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create_grid command

Syntax:

create_grid Nx Ny Nz keyword args ... 

Examples:

create_grid 10 10 10
create_grid 10 10 10 block * * *
create_grid 10 10 10 block 4 2 5
create_grid 10 10 10 levels 4 level 2*4 * * * 2 2 3
create_grid 20 10 1 levels 2 level 2 10*15 3*7 1 2 2 1
create_grid 20 10 1 levels 3 region 2 b2 2 2 1 region 3 b3 2 3 1 inside any
create_grid 20 10 1 levels 2 level 2 10*15 3*7 1 2 2 1 region 3 b3 2 3 1
create_grid 8 8 10 levels 3 level 2 5* * * 4 4 4 level 3 1 2*3 3* 2 2 1 

Description:

Overlay a grid over the simulation domain defined by the create_box command. The grid can also be defined by the read_grid command.

The grid in SPARTA is hierarchical, as described in Section howto 4.8. The entire simulation box is a single parent grid cell at level 0. It is subdivided into Nx by Ny by Nz cells at level 1. Each of those cells can be a child cell (no further sub-division) or can be a parent cell which is further subdivided into Nx by Ny by Nz cells at level 2. This can recurse to as many levels as desired. Different cells can stop recursing at different levels. Each level can define its own unique Nx, Ny, Nz values for subdivision. Note that a grid with a single level is simply a uniform grid with Nx by Ny by Nz cells in each dimension.

Each child grid cell is owned by a unique processor. The details of how child cells are assigned to processors by the various options of this command are described below. The cells assigned to each processor will either be "clumped" or "dispersed".

The block and clump keywords produce clumped assignments of child cells to each processor. This means each processor's cells will be geometrically compact. The random and stride keywords, produce dispersed assignments of child cells to each processor.

IMPORTANT NOTE: See Section 6.8 of the manual for an explanation of clumped and dispersed grid cell assignments and their relative performance trade-offs. The balance_grid command can be used after the grid is created, to assign child cells to processors in different ways. The "fix balance" command can be used to re-assign them in a load-balanced manner periodically during a running simulation.


A single-level grid is defined by specifying only the arguments Nx, Ny, Nz, with no additional levels keyword. This will create a uniform Nx by Ny by Nz grid of child cells. For 2d simulations, Nz must equal 1.

One of the keywords block, clump, random, or strided can be used to determine which processors are assigned which cells in the grid. The inside keyword is ignored for single-level grids. If no keyword is used, a setting of block 0 0 0 is the default.

The block keyword maps the P processors to a Px by Py by Pz logical grid that overlays the actual Nx by Ny by Nz grid. This effectively assigns a contiguous 3d sub-block of cells to each processor.

Any of the Px, Py, Pz parameters can be specified with an asterisk "*", in which case SPARTA will choose the number of processors in that dimension. It will do this based on the size and shape of the global grid so as to minimize the surface-to-volume ratio of each processor's sub-block of cells.

The product of Px, Py, Pz must equal P, the total # of processors SPARTA is running on. For a 2d simulation, Pz must equal 1. If multiple partitions are being used then P is the number of processors in this partition; see Section 2.6 for an explanation of the -partition command-line switch.

Note that if you run on a large, prime number of processors P, then a grid such as 1 x P x 1 will be required, which may incur extra communication costs.

The random keyword means that each grid cell will be assigned randomly to one of the processors. Note that in this case different processors will typically not be assigned exactly the same number of cells.

The clump keyword means that the Pth clump of cells is assigned to the same processor, where P is the number of processors. E.g. if there are N = 100 cells and 10 processors, then the 1st processor (proc 0) will be assigned cells 1 to 10. The 2nd processor (proc 1) will be assigned cells 11 to 20. And The 10th processor (proc 9) will be assigned cells 91 to 100.

The stride keyword means that every Pth cell is assigned to the same processor, where P is the number of processors. E.g. if there are 100 cells and 10 processors, then the 1st processor (proc 0) will be assigned cells 1,11,21, ..., 91. The 2nd processor (proc 1) will be assigned cells 2,12,22 ..., 92. The 10th processor (proc 9) will be assigned cells 10,20,30, ..., 100.

The argument for stride and clump determines how the N grid cells are ordered and is some permutation of the letters x, y, and z. Each of the N cells has 3 indices (I,J,K) to describe its location in the 3d grid. If the stride argument is yxz, then the cells will be ordered from 1 to N with the y dimension (J index) varying fastest, the x dimension next (I index), and the z dimension slowest (K index).


