TIME INTEGRATION IN THE DUAL RECIPROCITY BOUNDARY-ELEMENT ANALYSIS OFTRANSIENT DIFFUSION

This paper presents a comprehensive study of the time integration in t he dual reciprocity boundary element analysis of transient diffusion. Detailed numerical experiments are performed using four representative test problems to assess the stability and presence of numerical oscil lations, convergence rate, and the time response of various time integ ration algorithms, viz. one and two step least squares methods, cubic Hermitian schemes, and one step and multistep theta-methods. A discuss ion of computational aspects such as the effect of flux averaging for Dirichlet problems, starting procedure for multistep methods and the c omputational efficiency is also included. The results indicate that fo r Dirichlet problems, a one step backward difference method should be preferred for short term response, whereas higher order schemes should be used for long term response. For problems free from Dirichlet boun dary conditions, all the higher order schemes yield accurate results o ver the entire time domain. For all the problems, a one step least squ ares algorithm appears to be the most accurate and efficient for mediu m to long term response. Further, an alternative time integration appr oach, which involves the partitioning of the boundary element system i nto differential and algebraic components, is proposed. Numerical resu lts indicate that the partitioned approach effectively damps out spuri ous numerical oscillations and results in more accurate solutions than the regular approach in which the differential algebraic system is so lved in the usual way without partitioning. (C) 1997 Elsevier Science Ltd.