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Programa

Objetivos

  1. Manejar órdenes y algoritmos básicos en lenguaje de programación m de Octave/Matlab para trabajar con listas de números, vectores, matrices, sistemas lineales, funciones, graficar funciones de una o dos variables y manipulación de archivos (lectura/escritura).
  2. Comprender el proceso computacional involucrado en la creación y ejecución de programas en guiones (scripting) desde la ventana de órdenes o desde el editor gráfico.
  3. Adquirir conocimientos y habilidades de programación básica en lenguaje "m" de Octave/Matlab para resolver problemas simples de computación científica en ingeniería.

Laboratori de Càlcul Numèric - UPC

Laboratori de Càlcul Numèric (LaCàN) is a research group located in the Universitat Politècnica de Catalunya (UPC). The acronym stands for Mathematical and Computational Modeling. Our goal is to develop new mathematical and computational models to enable quantitative and predictive science and engineering. A central theme in all activities of the group is pushing the state of the art in the mathematical modeling of complex phenomena using partial differential equations and their numerical approximation with novel computational methods. Our interdisciplinary research is organized into three research programs with multiple cross-interactions.



Barcelona Supercomputing Center - UPC

Alya Red es un proyecto del Barcelona Supercomputing Center para simular un corazón humano. Este fue elegido como el mejor video científico del 2012 por la National Science Foundation y la revista Science.



Meshfree finite deformation thin‐shell analysis

Calculations on general point-set surfaces are attractive because of their flexibility and simplicity in the preprocessing but present important challenges. The absence of a mesh makes it nontrivial to decide if two neighboring points in the three-dimensional embedding are nearby or rather far apart on the manifold. Furthermore, the topology of surfaces is generally not that of an open two-dimensional set, ruling out global parametrizations. We propose a general and simple numerical method analogous to the mathematical theory of manifolds, in which the point-set surface is described by a set of overlapping charts forming a complete atlas. We proceed in four steps: (1) partitioning of the node set into subregions of trivial topology; (2) automatic detection of the geometric structure of the surface patches by nonlinear dimensionality reduction methods; (3) parametrization of the surface using smooth meshfree (here maximum-entropy) approximants; and (4) gluing together the patch representations by means of a partition of unity. Each patch may be viewed as a meshfree macro-element. We exemplify the generality, flexibility, and accuracy of the proposed approach by numerically approximating the geometrically nonlinear Kirchhoff--Love theory of thin-shells. We analyze standard benchmark tests as well as point-set surfaces of complex geometry and topology.