Análise de problemas de valor de contorno primais estacionários via acoplamento MEF/MDF

Abstract

Several practical engineering problems are associated with physical phenomena that can be modeled by partial difeerential equations. Usually, the analytical solutions associated with these equations are dificult to obtain, which justifies the largescale use of numerical methods to solve such problems. At the heart of the idea of combining diferent numerical techniques is the improvement in modeling eficiency. This thesis presents a non-iterative multi-method scheme for solving general linear stationary primary boundary value problems with an arbitrary number of degrees of freedom. The main objective is to combine the performance of the finite element method for domains with arbitrary geometry with the eficiency of the finite difference method related to its low computational cost. Considering two-dimensional cases, a domain decomposition scheme to define rectangular subdomains is defined. In this way, a finite element mesh is generated so that the elements in the regular regions are rectangles. A suitable overlap scheme allows the nite element method to be used in regions with irregular elements, while the nite di erence method can be used in regions with regular elements. In the end, six computational experiments are presented, exemplifying diferent applications, showing the best performance in CPU time of the proposed scheme compared to the classical finite element method, while maintaining solution accuracy