Recent Advances in VisIt: AMR Streamlines and Query-Driven Visualization Page: 3 of 6
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Recent Advances in VisIt: AMR Streamlines and Query-driven Visualization
Figure 1. Streamlines extracted from simulated astrophysical data set using
a parallel approach..
For a stationary vector field v that does not depend on time, an integral
curve is called a streamline and is given by the ordinary differential equation
S(t) = v(S(t, x)) and S(to) = o. (1)
Hence, it describes a parameterized curve that starts at the seed point xo and is
tangent to v over its parameter interval [to, ti] for to < ti.
In the discrete setting we are concerned with in this paper, streamlines are
approximated using numerical integration methods to approximate the describ-
ing ordinary differential equations. There is an extensive body of work on this
topic, and we refer the interested reader to Hairer, Nbrsett, & Wanner (1993) for
an overview. In our streamline implementation, we use an integration scheme of
Runge-Kutta type with adaptive stepsize control as proposed by Prince, & Dor-
mand (1981). The visualization and analysis of vector fields is an active research
area, and so-called integration-based techniques that derive vector field visual-
ization from integral curves have progressed well beyond the direct depiction of
individual streamlines or a small subset of them (McLoughlin et al. 2009).
2.2. Efficient Parallel Streamline Calcuation
Compared to isosurface extraction or direct volume rendering, it is difficult to
parallelize streamline generation. While it is possible to extract isosurfaces inde-
pendently within each block of a multi-block data set, or to take samples along
a ray within each block independently for volume rendering, it is not possible
to extract the portion of a streamline in data blocks independently. This is
due to the fact that the streamline depends on the seed point, and for blocks
along the path of a streamline it is not known a-priori where on the boundary
a streamline enters the block. As a consequence, it is necessary to compute a
streamline piece-by-piece, communicating intermediate results between proces-
sors as the streamline passes from blocks owned by a processor to blocks owned
by a different processor.
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Weber, Gunther; Ahern, Sean; Bethel, Wes; Borovikov, Sergey; Childs, Hank; Deines, Eduard et al. Recent Advances in VisIt: AMR Streamlines and Query-Driven Visualization, article, November 12, 2009; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc1013741/m1/3/: accessed February 17, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.