The Bloch Approximation in Periodically Perforated Media
We consider a periodically heterogeneous and perforated medium filling an open domain {omega} of R{sup N}. Assuming that the size of the periodicity of the structure and of the holes is O({epsilon}),we study the asymptotic behavior, as {epsilon} {sup {yields}} 0, of the solution of an elliptic boundary value problem with strongly oscillating coefficients posed in {omega}{sup {epsilon}}({omega}{sup {epsilon}} being {omega} minus the holes) with a Neumann condition on the boundary of the holes. We use Bloch wave decomposition to introduce an approximation of the solution in the energy norm which can be computed from the homogenized solution and the first Bloch eigenfunction. We first consider the case where {omega}is R{sup N} and then localize the problem for abounded domain {omega}, considering a homogeneous Dirichlet condition on the boundary of {omega}.
- OSTI ID:
- 21067438
- Journal Information:
- Applied Mathematics and Optimization, Vol. 52, Issue 1; Other Information: DOI: 10.1007/s00245-005-0822-5; Copyright (c) 2005 Springer; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
Similar Records
Homogenization of a mixed problem with Signorini condition for an elliptic operator in a perforated domain
On the Homogenization of a Damped Wave Equation