A novel fast Remesh-free mesh deformation method and its application to optimal design of electromagnetic devices

Optimal shape design of electromagnetic devices using finite-element (FE) parameter sweeping analysis is becoming a routine procedure today. In the optimal design process, different meshes for different device shapes are required for subsequent FE computations to obtain the values of objective function from the field solution. Traditional full or partial remeshing methods usually cost excessive computing time when generating these FE meshes, especially for 3-D problems. The proposed remesh-free method being reported requires only one set of fine computational mesh and an initial coarse mesh, which also forms a convex decomposition of the solution domain. For new geometry shapes, new deformed meshes can be quickly derived using a coordinate mapping technique once the new coordinates of the nodes on the initial boundary mesh are given. In this way, each mesh for each set of parameters can be produced quickly without remeshing, as only the existing fine mesh topological information is needed to update the nodal positions. The method can be applied to both 2-D and 3-D problems. 2-D and 3-D numerical examples are given to showcase the effectiveness of the proposed method.