An ANN-based element extraction method for automatic mesh generation

Abstract

This paper proposes an artificial neural network based element extraction method for automatic finite element mesh generation. A finite element mesh is a discretized representation of a geometric domain. A domain is discretized into elements, which may be triangles, quadrilaterals, tetrahedron, or hexahedron. The element extraction method repeatedly generates element (s) within the domain using some predefined ‘if-then’ rules until the whole domain is filled with required elements. This method has an advantage of creating meshes for domains with complex boundaries. However, the ‘if-then’ rules for element extraction are usually difficult to acquire, because these rules not only generate elements but also change the problem they are designed to solve. In this paper, a Back-Propagation (BP) neural network is used to represent the ‘if-then’ element extraction rules and to train the relationship behind these rules. The input for this network includes the coordinates of some boundary points while the output defines the parameters for extracting an element. In order to generate good quality element while keeping the updated problem still solvable, the design and definition of the neural network is more complex than those in the traditional classification problems. This paper discusses issues related to the design of the neural network for element extraction. Numerical experiments on quadrilateral mesh generation have shown that this method is effective.