Diffuse element method
Encyclopedia
The diffuse element method (DEM) is a computer simulation
technique used in engineering analysis. It 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
. In the paper they describe a "diffuse approximation method", a method for function approximation from a given set of points.
In fact it seems they rediscovered an already known technique, moving least squares
. Using this function approximation method, partial differential equation
s and thus fluid dynamic problems can be solved. For this, they coined the term Diffuse Element Method (DEM).
Advantages over finite element method
s are that DEM doesn't rely on a grid, and is more precise in the evaluation of the derivations of the reconstructed functions.
Computer simulation
A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system...
technique used in engineering analysis. It is a meshfree method
Meshfree methods
Meshfree methods are a particular class of numerical simulation algorithms for the simulation of physical phenomena. Traditional simulation algorithms relied on a grid or a mesh, meshfree methods in contrast use the geometry of the simulated object directly for calculations. Meshfree methods exist...
.
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
Smoothed-particle hydrodynamics is a computational method used for simulating fluid flows. It has been used in many fields of research, including astrophysics, ballistics, volcanology, and oceanography...
. In the paper they describe a "diffuse approximation method", a method for function approximation from a given set of points.
In fact it seems they rediscovered an already known technique, moving least squares
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 requested....
. Using this function approximation method, partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
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
The finite element method is a numerical technique for finding approximate solutions of partial differential equations as well as integral equations...
s are that DEM doesn't rely on a grid, and is more precise in the evaluation of the derivations of the reconstructed functions.
See also
- Moving least squaresMoving least squaresMoving 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 requested....
- Finite element methodFinite element methodThe finite element method is a numerical technique for finding approximate solutions of partial differential equations as well as integral equations...
- Smoothed Particle HydrodynamicsSmoothed particle hydrodynamicsSmoothed-particle hydrodynamics is a computational method used for simulating fluid flows. It has been used in many fields of research, including astrophysics, ballistics, volcanology, and oceanography...
- Meshfree methodsMeshfree methodsMeshfree methods are a particular class of numerical simulation algorithms for the simulation of physical phenomena. Traditional simulation algorithms relied on a grid or a mesh, meshfree methods in contrast use the geometry of the simulated object directly for calculations. Meshfree methods exist...
- Computational Fluid DynamicsComputational fluid dynamicsComputational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with...