A knowledge‐based A‐priori approach to mesh generation in thermal problems

Abstract

AbstractA new approach to the finite element mesh generation for two‐dimensional steady state thermal problems of conduction and convection is presented. Unlike other approaches, the proposed technique incorporates the information about the object geometry as well as the boundary and loading conditions to generate an a‐priori finite element mesh which is more refined around the critical regions of the problem domain. A blackboard architecture expert system is developed to intelligently identify critical regions and to choose the proper mesh size for them by performing an approximate heat flux calculation. From the results of the blackboard system, nodes are generated in the problem domain using the new concept of wave propagation. The wave propagation technique is fully automatic and does not require any user‐provided information except the data which define the object geometry and boundary conditions. After nodes are generated, well‐shaped triangular elements are formed ensuring the Delaunay property. During the triangulation process and to reduce the computation time for checking the overlapping problem, a new and efficient algorithm is proposed which defines a certain range only in which a potential triangular element might overlap the previously generated elements and boundary segments. Several examples are presented and discussed. When incorporated into and compared with the traditional approach to the adaptive finite element analysis, it is expected that the proposed approach, which starts the process with near‐optimal initial meshes, will result in lower levels of error and faster convergence of the solution to the desired accuracy in less time and at less cost.