Differential quadrature Trefftz method for Poisson-type problems on irregular domains

In this paper differential quadrature Trefftz method (DQTM), a new meshless method based on coupling the dual reciprocity method (DRM) with the differential quadrature method (DQM) and the Trefftz method, is used to analyze Poisson-type interior and exterior problems. In this method, the DRM is used to construct equivalent equations to the original differential equation. Then the DQM is employed to approximate the particular solutions, while Trefftz method leads to a boundary-only formulation for homogeneous solution. As a result, an inherently meshless, integration-free, boundary-only DQ Trefftz collocation technique is developed for solving Poisson-type problems. Due to the flexibility in choosing points on boundaries, the new method also works well on irregular domains. Numerical results show that the present method works efficiently with quite few points on both uniform and irregular domains.