اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدMetodos de Multiresolucion y su Aplicacion a un Modelo de Ingenieria
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Ricardo Ruiz Baier
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The main objective of this dissertation is to present an adaptation of some finite volume methods used in the resolution of problems arising in sedimentation processes of flocculated suspensions (or sedimentation with compression). This adaptation is based on the utilization of multiresolution techniques, originally designed to reduce the computational cost incurred in solving using high resolution schemes in the numerical solution of hyperbolic systems of conservation laws.
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A modification to the gnomonic factor using the concept of triangle of Plato is presented. With the aid of the platonic gnomonic factor (fgp) as we called it, we find that the oracles mentioned by Herodotus in his History, Dodona in Greece and Ammon
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own bidominio equations that model the electrical activity of the tissue in the myocardium. Two simple models are considered for membrane flows and ionic currents. First we define an approximate solution and we verify its convergence to the corresponding weak solution of the continuum problem, obtaining in this way an alternative demonstration that the continuum problem is well-posed. Next we introduce the multiresolution technique and derive an optimal noise reduction threshold. The efficiency and precision of our method is seen in the reduction of machine time, memory usage, and errors in comparison to other methods. ----- En este trabajo se presenta un metodo de volumenes finitos enriquecido con un esquema de multiresolucion completamente adaptativo para obtener adaptatividad espacial, y un esquema Runge-Kutta-Fehlberg con paso temporal de variacion local para obtener adaptatividad temporal, para resolver numericamente las conocidas ecuaciones bidominio que modelan la actividad electrica del tejido en el miocardio. Se consideran dos modelos simples para las corrientes de membrana y corrientes ionicas. En primer lugar definimos una solucion aproximada y nos referimos a su convergencia a la correspondiente solucion debil del problema continuo, obteniendo de este modo una demostracion alternativa de que el problema continuo es bien puesto. Luego de introducir la tecnica de multiresolucion, se deriva un umbral optimo para descartar la informacion no significativa, y tanto la eficiencia como la precision de nuestro metodo es vista en terminos de la aceleracion de tiempo de maquina, compresion de memoria computacional y errores en diferentes normas.
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