In the BEM, one reduces the order of the problem by one, i.e., a two-dimensional domain is reduced to a line integral – a three-dimensional domain becomes a two-dimensional surface. The BEM only requires the discretization of the boundaries of the problem domain – no internal MESHING is required, as in the FDM, FVM, and FEM schemes. The BEM requires two applications of the Green-Gauss Theorem (VERSUS one in the FEM and employing Galerkin’s Method). The method is ideal for handling irregular shapes and setting boundaries that may extent to (near) infinity. One can PLACE interior nodes within the BEM to obtain internal values easily. The BEM works quite effectively for linear differential equations – principally elliptic equations. However, if one desires to solve nonlinear advection-diffusion transport equations, the method becomes very cumbersome and computationally demanding – BEM MATRICES are dense, and do not readily permit efficient, sparse matrix solvers to be used as in the FEM.

In the BEM, one reduces the order of the problem by one, i.e., a two-dimensional domain is reduced to a line integral – a three-dimensional domain becomes a two-dimensional surface. The BEM only requires the discretization of the boundaries of the problem domain – no internal meshing is required, as in the FDM, FVM, and FEM schemes. The BEM requires two applications of the Green-Gauss Theorem (versus one in the FEM and employing Galerkin’s Method). The method is ideal for handling irregular shapes and setting boundaries that may extent to (near) infinity. One can place interior nodes within the BEM to obtain internal values easily. The BEM works quite effectively for linear differential equations – principally elliptic equations. However, if one desires to solve nonlinear advection-diffusion transport equations, the method becomes very cumbersome and computationally demanding – BEM matrices are dense, and do not readily permit efficient, sparse matrix solvers to be used as in the FEM.