Neural and Evolutionary Computing in Finite Element Analysis

Abstract

This paper presents a discussion of current neural and evolutionary techniques, applied to the field of Finite Element Analysis and Finite Element Mesh Generation. This numerical method is widely used in many science, and engineering analyses to compute many forms of static and dynamic fields and potentials, such as heat, stress or velocity, on a mesh of interconnecting elements. The accuracy of the underlying finite element mesh determines the magnitude of the error of the solution to the differential equations. Meshes have to be adapted to limit this as far as possible, usually in an a-posteriori sense. These techniques have been widely automated and used with great success, but no means yet exist which allow the efficient a-priori evaluation of a prospective finite element mesh before the equations are to be solved. As such, the application of expert and heuristic knowledge is largely required to produce visible benefits from adaptive remeshing processes. This paper discusses how neural and evolutionary architectures have addressed this problem and presents a complementary evolutionary model, which may aid in the generation of finite element meshes, as a result of on-going research into the development of such 'intelligent' techniques.