We, Yuri Vassilevski and Konstantin Lipnikov, have completed
the distributive versions of 2D (triangular) and 3D (tetrahedral)
unstructured mesh generators.
The main features of the software are:
1. Simplicity and portability. It is written in Fortran 77, contains
few files, and a very simple makefile. Since we have not used any
system dependent calls (except time measurement), it is assumed to
be widely portable.
2. Robustness, both in 2D and 3D. We could not break it down. Special
treatment of very rare intractable situations provides the robustness.
3. Careful checking the output mesh.
4. Very simple input interface. We know very well how complicated and restrictive
input interface may be. We did OUR BEST to simplify it. We have chosen
neither solid constructive geometry, nor surface description techniques.
In INPUT, we require the MESH. It may be very coarse mesh consisting of a few
elements (made by hands), or very fine mesh made by any other mesh generator.
The input mesh provides to the generator all the information about the domain.
Apart the standard mesh data (list of node coordinates, connectivity table, list
of boundary edges/faces ), we need two more things. First, a set of fixed
nodes which will never touched, and second, a curve-linear boundary data.
The latter is additional data for any boundary edge/face facing to a
curve-linear part of the boundary (parameter values associated to each node of the
edge/face and reference to a user-supplied parameterization function).
We refer the user to the respective examples.
5. Very simple output. These are just very standard in finite elements data.
In 2D we provide the ps-files of the input and the output meshes,
in 3D we provide the converter of our input and output grid files
to a gmv-file for GMV visualization tool (you can download GMV from
http://laws.lanl.gov/XCM/gmv/ ).
6. Ability to construct locally refined meshes, both isotropic and anisotropic.
This is very important in applications.
7. The generator construct a mesh with as many elements, as the user want.
8. Very simple control of the mesh properties. The user defines analytically
the metric (2x2 or 3x3 s.p.d. matrix depending on coordinates). The output
mesh is QUASI-UNIFORM in this metric, and consists of given number of elements.
For instance, if the metric is chosen to be identity, then the output mesh will
be quasi-uniform in common sense, if the metric is chosen to have an isotropic
peculiarity somewhere, then the output mesh will be isotropically refined there,
if the metric is chosen to anisotropic, then the output mesh will be anisotropic,
too.
9. Very easy interface to make an adaptive loop. If the user does not want
to provide the governing metric analytically, he may provide just a scalar
discrete function associated to the input mesh (for example, discrete solution
of a b.v.p.). The generator will generate the governing metric based on the
discrete Hessian recovery of the given discrete function. Thus, one can
organize an adaptive loop:
discrete solution+mesh -> generator -> new mesh -> new discrete solution ->
generator -> new mesh -> new discrete solution -> generator -> ....
10.Algorithmic description and some theory is available in two papers:
(a) Yu.Vassilevski, K.Lipnikov,
An Adaptive Algorithm for Quasioptimal Mesh Generation,
Computational Mathematics and Mathematical Physics,
Vol.39,No.9,1999,1468-1486.
(b) A.Agouzal, K.Lipnikov, Yu.Vassilevski,
Adaptive Generation of Quasi-optimal Tetrahedral Meshes,
East-West Journal, Vol.7,No.4,1999,223-244.
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We think that our friends and colleagues may want to use the tentative version
of the software in their research or application. We suggest you can try
to use it (free) and send your remarks, comments and wishes to us, for we can make
the code better.
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If you are interested in getting the software, please, respond to Yuri Vassilevski
vasilevs@dodo.inm.ras.ru,
CC: lipnikov@homail.com
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