Object Oriented Approach to Consistent Implementation of Meshless and Classical FEM

摘要

Numerical experiments show that the full potential of Finite Element Method (FEM) can be exploited by combination of classical with meshless FEM. A class structure for flexible consistent implementation of both methods is presented.Fully automatized 3D mesh-generations still constitutes a serious problem in software development concerning FEM. In the recent years various methods of meshless FEM have been developed as an alternative to overcome this problem. In this work meshless and classical FEM have been implemented.A further objective of this work is to implement different classical and meshless methods together with an appropriate mesh/point-set generation method. An appropriate class structure for realizing this in a consistent manner with classical FEM is developed and implemented in C++. The performance of the discussed methods was tested with problems relevant in electrical and civil engineering I.e. static electrical field calculations (Poisson equation) and elasticity problems.