approved

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Arjmand, Doghonay

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