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The Problem: Essentially, the problem here is to find a way to
follow field lines on an EMR grid in an efficient way on parallel machines.
Conventional algorithms which proceed sequentially through all of the
blocks containing a given line are inefficient on parallel machines because
only one block is processed at a time, thus leaving many of the machine's
processors idle.
The Solution: Rather than follow each line through a sequence of
blocks, Darren DeZeeuw, Aaron Ridley and Gabor Toth devised an algorithm
in which parallel processing enables each block to follow the field lines
that pass through it, and then the results of this processing are interpolated
at the interfaces between blocks to reveal the paths of the field lines.
Thus, the computationally intensive work of integrating the field lines
is done in parallel.
This occurs in 3 steps:
1. Integrate B in both directions within block staring from surface:
2. Iterate and interpolate until all surface points are assigned:
3. Integrate field lines in both directions starting at cell centers and
interpolate footpoint coordinates at block surface:
Notes:
- This algorithm works well for simple things, but does not work as
well in complex areas where there are many field lines close together.
- There seems to be a tradeoff between parallelism and accuracy.
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