Journal article
Topology optimization for nano-scale heat transfer
We consider the problem of optimal design of nano-scale heat conducting systems using topology optimization techniques. At such small scales the empirical Fourier's law of heat conduction no longer captures the underlying physical phenomena because the mean-free path of the heat carriers, phonons in our case, becomes comparable with, or even larger than, the feature sizes of considered material distributions.
A more accurate model at nano-scales is given by kinetic theory, which provides a compromise between the inaccurate Fourier's law and precise, but too computationally expensive, atomistic simulations. We analyze the resulting optimal control problem in a continuous setting, briefly describing the computational approach to the problem based on discontinuous Galerkin methods, algebraic multigrid preconditioned generalized minimal residual method, and a gradient-based mathematical programming algorithm.
Numerical experiments with our implementation of the proposed numerical scheme are reported.
Language: | English |
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Publisher: | John Wiley & Sons, Ltd. |
Year: | 2009 |
Pages: | 285-300 |
ISSN: | 10970207 and 00295981 |
Types: | Journal article |
DOI: | 10.1002/nme.2413 |
ORCIDs: | Evgrafov, Anton |