Tris leaving artifacts in smooth shading

Hey everyone,
I need your help. I’ve modeled a simple dome, with two circular cutouts as windows and a door frame.
There are visible artifacts around the cutouts in smooth shading, caused by some tris that I can’t seem to get rid of.
Any ideas on how I could fix this?

I uploaded the model here: http://www.pasteall.org/blend/32138

there are always problems when taking the quick way. the edges around the door and windows are full of triangles, and n-gons, and the edge flow does not reflect the form of the model. you have your basic shape, so I would suggest retopo-ing, at least around the doors and windows. be sure to only use quads, and to flow around the features with your edge loops. if you don’t know what retopo is or how to use it, just say something, and I will explain.
(edit) here’s an example. it’s a bit crude, but basically this is about how you’ll want your edges to flow:

Thanks for the quick reply. I do know what retopology is, but I’ve never really done it myself in Blender.

Suggesting the same as Modron but here’s another image of it


Edit: did it again but this time used retopo way using shrinkwrap modifier and also recorded the screen. Just a quick example of the steps, didn’t really put much care on the mesh

Main tools I used were inset (i key) with boundary off (b key while inset active) for the door, inset for the window, looptools addon -> circle to get it round. Edge and vertex slide (G key twice).

Thanks for the quick replies! The result looks great! That video is really helpful, thanks a ton!