LIU Bo, WANG Ke-yong, WANG Ming-hong. A Trefftz Finite Element Method for Solving Axisymmetric Poisson’s Equations[J]. Applied Mathematics and Mechanics, 2015, 36(2): 140-148. doi: 10.3879/j.issn.1000-0887.2015.02.003
Citation: LIU Bo, WANG Ke-yong, WANG Ming-hong. A Trefftz Finite Element Method for Solving Axisymmetric Poisson’s Equations[J]. Applied Mathematics and Mechanics, 2015, 36(2): 140-148. doi: 10.3879/j.issn.1000-0887.2015.02.003

A Trefftz Finite Element Method for Solving Axisymmetric Poisson’s Equations

doi: 10.3879/j.issn.1000-0887.2015.02.003
  • Received Date: 2014-09-09
  • Rev Recd Date: 2014-11-13
  • Publish Date: 2015-02-15
  • A Trefftz finite element formulation was proposed for solving a kind of axisymmetric Poisson’s equations by means of the radial basis functions (RBFs). The non-zero right-hand side term brought the particular solution into the Trefftz intra-element field, which gave rise to domain integration related to the resultant element stiffness equation. The involved domain integration was eliminated through approximation of the particular solution with the RBFs. Furthermore, the‘boundary integration only’advantages were preserved for the Trefftz finite element method (TFEM). To obtain the particular solution, all elemental nodes and centroids in the whole solution domain were chosen as the fundamental interpolation points. In the meantime, a virtual boundary was constructed outside the solution domain, and a number of virtual points were selected as the additional interpolation points on the virtual boundary. Numerical examples demonstrate that the proposed method is valid and applicable.
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