Adaptive T-spline refinement for isogeometric analysis in planar geometries

[EN]We present a new strategy, based on the meccano method [1, 2, 3], to construct a T-spline parameterization of 2D geometries for the application of isogeometric analysis. The proposed method only demands a boundary representation of the geometry as input data. The algorithm obtains, as a result, high quality parametric transformation between 2D objects and the parametric domain, the unit square. The key of the method lies in defining an isomorphic transformation between the parametric and physical T-mesh finding the optimal position of the interior nodes by applying a new T-mesh untangling and smoothing procedure. Bivariate T-spline representation is calculated by imposing the interpolation conditions on points sited both on the interior and on the boundary of the geometry…

Tetrahedral mesh optimization combining boundary and inner node relocation and adaptive local refinement

[EN]This work introduces a new technique for tetrahedral mesh optimization. The procedure relocates boundary and inner nodes without changing the mesh topology. In order to maintain the boundary approximation while boundary nodes are moved, a local refinement of tetrahedra with faces on the solid boundary is necessary in some cases. New nodes are projected on the boundary by using a surface parameterization. In this work, the proposed method is applied to tetrahedral meshes of genus-zero solids that are generated by the meccano method. In this case, the solid boundary is automatically decomposed into six surface patches which are parameterized into the six faces of a cube with the Floater parameterization...