Nadir,
In a tied constraint you define the allowable distance between geometry to tie. Therefore, you do not need coincident points. Hope this helps.
Rob Stupplebeen
I tried it but a new error appears saying that the slave surface doesn't exist. For the problem, I have used a rigid body with a reference point as a center of the other points and it works 9for the momement) ).
After you partition, you will likely need to go back and re-define your constraint/interaction/tie with your newly partitioned model. Otherwise your original edge/surface data will no longer be valid, hence the new error message.