This work is concerned with the development of a D-BEM approach to the solution of 2D scalar wave propagation problems. The time-marching process can be accomplished with the use of the Houbolt method, as usual, or with the use of the Newmark method. Special attention was devoted to the development of a procedure that allows for the computation of the initial conditions contributions. In order to verify the applicability of the Newmark method and also the correctness of the expressions concerned with the computation of the initial conditions contributions, four examples are presented and the D-BEM results are compared with the corresponding analytical solutions.

SUMMARYThis work is concerned with the development of different domain-BEM (D-BEM) approaches to the solution of two-dimensional diffusion problems. In the first approach, the process of time marching is accomplished with a combination of the finite difference and the Houbolt methods. The second approach starts by weighting, with respect to time, the basic D-BEM equation, under the assumption of linear and constant time variation for the temperature and for the heat flux, respectively. A constant time weighting function is adopted. The time integration reduces the order of the time derivative that appears in the domain integral; as a consequence, the initial conditions are directly taken into account. Four examples are presented to verify the applicability of the proposed approaches, and the D-BEM results are compared with the corresponding analytical solutions.