An optimization scheme and matrix partitioning strategy are developed in conjunction with a boundary element solution procedure for inverse design in heat transfer. The optimal control problem is to locate interior heating or cooling passages inside a coated conducting domain to achieve a desired boundary temperature when the heat flux is specified (or vice versa). As the interior passages can be parameterized with a few variables, the optimization problem is of low dimension, the matrix partitioning scheme for the boundary element system and optimization search procedure lead to a fast computational scheme for this class of problems.

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