Isogeometric analysis based mesh adaptation for time dependent problems

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 equat...

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Bibliographic Details
Published in:Engineering with computers 2024-12, Vol.40 (6), p.3851-3874
Main Authors: Bahari, Mustapha, Habbal, Abderrahmane, Ratnani, Ahmed
Format: Article
Language:English
Subjects:
Accuracy
Adaptation
Adaptive algorithms
Algorithms
CAE) and Design
Calculus of Variations and Optimal Control
Optimization
Classical Mechanics
Computer Science
Computer-Aided Engineering (CAD
Computers
Control
Math. Applications in Chemistry
Mathematical and Computational Engineering
Methods
Monge-Ampere equation
Original Article
Partial differential equations
Solvers
Systems Theory
Time dependence
Citations: Items that this one cites
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Summary: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.
ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-024-02009-8