Advanced Thermoelastic Analysis

Abstract

The boundary element method (BEM) is now a versatile and powerful tool of computational mechanics which has become a popular alternative to the well-established finite element method (FEM). Recently, some authors indicated that the presence of any domain integrals undermines most advantages of the BEM. We believe that this is not true if the domain integral contains known quantities (such as body sources or initial values). The actual sources of advantages of the BEM formulation are not determined by the question of if it is necessary to discretize the domain or not. The BEM formulation for the solution of a boundary value problem exhibits pure boundary character if the solution at any internal point can be expressed in terms of the boundary integrals of relevant quantities and the domain integrals of known body sources and initial values, if any. In other words, the solution can be expressed at an internal point without the need to know the solution at any other internal point. If the boundary values of the relevant quantities were known exactly and the integrations were performed with absolute accuracy, the integral representation would present the exact solution of the boundary value problem. That is why in the BEM solution, extreme emphasis is put on the accuracy of the approximations of boundary values and computation of boundary integrals. Since in the domain discretization techniques (such as FEM, finite difference method, collocation methods) the unknowns at all nodal points are computed simultaneously, the computational error is accumulated.