# Finite point method

The Finite Point Method  (FPM) (also known as the Finite Point Method , Diffuse Element Method , Finite Point Model or Finite Poinset Method ) is a numerical calculation method derived from the Finite Element Method  (FEM) is derived and, in contrast to this, does not require any elements, but only needs points.

The solution area is discretized element-free and only with finite points . The solution function sought is defined in the vicinity of the finite points (nodes) and interpolated by polynomials between the neighboring points . As with FEM, the Galerkin method is usually used to minimize the weighted error. The decisive advantage of the FPM is that no FE grid is necessary, i.e. no mesh generation and adaptation with the associated problems (for example mesh distortion). The discontinuity of the approximate solution at the element boundaries is also eliminated. When changes are made, points can be added or deleted more easily than elements that would have to be re-meshed and numbered. However, element structures are used in the background with different variants of the FPM.

The FP method came up in the 1990s. Initially, the method was mainly used for stationary problems, especially in solid mechanics and for the simulation of flows in open channels with a free surface, but today a wide range of applications can also be found in the transient area of fluid mechanics . The method is used in the commercial software Nogrid points .

## literature

1. TIWARI S., KUHNERT J .: A meshfree method for incompressible fluid flows with incorporated surface tension . No. 11 7-8 . Revue europeaenne des elements finis, 2002.
2. MOELLER A .: Influence of the counter blow air flow during container glass blow and blow process . Proceedings 12th ESG (European Glass Society), Parma, Italy 2014.
3. ^ Hichem Abdessalam et al .: Prediction of acoustic foam properties by numerical simulation of polyurethane foaming process . 12th International Conference on Numerical Methods in Industrial Forming Processes, Troyes, France 2016.
• A finite point method for stationary two-dimensional flows with a free surface, Chongjiang Du, 1997/1998
• The element-free Galerkin method: basics and possible uses, U. Häussler-Combe, C. Korn, J. Eibl, 1998