Numerical modeling and simulation provide an easier, cheaper, and highly efficient way of determining solutions for complex mathematical equations. In engineering, numerical modeling and simulation are widely used to solve complex problems. The development of computational numerical modeling has been advantageous in simplifying the problem-solving procedure.
In numerical modeling, various methods such as the discrete element method DEM , finite difference method FDM , boundary element method BEM , and finite element method FEM are used to develop models and solve problems.
While these methods are mostly analogous, here we will compare the boundary element method vs. In engineering designs, we come across several mathematical calculations, and the task of solving them involves devising the best possible solution. Conducting experiments is one method to reach a solution, but it requires significant effort, time, and money. Despite being prepared, technical difficulties and troubleshooting may delay a whole project.
Numerical modeling and simulation eliminate the need for experimental setup and provide an easier, cheaper, faster, accurate, and highly efficient way of determining solutions for complex mathematical equations. Numerical models are developed to match the physical system perfectly, and solutions can be analyzed and verified with a real system. Most engineering systems are governed by differential equations or partial differential equations.
With the help of numerical methods such as BEM and FEM, we can streamline approaches to the physical system and solve it in no time. The boundary element method solves engineering problems involving differential equations. BEM is also referred to as the boundary integral equation method BIEM , as it is efficient in solving boundary value problems.
Compared to other numerical methods, BEM is suitable for solving boundary integral equations and other physical problems with complicated boundaries. BEM can be applied widely to electromagnetic problems associated with electrical machines, actuators, antennas, waveguides, actuators, and others.
BEM is a versatile numerical method because it easily generates surface mesh with the aid of discontinuous elements. Additionally, it provides highly accurate solutions obtained with boundary elements. This BEM is derived through the discretization of an integral equation which is equivalent mathematically to the original PDE. This integral equation will then be defined at the boundary of the domain and it relates the boundary solutions to the solutions at points inside the domain.
Since in BEM, the discretization is done only at the boundary, it will result in more efficient computation and easier to be used compared with FEM. Besides, regarding its characteristics, BEM is also very suitable for modeling symmetrical problems as well as problems which involve infinite domains such as the case of potential flow past an obstacle.
BEM is also especially popular to solve Laplace and Helmholtz problems. Besides, in the case of inhomogenous and non-symmetric or non-linier problems, fully populated system of equations will often occur in BEM thus making the storage requirement and computational time become increasing significantly. Further, BEM also requires more knowledge about the suitable fundamental solutions compared than if we use FEM for the simulation of the physical system.
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