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Erschienen in:

01.07.2024 | Original Article

Isogeometric analysis based mesh adaptation for time dependent problems

verfasst von: Mustapha Bahari, Abderrahmane Habbal, Ahmed Ratnani

Erschienen in: Engineering with Computers | Ausgabe 6/2024

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Abstract

This article presents a new algorithm designed to create a dynamic r-adaptive mesh within the framework of isogeometric analysis. The approach is based on the simultaneous computation of adaptive meshes using a nonlinear parabolic Monge–Ampere equation with a resolution of partial differential equations in multidimensional spaces. The technique ensures the absence of geometric boundary errors and is simple to implement, requiring the solution of only one Laplace scalar equation at each time step. It utilizes a fast diagonalization method that can be adapted to any dimension. Various numerical experiments were conducted to validate an original parabolic Monge–Ampere solver. The solver was respectively applied to Burgers, Allen–Cahn, and Cahn–Hilliard problems to demonstrate the efficiency of the new approach.

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Metadaten
Titel
Isogeometric analysis based mesh adaptation for time dependent problems
verfasst von
Mustapha Bahari
Abderrahmane Habbal
Ahmed Ratnani
Publikationsdatum
01.07.2024
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 6/2024
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-024-02009-8