YTEP-0005: Octrees for Fluids and Particles¶
Created: December 24, 2012 Author: Matthew Turk
In the yt 2.x series, octree AMR codes have largely been supported by re-gridding data to create larger grid patches consisting of both high-resolution data and coarse data. This has the overhead of requiring that each time a dataset (as in from RAMSES or ART) is loaded, the data has to be placed into these grids. This is an expensive process and requires a considerable amount of RAM. This YTEP describes the mechanism in yt 3.0 that directly accesses Octree data, avoiding the costly regridding step and enabling higher-fidelity data access. Additionally, it describes how the Octree data structure will be used for particle data access from datasets such as N-body or SPH simulation output.
This YTEP is in progress. Most aspects have been implemented in yt 3.0. A major deficiency (described below) is the lack of a distributed memory octree. Discussion of distributed memory Octrees is reserved for a future YTEP.
Here is where you should write detailed description of what the YTEP proposes. This needs to include:
- Nature of the problem
- Nature of the solution
- How will the solution be implemented * Brief outline of the code needed to implement this * Code examples of using the solution, in appropriate * How will the solution be tested?
- What are any stumbling points
- What is the proposed method for reaching out to the community about this?
In the 2.x branch of yt, RAMSES and (NMSU) ART data are read and processed in a way that mocks up patch-based AMR data. This is sub-par for several reasons:
- A costly re-gridding step is required, where octs are deposited into grid patches that are split with some efficiency measure.
- To conduct IO, coarse grid cells are deposited multiple times into grid patches at finer levels. This results in extremely inefficient IO, as it means that if multiple fine grids overlap with a single cell at coarse resolution, that coarse cell will be read multiple times. It’s also very slow.
- The end result is data that is not exactly what is in the file, reducing the ability of individuals to examine data in a detailed way.
- The regridding code is difficult to parse and understand, and even harder to extend.
In addition to this, particle codes are simply not available in yt 2.x. All attempts to include them have involved a regridding method similar to that for Octree AMR codes, which is not efficient or high-fidelity. Finally, the RAMSES code is broken in 2.x.
Why is it this way?¶
The 2.x branch of yt is relatively inflexible in how data is accessed. There are a number of locations that the attributes grids or _grids are accessed, which are implicitly assumed to be grid patches with a relatively sizable extent. This is used in things like projections, data masking, and the like. For patch-AMR codes where the grids are actually somewhat larger, this is efficient; however, the overhead of python objects and iteration dominate if the grids are smaller than some minimum size or extent. The first implementation of support for RAMSES implemented Octs as grid patches by themselves; this was found to be unbearably slow.
To get around this, a regridding step was applied. This regridding step was based on refinement algorithms, where octs were deposited into grid patches that covered some fraction of the domain. These grid patches were then split to attempt to achieve some minimum efficiency ratio of “refined” (i.e., fine) versus “unrefined” (i.e., coarse) data. When IO was conducted, these were filled in a non-interpolating inverse cascade, where grid patches were filled with fine data, then coarser data. This could be very slow. Additional improvements such as restricting grid patches not to cross “domains” (the RAMSES term for individual files or domains of a specific processr) were eventually added. The NMSU ART data was also loaded in a similar way.
All of this is because yt 2.x relies on “grids” as the fundamental object. As described in YTEP-0001: IO Chunking, in yt 3.0 we no longer rely on grids as the object by which all IO is mediated. Data can now be streamed from disk to memory, and coordinates and resolution information can be seen as independent of that data. This allows octrees to exist without a regridding step.
The octree implementation is designed around having a full Octree which contains subsets of that octree that are distribute amongst different “domains.” The term “domain” comes from RAMSES, and it is best thought of as whatever the natural, IO-oriented subdivision of the data is. For instance, RAMSES divides into multiple files, each of which is called a domain. For purposes of consolidating IO costs, reading on a per-domain basis makes some sense. NMSU ART does not have the concept of multiple domains, and so we can choose to divide data into domains however we like.
Octrees can then be walked to identify which Octs, and then which cells, contribute to a given geometric selector. This can default back to selecting based on the point-by-point location of the Octs, but it can also be queried much more efficiently by early-terminating an octree traversal if a coarse node is not included inside a geometric selector.
This leads nicely to a future where subsets of the octree are not present on every processor; instead, portions can be passed around at will or pinned to specific processors. This is not yet in place, but the Octree has been designed to be forward compatible with this.
