1 research outputs found
A Method for Geometry Optimization in a Simple Model of Two-Dimensional Heat Transfer
This investigation is motivated by the problem of optimal design of cooling
elements in modern battery systems. We consider a simple model of
two-dimensional steady-state heat conduction described by elliptic partial
differential equations and involving a one-dimensional cooling element
represented by a contour on which interface boundary conditions are specified.
The problem consists in finding an optimal shape of the cooling element which
will ensure that the solution in a given region is close (in the least squares
sense) to some prescribed target distribution. We formulate this problem as
PDE-constrained optimization and the locally optimal contour shapes are found
using a gradient-based descent algorithm in which the Sobolev shape gradients
are obtained using methods of the shape-differential calculus. The main novelty
of this work is an accurate and efficient approach to the evaluation of the
shape gradients based on a boundary-integral formulation which exploits certain
analytical properties of the solution and does not require grids adapted to the
contour. This approach is thoroughly validated and optimization results
obtained in different test problems exhibit nontrivial shapes of the computed
optimal contours.Comment: Accepted for publication in "SIAM Journal on Scientific Computing"
(31 pages, 9 figures