Reunaelementtimenetelmä

Reunaelementtimenetelmä is a numerical method used in engineering and physics to solve partial differential equations. It is an alternative to more common methods like the finite element method (FEM) or the finite difference method (FDM). The core idea of the reunaelementtimenetelmä is to discretize the boundary of the problem domain rather than the entire domain itself.

This boundary discretization leads to a system of equations that only involves unknown values on the boundary. For problems that are computationally expensive due to large domains or complex geometries, this can significantly reduce the number of degrees of freedom and thus the computational cost. The method is particularly well-suited for problems with infinite or semi-infinite domains, where discretizing the entire domain would be impractical.

The reunaelementtimenetelmä typically involves formulating the problem in an integral form. This integral equation is then discretized by dividing the boundary into a series of elements. Within each element, the unknown quantities are approximated using basis functions. Solving the resulting system of algebraic equations yields the values of the unknown quantities on the boundary, which can then be used to determine the solution within the domain. Common applications include solving problems in acoustics, elasticity, and fluid mechanics. While powerful, the method can be more complex to implement and understand compared to domain-based methods.