Newton linearization of the curvature operator in structured grid generation with sample solutions
type: Item
instance of: scholarly article
title: Newton linearization of the curvature operator in structured grid generation with sample solutions
zbMATH Open document ID: 1497.65207
DOI: 10.1155/2022/7266801
author: Pat Piperni
author: Maahi M. Talukder
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2022-09-30T00:00:00Z
review text: Summary: Elliptic grid generation equations based on the Laplacian operator have the well-known property of clustering the mesh near convex boundaries and declustering it near concave boundaries. In prior work, a new differential operator was derived and presented to address this issue. This new operator retains the strong smoothing properties of the Laplacian without the latter's adverse curvature effects. However, the new operator exhibits slower convergence properties than the Laplacian, which can lead to increased turnaround times and in some cases preclude the achievement of convergence to machine accuracy. In the work presented here, a Newton linearization of the new operator is presented, with the objective of achieving more robust convergence properties. Sample solutions are presented by evaluating a number of solvers and preconditioners and assessing the convergence properties of the solution process. The efficiency of each solution method is demonstrated with applications to two-dimensional airfoil meshes.
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N55
zbMATH DE Number: 7595568
Wikidata QID: Q114068029
describes a project that uses: PETSc
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2022/7266801
OpenAlex ID: W4284969398
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description: scientific article; zbMATH DE number 7595568