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Posted by / 23-Mar-2019 14:12

Updating meshes on deforming domains

Numerical results show that the proposed mesh optimization algorithm outperforms the existing mesh optimization algorithm in terms of improving the worst element quality and eliminating inverted elements on the mesh.

It is well known that mesh qualities affect both the accuracy and efficiency of partial differential equation (PDE) solutions [1, 2].

Researchers have pointed out that mesh smoothing is preferred to topological changes for many PDE-based applications, since it is able to improve element qualities, while keeping mesh topologies [5].We propose a derivative-free mesh optimization algorithm, which focuses on improving the worst element quality on the mesh.The mesh optimization problem is formulated as a min-max problem and solved by using a downhill simplex (amoeba) method, which computes only a function value without needing a derivative of Hessian of the objective function.Optimization-based mesh quality improvement algorithms [2, 11, 13] are now becoming more popular, because these methods are able to offer high-quality meshes though with high computational costs.These methods formulate the nonlinear objective function over the entire mesh domain and improve mesh qualities by minimizing the objective function, while keeping mesh topologies [5, 14].

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