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Isogeometric analysis based mesh adaptation for time dependent problems

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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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Authors and Affiliations

  1. The UM6P Vanguard Center, Mohammed VI Polytechnic University, Lot 660, Hay Moulay Rachid, Benguerir, 43150, Morocco

    Mustapha Bahari, Abderrahmane Habbal & Ahmed Ratnani

  2. Université Côte d’Azur, Inria, CNRS, LJAD UMR 7351, Parc Valrose, Nice, 06108, France

    Mustapha Bahari & Abderrahmane Habbal

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  1. Mustapha Bahari
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Bahari, M., Habbal, A. & Ratnani, A. Isogeometric analysis based mesh adaptation for time dependent problems. Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02009-8

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