Topology optimization and boundary elements—a preliminary implementation for linear heat transfer

A numerical approach for topology optimization of thermal conducting solids using the boundary element method (BEM) is introduced. The formulation is based on some recent results concerning the evaluation of topological derivative, which is preliminarily applied for a class of potential problems. Since no homogenization procedures are used, sub-optimal solutions are obtained without intermediary material densities. Domain meshes are unnecessary, thus preserving one of the BEM advantages. Results for some cases of diffusive heat transfer problems are presented showing good agreement with the available literature, and opening a broad class of problems to be solved using integral equation methods.