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Existing surface multigrid methods rely on composed local parameterizations or 3D projections for cross\u2010level transfer, requiring repeated per\u2010level local approximations that can degrade convergence. Our key insight is that a global conformal parameterization with cone singularities provides a shared coordinate system with low, controllable distortion, where prolongation reduces to exact planar barycentric interpolation. We construct the hierarchy directly in this domain using a seam\u2010aware simplification strategy, yielding sparse prolongation matrices with three entries per row. ParaMG converges in fewer V\u2010cycles than prior surface multigrid methods and delivers substantial speedups in applications with changing linear systems, including geometric flows, thin\u2010shell simulation, and polycube deformation.<\/jats:p>","DOI":"10.1111\/cgf.70491","type":"journal-article","created":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T11:19:46Z","timestamp":1786619986000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Surface Multigrid via Global Parametric Domain Simplification"],"prefix":"10.1111","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-0831-6279","authenticated-orcid":false,"given":"Anyu","family":"Zhao","sequence":"first","affiliation":[{"name":"University of Science and Technology of China  China"},{"name":"Shanghai Innovation Institute  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