[pooma-dev] Sparse Engine

[John H. Hall]

Richard:
OK. Here goes. The basic idea is that we have a hierarchical field  
structure (built using hierarchical engines similar to the current  
multi-material field abstraction) which has a collection of 1-D  
dynamicFields (for the sparse unstructured storage), a shared Index  
(n-D) integer Array (or Field), and a single (n-D) scalar, vector or  
tensor field which has either the data for a pure cell, or a cell  
average value for mixed-material cell's data. As the problem evolves  
the material interfaces migrate and so the actual position of the  
unstructured cells changes. However, all the indirect indexing is still  
local to the processor (except for normal guard cell communications).  
So this is much simpler than a real unstructured problem with  
all-to-all communications. In the general case, the sparse dynamic  
fields are only used to compute the cell-average quantities before a  
data-parallel computation across the single multi-material or  
cell-average field is performed. We would also like to take some views  
of the field in which all of the data for a particular material is  
gathered/scattered to/from a single spare dynamic work Array that is  
shared in this hierarchical structure.

Field<Mesh_t, Real, MixedCellEngine> would look like this:
___________________
|__________________| Single material Gather/Scatter 1-D Dynamic Work  
Array (both mixed and pure cells)
______
|_____| mat A (1-D Dynamic Array/Field)
_______
|______| mat B (1-D Dynamic Array/Field)
______
|_____| mat C (1-D Dynamic Array/Field)
_______________________________________________________________________
|______________________________________________________________________| 
  Cell Average Quantities (n-D)
_______________________________________________________________________
|______________________________________________________________________| 
  Integer Index Array (n-D)
Single Index Array is shared by all Sparse Fields (e.g. Density,  
Pressure, etc.). This shares duty between
providing the material index for a pure cell and an offset into a  
collection tracking the unstructured
mixed cell data for a mixed cell.

Multi-Patch should still work although the guard cell communications  
might be slightly more complicated.

The number of cells which are indirectly addressed is very small (< 5%  
of the total) so even using compressible brick we are wasting a lot of  
memory bandwidth and performing numerous extraneous computations. A  
comparison code using this structure is running 20 times faster than  
the equivalent data parallel POOMA R1 computation for the single  
processor serial case. We believe we can match that performance by  
building an engine that encapsulates the sparse nature reflected in the  
problem and by making more use of the new engines POOMA R2 provides  
(stencil, etc.).

Again, most of the computations are performed on the Cell-Average  
Quantities, so we just take a view, operator[]?, that returns that  
single field.
John and Jean

On Friday, September 26, 2003, at 01:11  AM, Richard Guenther wrote:

> On Fri, 26 Sep 2003, Jean Marshall wrote:
>
>> Hi guys:
>>
>> John and I are starting to write a sparse engine -- for sparse  
>> storage of
>> our material-dependent fields.  We think we have come up with an
>> optimization for our Eulerian code that should really make it scream.  
>>  We
>> have been studying the IndirectionEngine example, which is very  
>> similar to
>> what we need.
>
> Can you elaborate some more on the use and principle of this engine?  
> Is it
> like compressed brick?
>
> Richard.
>
>>
>> Unfortunately, the IndirectionEngine example problem,  
>> indirect_test1.cpp,
>> only demonstrates how to build the engine, not an array or a field.   
>> Could
>> someone please show us how to move forward with this example to  
>> building a
>> complete array and field version?
>>
>> Unlike the IndirectionEngine example, we only need local  
>> communications
>> (not all-to-all) along with the same type of guard cell update found  
>> in a
>> normal field.
>>
>> Any help will be greatly appreciated!
>>
>> Jean, John, Don
>>
>> Jean and Don Marshall
>>
>> 84250 Indio Springs Dr #291
>> Indio, CA 92203-3413
>>
>> 760-775-1576  home
>> 760-574-0182  Jean's cell
>> 760-574-0192  Don's cell
>>
>>
>
> --
> Richard Guenther <richard dot guenther at uni-tuebingen dot de>
> WWW: http://www.tat.physik.uni-tuebingen.de/~rguenth/
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