For RAMSES data (where the number of Octs is known before any are added to the
system), the octree is composed of a set of
for each domain, which are pre-allocated and include all of the Octs
themselves. Additionally, there is a base class
OctreeContainer and a
RAMSESOctreeContainer. The base class handles and exposes the
majority of methods for traversing the octree and querying the octree. The
subclass specifies how
Octs get added to the octree.
Octs are defined to have the following attributes:
ind– index into the local
local_ind– index into the global Octree container.
domain– the domain to which an Oct belongs.
pos– the integer index, based on the local level’s refinement (i.e., the center divided by the local dx)
level– the level of refinement of the Oct
*sd– this is optional, and a pointer to particle arrays. This is typically only used for N-body data and will otherwise be null.
*children– Pointers to child nodes. Typically, ifany are null, all are null and the Oct is not refined. However, in ART simulations, the root mesh is defined in cells, rather than octs. This is mocked up in yt as a false mesh of Octs, and so the
childrenvalues can be either NULL (for a refined cell) or not, but may not be homogeneously refined.
*parent– an upward pointer, for easier traversal of the Octree.
Particle ad N-body data, which does not typically know the organization and
structure of the resultant Octree in advance, Uses the additional
ParticleArrays class for storing particle data that will help govern
ParticleArrays have enough data to decide where all of the
particles will go during a refinement. This has the downside of mandating that
the positions (but no other fields) of all particles in a simulation must, at
present, be held in memory. This is a key motivating factor in moving to a
Particle arrays have the following attributes:
*oct– the Oct to which this particle array belongs.
*next– the next particle array in sequence
**pos– the array of positions for this particle array
*domain_id– the domain ID (multiple domains mandates refinement in N-body data, as we do not want to span two domains in a single oct.)
np– the number of particles here.
As noted above there are a number of downsides. Many of these will be simple to fix: for instance, IO right now is characterized by reading in large portions of octrees simultaneously. Furthermore, masks are passed around, although masks are likely an artifact that is no longer necessary (and larget than they need be.)
To add on support for a new Octree code, a subclass of
be made (or
RAMSESOctreeContainer, if you would like to re-use the
OctAllocationContainer logic) that implements the following routines:
add– to add new octs to the octree
count– for counting based on a selector
fcoords, and IO routines
Additionally, right now the domain subset code is general but not set into base classses. This is also necessary.
- Generalize the multi-domain support to allow routines such as
icoordsto be applied generally rather than specifically only for each system of allocation.
- Allow domains to be pinned to processors (distributed memory) and reduce the overhead for individual processors of storing the entire Octree mesh.
- Convert FLASH to use the Octree code.
- Generalize Octree support structures beyond RAMSES.
- Ensure that children can be independently refined.
- Spatial data and ghost zones is currently not implemented, and implementation may pose challenes. Part of the reason the implementation for patch-based codes is straightforward is that the arrays come back as 3D arrays, to which (for instance) stencils can be applied. However, for Octree data, we may need to move to returning 4D data to reduce the overhead of processing 10^3 arrays. This means (X,Y,Z,N) where the final dimension is all of the Octs. Retaining compatibility between We also do not want to read outside the domain if not necessary; for instance, RAMSES includes ghost zones in the domain file, even if they are active on a different processor. We should utilize this.
- Implementation requires a good deal of understanding of how other Octree codes are set up. We should improve readability and make this easier to use.
- Applying density estimators to particle codes is not yet implemented, and still somewhat unclear. The first implementation will use Voro++ and regions that have some fixed spatial growth affiliated with them. This will likely not be efficient.
Particle codes are currently supported for reading and creating octree structures. This means that particles can be read in and Octree selection applied to them, where the Octree is refined after either reaching a critical particle count threshold in a given Oct or where an Oct spans multiple domains.
Volume rendering no longer works with Octree codes, and will require spatial data support to do so. Additionally, it may be the case that we need to move to a different method for spatial data analysis (X,Y,Z,N) which will require rewriting old scripts.
I do not believe there are currently credible alternatives to directly understanding Octree data structures in yt. I believe that while we may be able to improve the implemented system, other options such as grid patch conversions are not worthwhile. The particle code support, relying on Octrees for fast selection, could also be implemented using a kD-tree, which may speed the density estimation.