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How to deal with this mess to make this mesh smooth. I was using circle to make it

enter image description here

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The subdivision modifier won't produce good results with triangles in the geometry. (Carlo mentioned this answer, which showcases how the modifier works on topology.)

To solve this, use quads only.

enter image description here

  1. Delete the center vertice, select the edge loop and do the Grid Fill operation.
    enter image description here
  2. Recreate the sperical shape. Set the Cursor as Pivot (.). Place it in the imaginary center of the spherical shape. Select the flat grid geometry and press ⇧ Shift⎇ AltS to scale to sphere.
    enter image description here
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