Finite element simulations: computations and applications to aerodynamics and biomedicine.

171 p.Las ecuaciones en derivadas parciales describen muchos fenómenos de interés práctico y sus solucionessuelen necesitar correr simulaciones muy costosas en clústers de cálculo.En el ámbito de los flujos turbulentos, en particular, el coste de las simulaciones es demasiado grande sise utilizan métodos básicos, por eso es necesario modelizar el sistema.Esta tesis doctoral trata principalmente de dos temas en Cálculo Científico.Por un lado, estudiamos nuevos desarrollos en la modelización y simulación de flujos turbulentos;utilizamos un Método de Elementos Finitos adaptativo y un modelo de ¿número de Reynolds infinito¿para reducir el coste computacional de simulaciones que, sin estas modificaciones, serían demasiadocostosas.De esta manera conseguimos lograr simulaciones evolutivas de flujos turbulentos con número deReynolds muy grande, lo cual se considera uno de los mayores retos en aerodinámica.El otro pilar de esta tesis es una aplicación biomédica.Desarrollamos un modelo computacional de Ablación (Cardiaca) por Radiofrecuencia, una terapiacomún para tratar varias enfermedades, por ejemplo algunas arritmias.Nuestro modelo mejora los modelos existentes en varias maneras, y en particular en tratar de obteneruna aproximación fiel de la geometría del sistema, lo cual se descubre ser crítico para simularcorrectamente la física del fenómeno

A Tool for Aligning Event Logs and Prescriptive Process Models through Automated Planning

In Conformance Checking, alignment is the problem of detecting and repairing nonconformity between the actual execution of a business process, as recorded in an event log, and the model of the same process. Literature proposes solutions for the alignment problem that are implementations of planning algorithms built ad-hoc for the specific problem. Unfortunately, in the era of big data, these ad-hoc implementations do not scale sufficiently compared with well-established planning systems. In this paper, we tackle the above issue by presenting a tool, also available in ProM, to represent instances of the alignment problem as automated planning problems in PDDL (Planning Domain Definition Language) for which state-of-the-art planners can find a correct solution in a finite amount of time. If alignment problems are converted into planning problems, one can seamlessly update to the recent versions of the best performing automated planners, with advantages in term of versatility and customization. Furthermore, by employing several processes and event logs of different sizes, we show how our tool outperforms existing approaches of several order of magnitude and, in certain cases, carries out the task while existing approaches run out of memory

Motion of three-dimensional elastic films by anisotropic surface diffusion with curvature regularization

Short time existence for a surface diffusion evolution equation with curvature regularization is proved in the context of epitaxially strained three-dimensional films. This is achieved by implementing a minimizing movement scheme, which is hinged on the $H^{-1}$-gradient flow structure underpinning the evolution law. Long-time behavior and Liapunov stability in the case of initial data close to a flat configuration are also addressed.Comment: 44 page

Higher order quasiconvexity reduces to quasiconvexity

In this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it is proved that a smooth strictly 2-quasiconvex function with p-growth at infinity, p>1, is the restriction to symmetric matrices of a 1-quasiconvex function with the same growth. As a consequence, lower semicontinuity results for second-order variational problems are deduced as corollaries of well-known first order theorems.Comment: 28 page