võrepunkt

Võrepunkt is a term used to describe a node in a lattice or mesh that is used to discretize a continuous domain for numerical analysis. At a võrepunkt, a value corresponding to a field (such as temperature, pressure or velocity) is defined or stored. The collection of võrepunktid forms a grid or mesh that approximates the geometry of the problem.

Võrepunktid can be arranged in different ways. In structured grids, they form a regular array with predictable indexing, for example in 2D on a Cartesian grid with coordinates (iΔx, jΔy). In unstructured meshes, võrepunktid are distributed more flexibly and connected by elements of varying shapes, which allows conforming to complex geometries. The choice between structured and unstructured arrangements affects how equations are discretized and solved.

In numerical methods, võrepunktid serve as the locations where governing equations are approximated. Finite difference methods use neighboring võrepunktid to approximate derivatives, while finite element and finite volume methods associate unknowns with the points or with the surrounding elements. The stencil or connectivity around a võrepunkt determines how operations like gradients and divergences are computed.

Applications of võrepunkt networks include computational fluid dynamics, heat transfer, structural analysis and geophysical simulations. Grid generation and refinement techniques adjust the distribution of võrepunktid to improve accuracy or efficiency, such as clustering points where the solution varies rapidly or near boundaries.

See also: grid, mesh, node, stencil, finite difference method, finite element method.