An accurate and stable space-time radial basis function collocation method for transient coupled thermo-mechanical analysis

Abstract

In this study, an accurate and stable space-time radial basis function (STRBF) collocation method is developed to solve two- and three-dimensional dynamic coupled thermo-mechanical problems. The proposed method enhances numerical precision by strategically positioning source points beyond the computational domain through space-time scaling factors. To address the challenge of selecting the optimal shape parameter, a new coupled STRBF is formulated by combining the Multiquadric function with the conical spline. Furthermore, a multiscale computational strategy is implemented to mitigate numerical instability in the resulting linear system. The effectiveness of the developed approach is demonstrated through four numerical examples involving complex geometries and different initial and boundary conditions. Numerical results show that, compared to the traditional RBF collocation method, the developed scheme not only enhances computational accuracy but also significantly reduces the dependence on the choice of shape parameter, making it a promising method for dealing with transient coupled thermo-mechanical problems.