Hybrid fundamental solution based finite element method for axisymmetric potential problems

This paper describes a new type of hybrid fundamental solution based finite element method (HFS-FEM) for analysis of axisymmetric potential problems in multiply connected domain. In this approach, two independent potential fields are assumed within the element domain and on its boundary respectively. The fundamental solutions are utilized as internal trial functions to construct the non-conforming intra-element potential field. And the inter-element continuity is enforced by the conforming frame potential field which is of the same form as in the conventional FEM. Then, the axisymmetric modified variational functional is employed to derive the HFS finite element formulation. Finally, three numerical examples are given to demonstrate the validity, high-efficiency and robustness of the proposed method.