CVT_BASIS_INOUT - Flow Solutions in a Cell with Inflow and Outflow

CVT_BASIS_INOUT is a set of velocity solutions to a flow problem in a cell with inflow and outflow, used by the CVT_BASIS program.

The region is a rectangle with inflow on a section of the lower left wall, and outflow on a section of the upper right wall:

       +----------------------+
       |                      -->
       |                      -->
       |                      -->
       |                      |
       |                      |
       |                      |
       |                      |
       |                      |
       |                      |
     -->                      |
     -->                      |
     -->                      |
       +----------------------+

Specifically, a partial differential equation (PDE) has been defined, specifying the time dependent flow of a fluid through a region. The PDE specification includes a parameter ALPHA whose value strongly affects the behavior of the flow. The steady state solution S0 is computed for a particular value of ALPHA. Then the time dependent problem is solved over a fixed time interval, with ALPHA varying from time to time. A set of several hundred solutions S(T(I),ALPHA(I)) are saved.

The need is to try to extract from this solution data the typical modes of behavior of the solution. Such a set of modes may then be used as a finite element basis that is highly tuned to the physics of the problem, so that a very small set of basis functions can be used to closely approximate the behavior of the solution over a range of values of ALPHA.

The method of extracting information from the solution data uses a form of K-Means clustering.

The data to be examined is assumed to be stored in a file. The file is assumed to contain a number of records, with each record stored on its own line. Each record, in turn, contains a fixed number of data values that describe a particular gene expression experiment. Each record will be regarded as a point in N dimensional space.

Files you may copy include:

xy.txt, the XY coordinates associated with the nodes.
steady.txt, the steady state solution.

There are 500 files containing solutions of the time-dependent PDE with varying values of the parameter. The solutions are ordered by time step, but no information is supplied about the value of ALPHA at any time.

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Last revised on 22 June 2002.