Two derivative-free optimization algorithms for mesh quality improvement

13 years 2 months ago

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High-quality meshes are essential in the solution of partial diﬀerential equations (PDEs), which arise in numerous science and engineering applications, as the mesh quality aﬀects the solution accuracy, the solver execution time, and the problem conditioning. Mesh quality improvement is necessary when the mesh is of less than desirable quality (either from mesh generation or deformation). Nondiﬀerentiable objective functions arise when the goal of the mesh optimization is to improve the worst quality element in the mesh. We propose two derivative-free methods for mesh optimization, namely the pattern search (PS) and multidirectional search (MDS) mesh quality improvement methods, to be used with nondiﬀerentiable objective functions representing the overall mesh quality. Experimental results show that these two methods are successful in improving the worst quality mesh elements. The PS method yielded higher quality 2D meshes than did the MDS method; however, its execution time w...

Jeonghyung Park, Suzanne M. Shontz

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