A topological optimization procedure applied to multiple region problems with embedded sources

The main objective of this work is the application of the topological optimization procedure to heat transfer problems considering multiple materials. The topological derivative (DT) is employed for evaluating the domain sensitivity when perturbed by inserting a small inclusion. Electronic components such as printed circuit boards (PCBs) are an important area for the application of topological optimization. Generally, geometrical optimization involving heat transfer in PCBs considers only isotropic behavior and/or a single material. Multiple domains with anisotropic characteristics take an important role on many industrial products, for instance when considering PCBs which are often connected to other components of different materials. In this sense, a methodology for solving topological optimization problems considering anisotropy and multiple regions with embedded heat sources is developed in this paper. A direct boundary element method (BEM) is employed for solving the proposed numerical problem.