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Numerical simulation of stationary diffusion problems using high-order hybridizable continuous and discontinuous Galerkin methods
Full text linkNumerical simulation of stationary diffusion problems using high-order hybridizable continuous and discontinuous Galerkin methods
No full textNumerical simulation of stationary diffusion problems using high-order hybridizable continuous and discontinuous Galerkin methods
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Numerical solution of PDEs in periodical domains
No full textWe present in this work two schemes of approximation for numerical solutions of PDEs. The first one is the maximum entropy method (max-ent) and the second one is the b-spline method. These methods let us impose a special kind of boundary conditions: periodic boundary conditions for unbounded domains. Some experiments need a large domain (or unbounded domain), however, this domain is divdided into some periodic cells. We develop a technique that let us simulate in the whole domain only doing a simulation in one cell. We apply this method for the resolution of second and fourth order problems (with periodic boundary conditions) like: Laplace, Kirchhoff plate and flexoelectricity
Computational modelling of flexoelectric materials based on C0-FEM for 4th order PDEs
No full textEl modelatge computacional de l'elasticitat de gradient de deformació i de l'acoblament electromecànic (és a dir, la exoelectricitat i la piezoelectricitat) sempre ha estat un repte atès l'alt ordre de les EDPs amb què es defineixen aquests fenòmens. En aquest treball presentem un plantejament basat en Elements Finits C0 estàndard que utilitza el Mètode de Penalització Interior (IPM, per les seves sigles en anglès) per imposar en forma feble continuïtat C1 entre elements. El mètode és validat amb experiments numèrics sobre exoelectricitat considerant
diferents solucions analítiques i la seva convergència és estudiada. Finalment, utilitzem el nostre mètode per resoldre exemples realistes extrets de la literatura
A C0 interior penalty method for 4th order PDE's
No full textFourth order Partial Differential Equations (PDE's) arise in many different physic's fields. As an example, the research group for Mathematical and Computational Modeling at UPC LaCàN is studying flexoelectricity, a very promising field which aims to replace some of the uses of piezoelectric materials, and whose equations involve 4th order derivatives. This work provides a method to solve these 4th order PDE's using the Finite Element Method (FEM) with C0 elements, which provides many advantages with respect to other methods that involve using C1 elements or decoupling the equation. The method is developed over the equations of the deformation of a Kirchoff plate, which is also a 4th order PDE. This method is then successfully validated with numerical experiments, both physical and artificial. An analysis of the convergence as well as the method's sensitivity to a newly added parameter is also provided. Due to the success of the method, LaCàN group will use this method to solve flexoelectricity's PDE's
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