BOUNDARY ELEMENT Meaning and
Definition
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Boundary element refers to a concept in mathematics and physics which describes an element or a part of a geometric object, such as a surface or a curve, that demarcates or separates different regions within that object. It is often employed in boundary element methods (BEMs), a numerical analysis technique used for solving various equations and problems, particularly in the field of engineering.
In BEMs, the boundary element is crucial as it divides the object into two distinct parts: the interior region and the exterior region. The boundary element itself acts as the interface between these two regions, facilitating the transfer of information or energy across the boundary. By discretizing the boundary into smaller, simpler elements, such as line segments or triangles, BEMs can optimize calculations and approximate the behavior of the entire object.
Boundary elements are commonly used for problems involving potential fields, such as electrostatics, heat conduction, and fluid flow. They allow for efficient and accurate computation by focusing on the boundary where the physical phenomena occur and disregarding the domain's interior. This approach greatly simplifies mathematical models and reduces computational complexity compared to other methods that assess the entire domain.
Overall, boundary elements serve as fundamental components in boundary element methods, enabling the analysis and prediction of various physical phenomena by accurately representing the behavior and interaction between different regions of a geometric object.
Etymology of BOUNDARY ELEMENT
The word "boundary" comes from the Middle English word "boundarie", which originated from the Old French term "boun" meaning "limit" or "boundary". It can be traced back further to the Latin word "bodina" meaning "boundary" or "enclosure". The term "element" comes from the Middle English and Latin word "elementum" meaning "component" or "basic principle". When combined, "boundary element" refers to the fundamental component or entity that defines a limit or boundary.
