Non-uniform 2D mesh questions

[yaron at oak-research.com]

Barry-
Maybe i'd better provide more details on what I'm trying to do

*) I'm modeling current flowing through several different "block types",
each of which describes a section of a semiconductor device. Each block
type has a different geometry, which is triangulated to create an AIJ
matrix (Each row/column in the matrix represents a coordinate, and the
matrix values represent electrical admittance). There are about 100
different types of these blocks, and since they have quite convoluted
geometries , their triangulation takes quite a while.

*) My complete problem is composed of many (up to 10K) tiles, each of
which is one of the 100 blocks . I want to reuse the triangulation which
was done for each of the block, do I'd like to have a way of taking the
matrix objects of the individual blcks, and combine them into a large
matrix, taking into account their relative locations.

*) This means that for each block instance, I would need to to translate
every internal coordinate/node, and map it to a global coordinate/node.

*) Once I have a mapping of local to global indices, I'd like to take the
matrix values of the instances, and combine them to form a large matrix
which describes the complete problem.


So my question is :
*) What data structures (DA/IS/AO/???) should I use to achieve the above?

Best Regards
Yaron


	-------Original Message-------
  From: Barry Smith
  Subject: Re: Non-uniform 2D mesh questions
  Sent: 02 Feb '07 13:38


   Yaron,

   Anything is possible :-) and maybe not terribly difficult to get
started.

  You could use DAGetMatrx() to give you the properly pre-allocated "huge"
Mat.

  Have each process loop over the "rectangular portion[s] of the domain"
that
  it mostly owns (that is if a rectangular portion lies across two
processes just
  assign it to one of them for this loop.)

  Then loop over the locations inside the rectangular portion calling
  MatSetValuesStencil() for that row of the huge matrix to put the entries
from
  the smaller matrix INTO the huge matrix using the natural grid i,j
coordindates
  (so not have to map the coordinates from the grid location to the
location in
  the matrix).

  This may require some thought to get right but should require little
coding
  (if you are writting hundreds and hundreds of lines of code then likely
  something is wrong).

   Good luck,

   Barry


  On Tue, 30 Jan 2007, [LINK:
http://webmail.oak-research.com/compose.php?to=yaron@oak-research.com]
yaron at oak-research.com wrote:

  > Barry-
  > So far I only thought of having a single large sparse matrix.
  >
  > Yaron
  >
  >
  > 	 -------Original Message-------
  > From: Barry Smith
  > Subject: Re: Non-uniform 2D mesh questions
  > Sent: 30 Jan '07 10:58
  >
  >
  > Yaron,
  >
  > Do you want to end up generating a single large sparse matrix? Like a
  > MPIAIJ
  > matrix? Or do you want to somehow not store the entire huge matrix but
  > still
  > be able to solve with the composed matrix? Or both?
  >
  > Barry
  >
  >
  > On Mon, 29 Jan 2007, [LINK:
  > [LINK:
http://webmail.oak-research.com/compose.php?to=yaron@oak-research.com]
http://webmail.oak-research.com/compose.php?to=yaron@oak-research.com]
  > [LINK:
http://webmail.oak-research.com/compose.php?to=yaron@oak-research.com]
yaron at oak-research.com wrote:
  >
  > > Barry-
  > > Yes, each block is a rectangular portion of the domain. Not so small
  > > though (more like 100 x 100 nodes)
  > >
  > > Yaron
  > >
  > >
  > > 	 -------Original Message-------
  > > From: Barry Smith
  > > Subject: Re: Non-uniform 2D mesh questions
  > > Sent: 29 Jan '07 19:40
  > >
  > >
  > > Yaron,
  > >
  > > Is each one of these "blocks" a small rectangular part of the
  > > domain (like a 4 by 5 set of nodes)? I don't understand what you
  > > want to do.
  > >
  > > Barry
  > >
  > >
  > > On Mon, 29 Jan 2007, [LINK:
  > > [LINK:
  > [LINK:
http://webmail.oak-research.com/compose.php?to=yaron@oak-research.com]
http://webmail.oak-research.com/compose.php?to=yaron@oak-research.com]
  > [LINK:
http://webmail.oak-research.com/compose.php?to=yaron@oak-research.com]
http://webmail.oak-research.com/compose.php?to=yaron@oak-research.com]
  > > [LINK:
  > [LINK:
http://webmail.oak-research.com/compose.php?to=yaron@oak-research.com]
http://webmail.oak-research.com/compose.php?to=yaron@oak-research.com]
  > [LINK:
http://webmail.oak-research.com/compose.php?to=yaron@oak-research.com]
yaron at oak-research.com wrote:
  > >
  > > > Hi all
  > > > I have a laplace-type problem that's physically built from
repeating
  > > > instances of the same block.
  > > > I'm creaing matrices for the individual blocks, and I'd like to
  > reuse
  > > > the individual block matrices in order to compose the complete
  > > problem.
  > > > (i.e if there 10K instances of 20 blocks, I'd like to build 20
  > > matrices,
  > > > then use them to compose the large complete matrix)
  > > > Is a 2D DA the right object to do that? And if so, where can I
find
  > a
  > > > small example of building the DA object in parallel, then using
the
  > > > different (for every instance) mappings of local nodes to global
  > nodes
  > > in
  > > > order to build the complete matrix?
  > > >
  > > >
  > > > Thanks
  > > > Yaron
  > > >
  > >
  >
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