Coupling dual reciprocity BEM and differential quadrature method for time-dependent diffusion problems

Abstract

This paper presents the very first combined application of dual reciprocity BEM (DRBEM) and differential quadrature (DQ) method to time-dependent diffusion problems. In this study, the DRBEM is employed to discretize the spatial partial derivatives. The DQ method is then applied to analogize temporal derivatives. The resulting algebraic formulation is the known Lyapunov matrix equation, which can be very efficiently solved by the Bartels–Stewart algorithms. The mixed scheme combines strong geometry flexibility and boundary-only feature of the BEM and high accuracy and efficiency of the DQ method. Its superiority is demonstrated through the solution of some benchmark diffusion problems. The DQ method is shown to be numerically accurate, stable and computationally efficient in computing dynamic problems. In particular, the present study reveals that the DRBEM is also very efficient for transient diffusion problems with Dirichlet boundary conditions by coupling the DQ method in time discretization.