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As a second step, we find the local optimal mesh with no inverted elements on the deformed domain by employing multiobjective mesh optimization with one term controlling element shape and a second term designed to untangle inverted elements.Numerical results show that our hybrid algorithm outperforms existing mesh deformation algorithms in terms of mesh quality and number of inverted elements and is able to preserve 'similar' element shape on the deformed domain while eliminating inverted elements on the deformed domain.Edge swaps are then performed to further improve the mesh quality. Our numerical results show that our framework can be used to generate high quality meshes with no inverted elements for very large deformations.In particular, the addition of topological changes to our hybrid mesh deformation algorithm (Kim et al., Computer and Mathematics with Applications, Submitted, November 2014) proved to be an extremely efficient way of improving the mesh quality.Our method usually yields better quality meshes than existing methods for improvement of the worst quality elements, such as the active set, pattern search, and multidirectional search mesh quality improvement methods.
Our method is faster and more robust than existing methods for mesh untangling, such as the iterative stiffening method.The update method has limitations, of course, the most important being that there is no guarantee that the deformed mesh will be invertible. ABSTRACT: We propose a hybrid mesh deformation algorithm which uses the direction of the boundary deformation to determine the positions of the interior mesh vertices in the deformed mesh.Our goal is to produce meshes on deformed domains which maintain mesh 'similar' element shape and possess no inverted elements.To the greatest extent possible, the meshes should have similar element shape; however, topological changes are performed as necessary in order to improve mesh quality. The first step is to perform anisotropic finite element-based mesh warping to estimate the interior vertex positions based upon an appropriate choice of the PDE coefficients.Our framework is based upon the previous work of two of the authors and their collaborators (Kim et al., Int. The second step is to perform multiobjective mesh optimization in order to eliminate inverted elements and improve element shape.The hybrid mesh deformation algorithm consists of two steps, anisotropic finite element-based mesh warping (FEMWARP) followed by multiobjective mesh optimization.