How to make flat surface into concave surface with fixed parameter

Hi I a flat suface with the rounded perimeter, and I want to give a slight curve to the surface so that it becomes a suncave surface. I tried to convert it to SubD and lift the center point up, but it did not keep the original peremeter. Any tips?? Should I use grasshopper command? Please help me~~

Hello- it’s possible that just a Patch surface may get you what you need in this case-

Possibly followed by QuadRemesh


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