ABSTRACT
This chapter derives boundary element formulation and develops the forward time marching process for the transient Fourier equation. It then develops the Laplace transform boundary element methods for the unsteady Poisson equation. These two methods, combined with the dual reciprocity method, Fourier series method, or multiple reciprocity method, will enable readers to get the boundary element methods for the unsteady Poisson equation, although will provide no details since it will be repetitious. The chapter is devoted to the transient Fourier-Kirchhoff and the Helmholtz equations which are numerically solved with both the transient dual reciprocity method and multiple reciprocity method, by using the θ-scheme. The forward time marching can be used with the Laplace transform technique. The chapter illustrates the time–marching process by considering a one-dimensional example.
