Time Dependent Problems

Abstract

Important advances have recently been made in the solution of time dependent problems using boundary elements. Some of the resulting papers have been published in the proceedings of the latest Boundary Element Conferences (C.A. Brebbia, 1981, 1982, 1983); while more definite work appeared as chapters in the Progress on Boundary Element Methods Series (C.A. Brebbia, 1981, 1983, 1984). The present chapter attempts to review some of the advances and applications of boundary elements for the solution of time dependent problems, including parabolic and hyperbolic cases with particular reference to temperature diffusion, wave propagation and elastodynamics. The case of diffusion problems follows the formulation described in more detail in ‘Time Dependent Potential Problems’ (Wrobel and Brebbia, 1981). The scalar wave propagation solution has been analysed in ‘Formulation of the Boundary Element Method for Transient Problems governed by the Scalar Wave Equation’ (Mansur and Brebbia, 1982) and ‘Numerical Implementation of the Boundary Element Method for two dimensional Transient Scalar Wave Propagation Problems’ (Mansur and Brebbia, 1982) while the case of transient elastodynamics is discussed in ‘Transient Elastodynamics’ (Mansur and Brebbia, 1984).