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In the topology optimization of electromagnetic devices, the convexity-oriented mapping method is efficient at avoiding local minimizers. The results are not affected by the initial material distribution and are in practice better than those obtained with conventional methods. However, as any other topology optimization method, the splitting of the design space into cells limits the resolution of the solutions. This paper suggests performing an adaptive remeshing during the optimization in order to enhance the resolution while keeping a reasonable number of cells and hence an acceptable computation time.