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The framework is geared towards isogeometric analysis (IGA) applications wherein the physical domain is comprised of more than four sides, hence requiring more than one patch. We adopt the concept of harmonic maps and propose several PDE-based problem formulations capable of finding a valid map between a convex parametric multipatch domain and the piecewise-smooth physical domain with an equal number of sides. In line with the <jats:italic>isoparametric paradigm<\/jats:italic> of IGA, we treat the parameterisation problem using techniques that are characteristic for the analysis step. As such, this study proposes several IGA-based numerical algorithms for the problem\u2019s governing equations that can be effortlessly integrated into a well-developed IGA software suite. We augment the framework with mechanisms that enable controlling the parametric properties of the outcome. Parametric control is accomplished by, among other techniques, the introduction of a curvilinear coordinate system in the convex parametric domain, for which more general elliptic PDEs are adopted. Depending on the application, parametric control allows for building desired features into the computed map, such as homogeneous cell sizes or boundary layers.<\/jats:p>","DOI":"10.1007\/s00366-024-01997-x","type":"journal-article","created":{"date-parts":[[2024,5,17]],"date-time":"2024-05-17T15:01:58Z","timestamp":1715958118000},"page":"3735-3764","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On the use of elliptic PDEs for the parameterisation of planar multipatch domains"],"prefix":"10.1007","volume":"40","author":[{"given":"Jochen","family":"Hinz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Annalisa","family":"Buffa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,5,17]]},"reference":[{"key":"1997_CR1","first-page":"4135","volume":"194","author":"TJR Hughes","year":"2005","unstructured":"Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. cmame 194:4135\u20134195","journal-title":"cmame"},{"key":"1997_CR2","doi-asserted-by":"publisher","DOI":"10.1002\/9780470749081","volume-title":"Isogeometric analysis: toward integration of CAD and FEA","author":"JA Cottrell","year":"2009","unstructured":"Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. 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The authors have no Conflict of interest to declare that are relevant to the content of this article. All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript. The authors have no financial or proprietary interests in any material discussed in this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}