A novel localized collocation solver based on a radial Trefftz basis for thermal conduction analysis in FGMs with exponential variations

Abstract

This paper introduces a novel localized radial Trefftz collocation method (LRTCM) for steady-state heat conduction analysis in 2D and 3D functionally graded materials (FGMs) with exponential variations. The LRTCM is constructed by combining the traditional radial Trefftz collocation method (RTCM) and the localized collocation scheme. In the proposed LRTCM, the radial Trefftz basis of the heat conduction equation in FGMs is derived by the variable transformation and domain mapping method, and the approximation solution at each node is expressed as a linear combination of a radial Trefftz basis in each local subdomain, thus the resulting sparse linear system naturally satisfies governing equation at interior nodes and boundary conditions at boundary nodes. The LRTCM not only inherits the advantages of the RTCM (meshlessness, no fictitious boundary and high accuracy), but also works well in large-scale structures or with more complicated boundary conditions when compared to the RTCM. Finally, the feasibility, accuracy, efficiency and stability of the proposed method are investigated by three examples.