Comparison of Boundary Integral Equation and FE Methods

The boundary integral equation (BIE) method, with its origin in classical elasticity, has only in recent years been developed and used in structural mechanics. This method requires only boundary data, which reduces the dimension of the problem by one and relates boundary tractions and displacements through a system of integral equations. Through discretization and numerically, an algebraic system of equations is obtained and solved numerically. It appears that the BIE method has great potential in solving various structural problems alone, especially those with high stress gradients, or in conjunction with the finite element (FE) method. The purposes of this note are to apply the BIE method to some structural mechanics problems and to compare the results and efficiency with FE solutions.