In this paper, we propose a new level set-based topology optimization method targeting metallic waveguide design problems. Since metallic waveguides are usually used in microwave range, the skin effect must be taken into account when metallic waveguides are designed. One of the simplest methods to deal with the skin effect is to impose the electric field constraint condition on the surface of the metal walls when the electric field is computed. Therefore, we impose this condition on the surface of the metal walls represented by the zero iso-contour of the level set function. That is, we solve a topology optimization problem where the design-dependent Dirichlet boundary condition is imposed. For this purpose, we provide a mesh which tracks the level set boundary. By imposing the Dirichlet boundary condition at the nodes on the level set boundary in this mesh, the electric field can be computed using the ordinary FEM. Since this mesh tracks the level set boundary by moving nodes at every optimization iteration, it can be viewed as an ALE mesh, and our proposed method also can be viewed as a level set-based topology optimization method incorporated with the ALE method. By using the Eulerian and ALE meshes, we solve the optimization problem. To demonstrate the usefulness of the proposed method, some numerical examples are provided.