A hierarchical grid with more than one level can be defined using the levels keyword. The Nlevels argument is the number of levels which must be 2 or more. The entire simulation box is level 0 in the hierarchy. The settings for Nx,Ny,Nz specify the level 1 grid. All other levels must be defined by using either the subset or region keyword in addition to the levels keyword.

A block, clump, random, or stride keyword can be specified in addition to the levels keyword for a hierarchical grid. As described above, they determine how level 1 grid cells are assigned to processors, as described above. In the hierarchical case all grid cells of level 2 or higher that are within a single level 1 cells are assigned to the processor that owns the level 1 cell.

The settings for every level, from 2 to Nlevels, must be specified exactly once via the Ilevel argument to either a subset or region keyword. Ilevel can be specfied as a single number or use a wildcard asterisk in place of or in conjuction with one or two integers to specify multiple levels at the same time. This takes the form “*” or “*n” or “n*” or “m*n”. An asterisk with no numeric values means all levels from 2 to Nlevels. A leading asterisk means all levels from 2 to n (inclusive). A trailing asterisk means all levels from n to Nlevels (inclusive). A middle asterisk means all levels from m to n (inclusive).

For the subset keyword, the Px, Py, Pz arguments specify which cells in the previous level are flagged as parents and sub-divided to create cells at the new level. For example, if the level 1 grid is 100x100x100, then Px, Py, Pz for level 2 could select any contiguous range of cells from 1 to 100 in x, y, or z. If the level 2 grid is 4x4x2 within any level 1 cell (as set by Cx, Cy, Cz), then Px, Py, Pz for level 3 could select any contiguous range of cells from 1 to 4 in x, y and 1 to 2 in z. Each of the Px, Py, Pz arguments can be a single number or be specified with a wildcard asterisk, the same as described above for Ilevel, where the bounds of Px (for example) are 1 to Cx in the preceeding parent level.

The Cx, Cy, Cz arguments are the number of new cells (in each dimension) to partition each selected parent cell into. Cz must be one for 2d. Any of Cx, Cy, Cz may have a value of 1, but they cannot all be 1. Note that for each new level, only grid cells that exist in the previous level are partitioned further. E.g. level 3 cells are only added to level 2 cells that exist, since some level 1 cells may not have been partitioned into level 2 cells.

For example this command creates a two-level grid:

create_grid 10 10 10 levels 2 level 2 * * * 2 2 3 

The 1st level is 10x10x10. Each of the 1000 level 1 cells is further partitioned into 2x2x3 cells. This means the total number of resulting grid cells is 1000 * 12 = 12000.

This command creates a 3-level grid:

create_grid 8 8 10 levels 3 level 2 5* * * 4 4 4 level 3 1 2*3 3* 2 2 1 

The first level is 8x8x10. The second level is 4x4x4 within each level 1 cell, but only half or 320 of the 640 level 1 cells are sub-divided, namely those with x indices from 5 to 8. Those with x indices from 1 to 4 remain as level 1 cells. Some of the level 2 cells are further partitioned into 2x2x1 level 3 cells. For the 4x4x4 level 2 grid within 320 or the level 1 cells, only the level 2 cells with x index = 1, y index = 2-3, and z-index = 3-4 are further partitioned into level 3 cells, which is just 4 of the 64 level 2 cells. The resulting grid thus has 24640 grid cells: 320 level 1 cells, 19200 level 2 cells, and 5120 level 3 cells.

For the region keyword, the subset of cells in the previous level which are flagged as parents and sub-divided is determined by which of them are in the geometric region specified by reg-ID.

The region command can define volumes for simple geometric objects such as a sphere or rectangular block. It can also define unions or intersections of simple objects or other union or intersection objects. by defining an appropriate region, a complex portion of the simulation domain can be refined to a new level.

Each grid cell at the previous level is tested to see whether it is "in" the region. The inside keyword determines how this is done. If inside is set to any, which is the default, then a grid cell is in the region if any of its corner points (4 in 2d, 8 in 3d) is in the region. If inside is set to all, then all 4 or 8 of its corner points must be in the region for a grid cell to be in the region. Note that the side option for the region command can be used to define whether the inside or outside of the geometric region is considered to be "in" the region.

If the grid cell is in the region, then it is refined using the Cx, Cy, Cz arguments in the same way the subset keyword uses them. Examples using the region keyword are given above.


Restrictions:

This command can only be used after the simulation box is defined by the create_box command.

Related commands:

create_box, read_grid

Default:

The default setting for block vs clump vs random vs stride is block with Px = Py = Pz = *. The inside keyword has a default setting of any.