A novel SCTBEM with inversion-free Padé series expansion for 3D transient heat transfer analysis in FGMs

In this study, a novel scaled coordinate transformation boundary element method (SCTBEM) is proposed to solve the transient heat transfer problem of three-dimensional (3D) functionally gradient materials. In order to compute the coefficient matrix only once when solving transient problems, the fundamental solution of Laplace operator is used to derive the boundary-domain integral equation. To maintain advantages of the boundary element method in dimensionality reduction, this study adopts the SCT technique proposed by Yu et al., to transform the domain integral into the boundary integral. With the aim of determining high precision heat flux, the dual interpolation technique is introduced for deriving integral equations only from the internal nodes of the surface element, which unifies the corner problem and achieves the coalescence of degrees of freedom. It is noteworthy that this study establishes the precise integration solution of the first order ordinary differential equation by means of Padé expansions without matrices inversion to improve the accuracy and efficiency of the solution. Numerical results show that both temperature and heat flux of 3D functionally gradient materials are highly accurate and stable, even for complex multi-connection models.