LEAST-SQUARES FINITE-ELEMENT FORMULATION IN THE TIME-DOMAIN FOR THE DUAL RECIPROCITY BOUNDARY ELEMENT METHOD IN HEAT-CONDUCTION

This paper presents a least squares finite element scheme applied to t he time domain in the dual reciprocity BEM as an alternative to two-po int finite difference or weighted residual schemes which have been use d so far in the literature to integrate the system of ordinary differe ntial equations in time arising from the spatial boundary element disc retization. The proposed scheme obtains the desired recurrence relatio ns via a least squares formulation in the context of one linear time e lement representing the entire time domain. Global boundary errors are used to obtain a measure of solution accuracy and convergence behavio r of the proposed scheme through detailed and systematic numerical exp eriments. Results are presented for four representative problems and c ompared with those obtained using three weighted residual schemes viz. the fully implicit, the Galerkin and the Crank-Nicolson schemes. The least squares scheme obtains, in general, the most accurate results at about the same computational cost as the weighted residual schemes an d exhibits superior convergence behavior. With linear time elements, t he proposed scheme shows nearly quadratic rate of convergence for all the problems considered; it indicates exponential convergence for the problems involving Dirichlet boundary conditions. Further, this least squares scheme gives very accurate large time solutions.