The generalized finite difference method for long-time dynamic modeling of three-dimensional coupled thermoelasticity problems

Abstract

In this study, a new framework for the efficient and accurate solutions of three-dimensional (3D) dynamic coupled thermoelasticity problems is presented. In our computations, the Krylov deferred correction (KDC) method, a pseudo-spectral type collocation technique, is introduced to perform the large-scale and long-time temporal simulations. The generalized finite difference method (GFDM), a relatively new meshless method, is then adopted to solve the resulting boundary-value problems. The GFDM uses the Taylor series expansions and the moving least squares approximation to derive explicit formulae for the required partial derivatives of unknown variables. The method, thus, is truly meshless that can be applied for solving problems merely defined over irregular clouds of points. For problem with complicated geometries, this paper also examines a new distance criterion for adaptive selection of nodes in the GFDM simulations. Preliminary numerical experiments show that the KDC accelerated GFDM methods are very promising for accurate and efficient long-time and large-scale dynamic simulations.