Curvilinear Mesh Adaptation using Radial Basis Function Interpolation and Smoothing

TL;DR

This paper introduces an iterative RBF-based method for generating and smoothing high-quality 2D and 3D curvilinear meshes from straight-sided or other meshes, effectively handling singular deformation maps.

Contribution

The paper presents a novel iterative RBF interpolation and smoothing technique that approximates coordinate deformation maps using boundary scattered nodes, applicable to 2D and 3D mesh generation.

Findings

Produces high-quality deformed meshes

Handles singular deformation maps effectively

Applicable to both 2D and 3D mesh generation

Abstract

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.