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

the diffuse element method (DEM) or simply diffuse approximation is a

meshfree 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, origina ...

. 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 astrophysica ...

. 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 among a that closely matches ("approximates") a in a task-specific way. The need for function approximations arises in many branches of applied mathematics, and comput ...

from a given set of points. In fact the method boils down to the well-known

moving least squares Moving least squares is a method of reconstructing continuous functions from a set of unorganized point samples via the calculation of a weighted least squares measure biased towards the region around the point at which the reconstructed value is ...

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 imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

s and thus

fluid dynamic In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and ...

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

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 ...

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