A boundary element approach for topology design in diffusive problems containing heat sources

The objective of this work is to present the application of a hard-kill material removal algorithm for topology optimization of heat transfer problems containing localized sources. The boundary element method is used to solve the governing equations. A topological-shape sensitivity approach is used to select the points showing the lowest sensitivities, where material is removed by opening a cavity. As the iterative process evolutes, the original domain has holes progressively punched out, until a given stop criteria is achieved. Both isotropic and orthotropic two-dimensional benchmarks are presented and analyzed. Because the BEM does not employ domain meshes in linear cases, the resulting topologies are completely devoid of intermediary material densities. Although the drawbacks of hard-kill methods are still present, the approach opens an interesting field of investigation for integral equation methods.