2. Universidad Cardenal Herrera-CEU

Post-processing meshing algorithms are widely used to achieve the desired quality in quadrilateral meshes. Assuming that the mesh quality depends on the distortion and the size error of each of its convex quadrilaterals, deficiencies arise by considering solutions based in minimizing either the distortion or the size error. To solve this undesirable situation, in this paper we propose a new smoothing post-processing meshing algorithm. This procedure provides a good compromise between the distortion and the size of each element in the mesh. It is formulated by using an elasticity-based argument and allows to be implemented either in sequential or parallel form. Moreover, it provides a good quality output compared with some of the usual smoothing post-processing meshing algorithms.

A novel algorithm called the Proper Generalized Decomposition (PGD) is widely used by the engineering community to compute the solution of high dimensional problems. However, it is well-known that the bottleneck of its practical implementation focuses on the computation of the so-called best rank-one approximation. Motivated by this fact, we are going to discuss some of the geometrical aspects of the best rank-one approximation procedure. More precisely, our main result is to construct explicitly a vector field over a low-dimensional vector space and to prove that we can identify its stationary points with the critical points of the best rank-one optimization problem. To obtain this result, we endow the set of tensors with fixed rank-one with an explicit geometric structure.