The natural element method (NEM) is a

meshless method In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original ...

to solve

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

, where the ''elements'' do not have a predefined shape as in the

finite element method The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...

, but depend on the geometry. A

Voronoi diagram In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed th ...

partitioning the space is used to create each of these elements. Natural neighbor interpolation functions are then used to model the unknown function within each element.

Applications

When the simulation is dynamic, this method prevents the elements to be ill-formed, having the possibility to easily redefine them at each time step depending on the geometry.

References

{{Numerical PDE Numerical differential equations Numerical analysis Computational fluid dynamics Computational mathematics Simulation