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A parameterized mesh generation is presented for design optimization of electromagnetic devices. The proposed method requires no mesh regeneration, and hence the numerical simulation time can be reduced significantly. When the coordinates of nodes in the refined mesh are changed, the mesh topology will be kept, that is, the node connection relationship will remain the same as before. Thus the nodal solutions can be carried over from previous FEM results to subsequent FEM computation without the need of mapping the nodes between two meshes. Additionally, the mesh quality can remain high using a swapping diagonal technique. Based on the sample points obtained from FEM with parameterized mesh, the optimal model is reconstructed using the response surface methodology (RSM). The particle swarm optimization (PSO) method is then used to arrive at the optimal solution swiftly and efficiently. An optimal design of electromagnetic device is reported to verify the efficiency and effectiveness of the proposed method.