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01-07-2024 | Original Article

Isogeometric analysis based mesh adaptation for time dependent problems

Authors: Mustapha Bahari, Abderrahmane Habbal, Ahmed Ratnani

Published in: Engineering with Computers | Issue 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.

previous article Correction to: Generic volume transfer for distributed mesh dynamic repartitioning

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Title: Isogeometric analysis based mesh adaptation for time dependent problems
Authors: Mustapha Bahari
Abderrahmane Habbal
Ahmed Ratnani
Publication date: 01-07-2024
Publisher: Springer London
Published in: Engineering with Computers / Issue 6/2024
Print ISSN: 0177-0667
Electronic ISSN: 1435-5663
DOI: https://doi.org/10.1007/s00366-024-02009-8

IGA Approximations of Elastic Interfaces and their Defects in an Elastic Medium with Couple Stress

Open Access
Original Article

Higher order phase-field modeling of brittle fracture via isogeometric analysis

Open Access
Original Article

Correction to: Generic volume transfer for distributed mesh dynamic repartitioning

Correction

Isogeometric analysis of architected materials and structures

Original Article

Goal-adaptive Meshing of Isogeometric Kirchhoff–Love Shells

Open Access
Original Article

Editorial: Special issue on isogeometric analysis

Editorial

Springer Professional

Abstract

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Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

IGA Approximations of Elastic Interfaces and their Defects in an Elastic Medium with Couple Stress

Higher order phase-field modeling of brittle fracture via isogeometric analysis

Correction to: Generic volume transfer for distributed mesh dynamic repartitioning

Isogeometric analysis of architected materials and structures

Goal-adaptive Meshing of Isogeometric Kirchhoff–Love Shells

Editorial: Special issue on isogeometric analysis