__________________________________________________________________
|                                                                  |
|                           README FILE                            |
|                           -----------                            |
|                                                                  |
|      Laplace Shape Functions for Polygonal Finite Elements       |
|      =====================================================       |
|                          [Fortran Code]                          |
|                                                                  |
|                            N. Sukumar                            |
|         Department of Civil and Environmental Engineering        |
|             	      University of California                     |
|                          Davis, CA 95616                         |
|                            August 2004                           |
|__________________________________________________________________|

I. Installation
---------------

Unpack the tar/zip archive on a UNIX machine using the command:

  tar -xvf laplace_polygon.tar OR unzip laplace_polygon.zip 

The archive consists of the following sub-directories under the
directory "Laplace_Polygon":

o Fortran files (suffix .F to enable use of MACRO definitions in the
  makefile), and UNIX makefile in directory "src". Check that the 
  settings (Fortran compiler, etc.) in the makefile are in-sync with
  the machine you are working on

o Executable "polyfem" is placed in directory "bin"

o Examples are placed in directory "Examples"--sub-directories "N4",
  "N7", "N8", and "N17" contain the specific examples for polygons
  with four, seven, eight, and seventeen vertices, respectively

o README (this file) in directory "Doc" as well as the publication
  "Conforming Polygonal Finite Elements" by NS and AT (PDF file)
  in directory "Doc"

o The program execution directory "Run" which contains a sample
  input data file

II. Compiling and Execution
---------------------------

Go into directory "src" and to compile and link, execute:

   make

and (hopefully) no errors arise. If so, the executable "polyfem"
will be placed in the "bin" directory.

Go into the "Run" directory to execute the program. A sample
input file "sample.input" is placed in the "Run" directory. The
input file consists of three parameters: the number (n) of
vertices of the polygon (integer), local x-coordinate of the
point (real), and local y-coordinate of the point. The point 
(x,y) must lie in the interior of the polygon; on the boundary
of the polygon, the resulting interpolant is linear and known. 
On the command line, execute the following command:

 ../bin/polyfem < sample.input

The following will be printed if the data file contains 4 0.5 0.5:

Point = (  0.5,  0.5)
Node =  1 ( -1., -1.) : phi =   0.0625
Node =  2 (  1., -1.) : phi =   0.1875
Node =  3 (  1.,  1.) : phi =   0.5625
Node =  4 ( -1.,  1.) : phi =   0.1875

In addition, various output files in Tecplot (Amtec Inc.) format
are also available. You can run Tecplot on these files to view the
polygon, nodes, point, and the Voronoi cell of the point.  EPS and
JPG plots are provided in Examples/N4, Examples/N7, Examples/N8, 
and Examples/N17. For example, Examples/N4/N4.input is the input
data file, output of the program is stored in Examples/N4/N4.output,
and Examples/N4/N4.eps and Examples/N4/N4.jpg are the plots in
EPS and JPEG formats.

III. Contact
============

If problems arise in the compilation and/or the execution of the
code, please contact me via e-mail at: nsukumar@ucdavis.edu. If
this code is used for "real" work, an acknowledgement in your 
work and a link to the study would be appreciated.