Numerical solutions of differential equations are typically performed directly. That is, the boundary conditions and physical properties of the domain are given and the dependent variable is numerically computed throughout the domain. In contrast, in inverse solutions of differential equations the dependent variable is known at select locations throughout the domain. However, the material properties and/or the boundary conditions are unknown. This paper presents a novel technique for solving an inverse heat conduction problem. In the problem examined, the temperature profile within a two-dimensional material and the available materials are known. However, the placement of these materials and the heat flux at the boundaries are unknown. The proposed technique uses the Adaptive Modeling by Evolving Blocks Algorithm (AMoEBA) to optimize material configurations via an evolutionary algorithm. The binary trees of AMoEBA describe segregation schemes for the different materials available. The domains described by each tree are solved directly. Using the least squares fit between these candidate solutions and the known profile, a population evolves until the fitness criterion is met. At this point, the material placement is found, and the boundary heat fluxes are calculated.
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