Asymptotic and numerical homogenization
Keyword(s):
Homogenization is an important mathematical framework for developing effective models of differential equations with oscillations. We include in the presentation techniques for deriving effective equations, a brief discussion on analysis of related limit processes and numerical methods that are based on homogenization principles. We concentrate on first- and second-order partial differential equations and present results concerning both periodic and random media for linear as well as nonlinear problems. In the numerical sections, we comment on computations of multi-scale problems in general and then focus on projection-based numerical homogenization and the heterogeneous multi-scale method.
2019 ◽
Vol 6
(1)
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pp. 299-306
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2016 ◽
Vol 299
◽
pp. 1
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2012 ◽
Vol 166-169
◽
pp. 2871-2875
2016 ◽
Vol 4
(1)
◽
pp. 1-2