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Asymptotic and numerical homogenization

  • B. Engquist (a1) and P. E. Souganidis (a1)


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.



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Acta Numerica
  • ISSN: 0962-4929
  • EISSN: 1474-0508
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