Generation of Curved High-order Meshes with Optimal Quality and Geometric Accuracy

We present a novel methodology to generate curved high-order meshes featuring optimal mesh quality and geometric accuracy. The proposed technique combines a distortion measure and a geometric Full-size image (<1 K)-disparity measure into a single objective function. While the element distortion term takes into account the mesh quality, the Full-size image (<1 K)-disparity term takes into account the geometric error introduced by the mesh approximation to the target geometry. The proposed technique has several advantages. First, we are not restricted to interpolative meshes and therefore, the resulting mesh approximates the target domain in a non-interpolative way, further increasing the geometric accuracy. Second, we are able to generate a series of meshes that converge to the actual geometry with expected rate while obtaining high-quality elements. Third, we show that the proposed technique is robust enough to handle real-case geometries that contain gaps between adjacent entities.This research was partially supported by the Spanish Ministerio de Economía y Competitividad under grand contract CTM2014-55014-C3-3-R, and by the Government of Catalonia under grand contract 2014-SGR-1471. The work of the last author was supported by the European Commission through the Marie Sklodowska-Curie Actions (HiPerMeGaFlows project).Peer ReviewedPostprint (published version

Huis Clos de Sartre, una estètica de les relacions amb el proïsme

La peça de teatre Huis Clos (HC) de Sartre mostra en forma de consciència no-tètica, en la forma estètica del "fer sentir" a l'espectador, les mateixes tesis que els capítols dedicats a la relacions concretes amb el proïsme a l'Ètre et le Néant (EN). Tot i això aquest teatre intel•lectual també pertany, per Sartre, al domini de la literatura, amb funcions ètiques, que separa del de la poesia, lligada a la imaginació, a la fuga a l'irreal i àdhuc al mal com analitza a St. Genet. Ambdues dimensions fan pensar que no es tracta què el teatre de S. il•lustri tesis, sinó que la seva filosofia tracta en el fons del "teatre de situacions" o conflictiva de les consciències. El nostre treball torna a fer reflexió o tesi a partir d'una lectura estètica de HC i aborda amb les categories sartreanes de EN el projectes impossibles de convivència que s'ordeixen a l'infern sartreà

Generation of curved high-order meshes with optimal quality and geometric accuracy

We present a novel methodology to generate curved high-order meshes featuring optimal mesh quality and geometric accuracy. The proposed technique combines a distortion measure and a geometric L2-disparity measure into a single objective function. While the element distortion term takes into account the mesh quality, the L2-disparity term takes into account the geometric error introduced by the mesh approximation to the target geometry. The proposed technique has several advantages. First, we are not restricted to interpolative meshes and therefore, the resulting mesh approximates the target domain in a non-interpolative way, further increasing the geometric accuracy. Second, we are able to generate a series of meshes that converge to the actual geometry with expected rate while obtaining high-quality elements. Third, we show that the proposed technique is robust enough to handle real-case geometries that contain gaps between adjacent entities.Peer ReviewedPostprint (published version

Minimization of the distortion of quadrilateral and hexahedral meshes

En este artículo se presenta un algoritmo para la minimización de la medida de la distorsión definida por Oddy para una malla formada por cuadriláteros o hexaedros. Aunque dicha medida ha sido ampliamente utilizada, su definición original presenta varias propiedades que limitan su utilización en un algoritmo de minimización. Por ejemplo, sólo es válida para cuadriláteros o hexaedros convexos y proporciona un valor infinito de la distorsión en un cuadrilátero en el que tres vértices están alineados. Con el fin de superar estas limitaciones, en este trabajo primero se deduce una interpretación geométrica de la definición original de la medida de la distorsión. Además se demuestra que dicha interpretación es válida tanto para cuadriláteros como para hexaedros. Seguidamente y basándose en dicha interpretación, se desarrolla una medida de la distorsión para cuadriláteros y hexaedros no convexos. Finalmente, se presenta un algoritmo para la minimización de la nueva medida de la distorsión de la malla basado en el método de Newton-Raphson. Es importante resaltar que ambas definiciones coinciden cerca de la solución óptima. Así mismo, se presentan varios ejemplos que confirman la eficiencia del algoritmo desarrollado.Peer Reviewe

An improved algorithm to smooth graded quadrilateral meshes preserving the prescribed element size

In the generation of quadrilateral unstructured meshes, special attention is focussed to the shape of the elements. This is because it is well known that the distortion of the elements and the accuracy of the analysis are closely related. However, in adaptive schemes it is also essential that the newly generated mesh meets the prescribed element sizes in order to obtain a solution with the desired precision. In 1982 Giuliani developed a robust rezoning algorithm based on geometrical criteria. It gives proven results in a smooth element size distribution, but elements do not verify the prescribed element size when sharp distributions appear. This paper presents a modification of the Giuliani method that generates non-distorted elements while preserving the element size. Similar to the original method, this modification can be extended to three-dimensional cases