Two- and three-dimensional transient heat conduction and thermoelastic analyses by BEM via efficient time convolution

Abstract

Efficient re-integration based convolution algorithms are presented for a large class of problems involving transient two- and three-dimensional heat conduction and uncoupled thermoelastic analyses based on the earlier works of Dargush and Banerjee [G.F. Dargush, P.K. Banerjee, Application of boundary element method to transient heat conduction, Int. J. Numer. Methods Engrg. 31 (1991) 1231–1248; G.F. Dargush, P.K. Banerjee, Development of a boundary element method for time-dependent planar thermoelasticity, Int. J. Solids Struct. 25 (1989) 999–1021]. The main motivation behind the current development is the fact that the storage based convolution approach used in earlier developments was not found to be very suitable for solving large scale practical problems, because of substantial computer disk space requirement and the inability to handle time-dependent boundary conditions. In this paper, a re-integration based “full convolution” as well as an efficient and simplified re-integration based “fast convolution” algorithms are presented, in which, all of the time convolution steps have been calculated by preserving the energy balance as expressed in the convolution while assuming equivalent values of variables to represent the total effect. The accuracy and efficiency of the developed algorithms are demonstrated via numerical examples.