cnemlib

CNEMLIB is an implementation of CNEM in 2d and 3d [1],[2]. The CNEM is a generalisation for non convex domain of the Natural Element Method[3]. The CNEM is a FEM like approach. The main advantages of the CNEM comparatively with the FEM, are the following:
     - nodes and quadrature points are identical, all the unknowns (primal and dual unknowns introduced in Galerkin approaches) are attached to the nodes,
    - due to the usage of Natural Neighbour Shape functions, the CNEM doesn't depend on mesh.
 
The main functionalities of CNEMLIB are:
    i) interpolation of scattered data spread on convex or non convex domains with :
        - in 2d, the Natural Neighbour interpolant (Sibson )
        - in 3d, the Natural Neighbour interpolant (Sibson or Laplace) or the linear finite element interpolant over the Delaunay tessellation.
    ii) a gradient matrix operator which allows to calculate nodal gradients for scattered data. The approach used is based on the stabilized nodal integration SCNI[4].
    iii) a general assembling tools to construct assembled matrix associated with a weak formulation (heat problem, mechanic problem, hydrodynamic problem, general purpose problem) as such used with the Finite Element Method (FEM).

The functionalities i) and ii) are written in c++ and wrapped for matlab (mex function) and python(c++ extension). They are parallelised for 3d applications (shared memory using tbb). The assembling tools iii) are provided in matlab and python.

[1] L.Illoul,P.Lorong, On some aspects of the CNEM implementation in 3D in order to simulate high speed machining or shearing, Computers and Structures , Volume 89 Issue 11-12, June, 2011
[2] F.Chinesta, Natural Element Method for the Simulation of Structures and Processes, Wiley-ISTE; 1 edition (March 29, 2011)
[3] N. Sukumar, http://dilbert.engr.ucdavis.edu/~suku/nem/
[4] J.Chen, http://www.seas.ucla.edu/~jschen/2004%20SCNI%20for%20NEM.pdf
[5] H.Si, http://tetgen.berlios.de/