Level set-based topology optimization using an immersed boundary element method

In this presentation, we propose a new immersed boundary element method (BEM) targeting level set-based topology optimization and construct a concrete topology optimization method using the immersed BEM. The key idea of the immersed BEM is replacing the nodal coordinates of the boundary element mesh with the nodal level set function values and the nodal coordinates of the Eulerian mesh maintaining the level set function. By this replacement, the boundary element mesh seems to be immersed in the Eulerian mesh. The relationship between the nodal coordinates of the boundary element mesh and the nodal level set function of the Eulerian mesh is clearly given in the immersed BEM, therefore, we can strictly derive the sensitivities of the nodal coordinates of the boundary element mesh with respect to the nodal level set function of the Eulerian mesh. That is, we can strictly derive the sensitivities of the objective function with respect to the nodal level set function, by using the immersed BEM. In the constructed topology optimization method, optimization is therefore performed using the strictly derived sensitivities while completely eliminating grayscale elements. The usefulness of the immersed BEM and the constructed topology optimization method is confirmed using a numerical example.