Finite pointset method

In <a href="/facts/Applied_mathematics/qyqklXXm">applied mathematics</a>, the finite pointset method (FPM) is a general approach for the numerical solution of problems in <a href="/facts/Continuum_mechanics/vI7LpFDk">continuum mechanics</a>, such as the simulation of <a href="/facts/Fluid_flow/y7uzSCfg">fluid flows</a>. In this approach the medium is represented by a finite set of points, each endowed with the relevant local properties of the medium such as <a href="/facts/Density/92p6hh9I">density</a>, <a href="/facts/Velocity/Q3o1LVDe">velocity</a>, <a href="/facts/Pressure/eyc37GRG">pressure</a>, and <a href="/facts/Temperature/QyGe4gmj">temperature</a>.
The sampling points can move with the medium, as in the Lagrangian approach to fluid dynamics or they may be fixed in space while the medium flows through them, as in the Eulerian approach. A mixed Lagrangian-Eulerian approach may also be used. The Lagrangian approach is also known (especially in the <a href="/facts/Computer_graphics/lapBE8wv">computer graphics</a> field) as <a href="/facts/Particle_method/EEdQdeAG">particle method</a>.
Finite pointset methods are <a href="/facts/Meshfree_method/uUhEQD3K">meshfree methods</a> and therefore are easily adapted to domains with complex and/or time-evolving geometries and moving phase boundaries (such as a liquid splashing into a container, or the <a href="/facts/Glass_blowing/dWf2rYAD">blowing of a glass bottle</a>) without the software complexity that would be required to handle those features with topological data structures. They can be useful in non-linear problems involving <a href="/facts/Viscosity/QLVfrdCz">viscous</a> fluids, <a href="/facts/Heat_transfer/1IV3WbFL">heat</a> and <a href="/facts/Mass_transfer/GrHKD4h2">mass transfer</a>, linear and non-linear <a href="/facts/Elastic_deformation/z1LEmkQX">elastic</a> or <a href="/facts/Plastic_deformation/2VKo6keA">plastic deformations</a>, etc.

Finite pointset method open-in-new

Finite pointset method