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Afreemesh in general has no restrictions in terms of element shapes, and has no specified pattern applied to it. Thus, can be used on irregular or complex geometries where mapped mesh is not possible. On the other hand a mapped mesh is restricted in terms of the element shape it contains and the pattern of the mesh. A mapped area mesh contains either only quadrilateral or only triangular elements, while a mapped volume mesh contains only hexahedron elements. In addition, a mapped mesh typically has a regular pattern, with obvious rows of elements. If you want this type of mesh, you must build the geometry as a series of fairly regular volumes and/or areas that can accept a mapped mesh. Also, there is no set distinction on which one is better you need to use your engineering judgement to decide.
Regards
Ishan.
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