Before the development of the boundary element method, a number of other estimation techniques were used to solve boundary problems and partial differential equations. These techniques included the finite difference method and the finite element method. The boundary element method is considered superior to these other methods of solving partial differential equations because it is both more efficient and more accurate.
The integral equation is seen as a specific solution for the partial differential equation it is derived from. By setting this limitation in the equation, the method sets conditions on the boundary, and then seeks solutions that fit those conditions. The base formula can then be used to solve for the domain along the boundary and to give a finite number of answers that satisfy the parameters.
Using the boundary element method has a number of advantages. There are a finite number of solutions to be found when only the boundary is analyzed. Less time is wasted in pre-processing the data and computer-aided design (CAD) data can be directly transferred into the formulization. There is greater accuracy in final solutions for the equation. It can be easily modeled in both 2D and 3D and simplifies the mathematics required for a symmetric system.
There are some problems that cannot be appropriately solved using boundary element methods. Problems that are non symmetric, i.e., inhomogeneous, cannot be solved. Non-linear problems cannot be put into the appropriate form. In addition, problems that do not have sustainable and fundamental solutions are unusable, as well as those best solved with finite element methods.