numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

the diffuse element method (DEM) or simply diffuse approximation is a meshfree method. The diffuse element method was developed by B. Nayroles, G. Touzot and Pierre Villon at the Universite de Technologie de Compiegne, in 1992. It is in concept rather similar to the much older

smoothed particle hydrodynamics Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows. It was developed by Gingold and Monaghan and Lucy in 1977, initially for astrophysic ...

. In the paper they describe a "diffuse approximation method", a method for

function approximation In general, a function approximation problem asks us to select a function (mathematics), function among a that closely matches ("approximates") a in a task-specific way. The need for function approximations arises in many branches of applied ...

from a given set of points. In fact the method boils down to the well-known moving least squares for the particular case of a global approximation (using all available data points). Using this function approximation method,

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...

s and thus fluid dynamic problems can be solved. For this, they coined the term diffuse element method (DEM). Advantages over

finite element method 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 tran ...

s are that DEM doesn't rely on a grid, and is more precise in the evaluation of the derivatives of the reconstructed functions.

References

Generalizing the finite element method: diffuse approximation and diffuse elements
B Nayroles, G Touzot. Pierre Villon, P, Computational Mechanics Volume 10, pp 307-318, 1992 Numerical differential equations Computational fluid dynamics {{fluiddynamics-stub

See also

References