In engineering, numerical modeling and simulation are widely used for solving complex problems.
The BEM approach is very interesting in this way, as it allows to solve numerous problems, especially those, that require the use of differential equations.
The method is based on the discretization of the domain of the solution only at the boundaries, reducing the size of the problem and thus simplifying the required input data.
It is based on the resolution of an integral equation defined on the boundary instead of on the direct resolution of partial differential equations as is the case of FEM. In BEM, the starting equation is reformulated with an integral equation defined on the boundary of the domain (BIE - Boundary Integral Equation), and an integral that correlates the solution on the boundary with the solution in the internal points.
BEM can be widely applied to electromagnetic problems associated with electrical machines; to problems of airborne acoustic emission, fracture mechanics, potential flow around the airfoil and all those problems in which it is possible to define an integral equation.
Advantages of BEM:
The main advantages of this method can be identified with the simplicity of building a 3D model having to discretize only the surface of the body, the high precision for calculations in which the results on the border have a preponderant importance compared to those inside and with the adaptability to problems with open or mobile boundaries.
Advantages of FEM:
Typical advantages of FEM are found in the simplicity of solving non-linear problems and in the versatility of being extended to transient problems.
Advantages of both, BEM and FEM:
It’s beneficial to verify results by comparing the 2 different methods.