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This paper deals with how to obtain the optimal shape of a permanent magnet of surface mounted permanent magnet brushless synchronous machine using the level set based topology optimization method. Two types of the flux linkage calculation method are formulated; one is a modified method based on traditional flux linkage calculation through transient analysis and the other is the mono-tooth method newly introduced in this study. The mono-tooth method makes it possible to avoid time-consuming transient analysis because it requires only magnetostatic field analysis and may deal with infinite design points. The level set based topology optimization method is combined with both types of flux linkage calculation method. The optimization problem for shape design of a surface mounted permanent magnet synchronous machine is defined focused on the permanent magnet shape design and optimization results by two different approaches are compared. The performance of the optimal model is also compared with that of a conventional magnet shape model.