Journal of Scientific Computing

, Volume 77, Issue 1, pp 397–418 | Cite as

Curvilinear Mesh Adaptation Using Radial Basis Function Interpolation and Smoothing

  • Vidhi Zala
  • Varun Shankar
  • Shankar P. Sastry
  • Robert M. Kirby


We present a new iterative technique based on radial basis function (RBF) interpolation and smoothing for the generation and smoothing of curvilinear meshes from straight-sided or other curvilinear meshes. Our technique approximates the coordinate deformation maps in both the interior and boundary of the curvilinear output mesh by using only scattered nodes on the boundary of the input mesh as data sites in an interpolation problem. Our technique produces high-quality meshes in the deformed domain even when the deformation maps are singular due to a new iterative algorithm based on modification of the RBF shape parameter. Due to the use of RBF interpolation, our technique is applicable to both 2D and 3D curvilinear mesh generation without significant modification.


Curvilinear mesh generation Radial basis functions Conformal mapping Mesh deformation Mesh adaptation Mesh quality 

Mathematics Subject Classification

65 (L/N/M)50 30E05 41A05 



VZ was supported by NSF OCI-1148291 and NSF IIS-1212806. VS was supported by NSF DMS-1521748. SPS was supported in part by the NIH/NIGMS Center for Integrative Biomedical Computing Grant 2P41 RR0112553-12 and a Grant from the ExxonMobil corporation. RMK was supported in part by DMS-1521748 and W911NF-15-1-0222.


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Authors and Affiliations

  1. 1.Scientific Computing and Imaging InstituteUniversity of UtahSalt Lake CityUSA
  2. 2.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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