Level set-based topology optimization of two dimensional heat conduction problems using the boundary element method

A level set-based topology optimization method is presented for the two-dimensional heat transfer problem with heat convection boundary conditions using the boundary element method (BEM). The level set method is used to represent the structural boundaries, and the boundary mesh is generated based on the level set function. The major novel aspect of this paper is that the governing equation is solved without the ersatz material approach and the approximated heat convection boundary condition, but by tracking the actual boundary with the mesh generation. First, the level set-based topology optimization method is briefly discussed. Using the level set based boundary expression, the topology optimization problem for the heat transfer problem with heart convection boundary condition is formulated. Next, the topological derivative is derived based on the formulation. Finally, two-dimensional numerical examples are provided to confirm the validity of the derived topological derivation and the proposed topology optimization method.