A hybrid mesh deformation algorithm using anisotropic PDEs and multiobjective mesh optimization

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. The hybrid mesh deformation algorithm consists of two steps, anisotropic finite element-based mesh warping (FEMWARP) followed by multiobjective mesh optimization. The first step estimates the interior vertex positions on the deformed mesh using the boundary deformation to choose appropriate partial differential equation (PDE) coefficients in the anisotropic FEMWARP method. 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.