This work proposes a methodology that uses Artificial Neural Networks to perform the Finite Element Method’s interpolation. The work proposes the use of a mesh with a smaller number of nodes, reducing the computational cost of the method. Subsequently, interpolation with Artificial Neural Networks is performed. The training is done using the points that are the mesh’s nodes. With its generalization capacity, the artificial neural network learns the behavior of greatness in that environment and interpolates the results for points that are not nodes. To evaluate the methodology, an electromagnetic problem in two dimensions is used. It was found that the Artificial Neural Network achieved better results than a linear interpolation for the homogeneous problem studied.

artificial neural networks, finite element method, interpolation, density of magnetic flux.

Received: February 3, 2021; Accepted: March 16, 2021: Published: March 20, 2021

How to cite this article: Leandro Mendes de Souza, Solving Differential Equations Using Artificial Neural Networks as a Mesh Expansion Strategy in the Finite Element Method, Far East Journal of Electronics and Communications 24(1) (2021), 21-33. DOI: 10.17654/EC024010021

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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