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.

In this paper, we will consider the problem of constructing stable maps between two closed orientable surfaces M and N with a given branch set of curves immersed on N. We will study, from a global point of view, the behavior of its families in different isotopies classes on the space of smooth maps. The main goal is to obtain different relationships between invariants. We will provide a new proof of Quine’s Theorem.

Modal analysis is widely used for addressing NVH—Noise, Vibration, and Hardness—in automotive engineering. The so-called principal modes constitute an orthogonal basis, obtained from the eigenvectors related to the dynamical problem. When this basis is used for expressing the displacement field of a dynamical problem, the model equations become uncoupled. Moreover, a reduced basis can be defined according to the eigenvalues magnitude, leading to an uncoupled reduced model, especially appealing when solving large dynamical systems. However, engineering looks for optimal designs and therefore it focuses on parametric designs needing the efficient solution of parametric dynamical models. Solving parametrized eigenproblems remains a tricky issue, and, therefore, nonintrusive approaches are privileged. In that framework, a reduced basis consisting of the most significant eigenmodes is retained for each choice of the model parameters under consideration. Then, one is tempted to create a parametric reduced basis, by simply expressing the reduced basis parametrically by using an appropriate regression technique. However, an issue remains that limits the direct application of the just referred approach, the one related to the basis ordering. In order to order the modes before interpolating them, different techniques were proposed in the past, being the Modal Assurance Criterion—MAC—one of the most widely used. In the present paper, we proposed an alternative technique that, instead of operating at the eigenmodes level, classify the modes with respect to the deformed structure shapes that the eigenmodes induce, by invoking the so-called Topological Data Analysis—TDA—that ensures the invariance properties that topology ensure.

In this paper, we de ne the concept of graph extension, embedded on a closed and orientable surfaces, associated to pairing of edges of regular polygons in order to show that the K-regular pairing of edges graphs can be obtained by the canonical extension of graphs (graphs with a single vertex). We will present examples of K-regular graphs associated to surfaces with genus g < 3.

The aim of this paper is to introduce a computational tool that checks theoretical conditions in order to determine whether a weighted graph, as a topological invariant of stable maps, can be associated to stable maps without cusps (i.e. fold maps) from closed surfaces to the projective plane.