Abstract

CASTANEDA-BALDERAS, Rubén; DIAZ-DIAZ, Alberto; DOMINGUEZ-ALVARADO, Axel Fernando  and  MARTINEZ-MORFIN, Claudio Iván. Solutions of Differential Equations by Finite Element (SEDEF). Ing. invest. y tecnol. [online]. 2020, vol.21, n.1, e00002.  Epub Aug 03, 2020. ISSN 2594-0732.  https://doi.org/10.22201/fi.25940732e.2020.21n1.002.

This paper presents the development of the first version of SEDEF, a free and open source software which proposes and solves a system of general differential equations that depends of two dimensions: spatial and temporal. These equations are proposed in a manner that they can model several physical phenomena. It’s worth mentioning that the spatial part of the general equations are solved by the finite element technique while the temporal part is solved by the BDF (“Backward Differentiation Formula”) method. These methods lead to the resolution of linear equations systems with sparse matrices. All the implementation is developed in C++ and the sparse matrices algebra is solved by the CSparse library created by Timothy A. Davis (2006). The software has an intuitive, easy to use graphic user interface (GUI) developed in RAD Studio XE. This GUI has three main modules that solve: heat transfer problems, in-plane Euler beam problems and mathematical problems which can be modeled by the generic unidimensional transient equations. Software validations are performed for each one of the modules by making the analysis of particular problems. Results obtained by SEDEF are compared with analytical solutions and results obtained by COMSOL Multiphysics, a commercial finite element software. The main purpose of SEDEF software is to provide academic institutions a tool that helps in understanding mathematics, physics and several engineering branches owing to the equations resolution and the friendly interface for preprocessing and postprocessing stages.

Keywords : Software; finite elements; differential equations; beams; heat transfer.

        · abstract in Spanish     · text in Spanish     · Spanish ( pdf )