Numerical Analysis Questions
The boundary element method (BEM) is a numerical technique used to solve differential equations, particularly those involving partial differential equations (PDEs). It is a meshless method that focuses on solving the problem on the boundary of the domain rather than within the entire domain.
In BEM, the domain is divided into two regions: the interior and the boundary. The PDE is transformed into an integral equation, known as the boundary integral equation (BIE), which is then solved on the boundary of the domain. The BIE relates the unknown function to its boundary values and is typically easier to solve compared to the original PDE.
The BEM approach eliminates the need for discretizing the entire domain, as only the boundary needs to be discretized. This reduces the computational effort and memory requirements, making BEM particularly suitable for problems with complex geometries or infinite domains.
Overall, the concept of the boundary element method involves transforming the PDE into a boundary integral equation and solving it on the boundary of the domain, providing an efficient and accurate numerical solution to differential equations.