Mustapha Bahari, Abderrahmane Habbal, Ahmed Ratnani
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引用次数: 0
摘要
本文介绍了一种新算法,旨在等几何分析框架内创建动态 r 自适应网格。该方法基于同时计算自适应网格,使用非线性抛物线蒙日-安培方程和多维空间偏微分方程解析。该技术可确保不出现几何边界误差,而且实施简单,只需在每个时间步解决一个拉普拉斯标量方程。它采用快速对角化方法,可适用于任何维度。为了验证最初的抛物线蒙日-安培求解器,我们进行了各种数值实验。该求解器分别应用于 Burgers、Allen-Cahn 和 Cahn-Hilliard 问题,以证明新方法的效率。
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 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.
期刊介绍:
Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.