Grid Geometry Abstraction

The purpose of the grid geometry abstractions is to provide an intuitive means for identifying and addressing regions in the computational domain. These abstractions can be used to direct computations to a particular region in the domain, to mask regions that should not be included in a given operation, or to specify region that need more resolution or refinement. The grid geometry abstractions represent coordinates, bounding boxes and doubly linked lists of bounding boxes.

• Coordinates: The coordinate abstraction represents a point in the computational domain. Operations defined on this class include indexing and arithmetic/logical manipulations. These operations are independent of the dimensionality of the domain.

• Bounding Boxes: Bounding boxes represent regions in the computation domain and is comprised of a triplet: a pair of Coords defining the lower and upper bounds of the box and a step array that defines the granularity of the discretization in each dimension. In addition to regular indexing and arithmetic operations, scaling, translations, unions and intersections are also defined on bounding boxes. Bounding boxes are the primary means for specification of operations and storage of internal information (such as dependency and communication information) within DAGH.

• Bounding Boxes Lists: Lists of bounding boxes represent a collection of regions in the computational domain. Such a list is typically used to specify regions that need refinement during the regriding phase of an adaptive application. In addition to linked-list addition, deletion and stepping operation, reduction operations such as intersection and union are also defined on a BBoxList.

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• Coords BBox BBoxList

  Operations

  • rank, x, y, z, ...
  • lb, ub, stride
  • union, intersection, cluster, refine/coarsen, difference, ...

     

Grid Hierarchy Abstraction

The grid hierarchy abstraction represents the distributed dynamic adaptive grid hierarchy that underlie parallel adaptive applications based on adaptive mesh refinement. This abstraction enables a user to define, maintain and operate a grid hierarchy as a first-class object. Grid hierarchy attributes include the geometry specifications of the domain such as the structure of the base grid, its extents, boundary information, coordinate information, and refinement information such as information about the nature of refinement and the refinement factor to be used. When used in a parallel/distributed environment, the grid hierarchy is partitioned and distributed across the processors and serves as a template for all application variables or grid functions. The locality preserving composite distribution based on recursive space-filling curves is used to partition the dynamic grid hierarchy. Operations defined on the grid hierarchy include indexing of individual component grid in the hierarchy, refinement, coarsening, recomposition of the hierarchy after regriding, and querying of the structure of the hierarchy at any instant. During regriding, the re­partitioning of the new grid structure, dynamic load-balancing, and the required data-movement to initialize newly created grids, are performed automatically and transparently. 

•   
  GridHierarchy GH(Dim,GridType,MaxLevs)

• Attributes:
  • number of dimensions 
    maximum number of levels 
    specification of the computational domain 
    distribution type 
    refinement factor 
    boundary type/width

Grid Function Abstraction

Grid Functions represent application variables defined on the grid hierarchy. Each grid function is associated with a grid hierarchy and uses the hierarchy as a template to define its structure and distribution. Attributes of a grid function include type information, and dependency information in terms of space and time stencil radii. In addition the user can assign special (Fortran) routines to a grid function to handle operations such as inter-grid transfers (prolongation and restriction), initialization, boundary updates, and input/output. These function are then called internally when operating on the distributed grid function. In addition to standard arithmetic and logical manipulations, a number of reduction operations such as Min/Max, Sum/Product, and Norms are also defined on grid functions. Grid Function objects can be locally operated on as regular Fortran 90/77 arrays.

• GridFunction(DIM)<T> GF("gf", Stencils,GH, ...)

• Attributes:
  • dimension and type                                      vector? 
    spatial/temporal stencils                               associated Grid Hierarchy 
    prolongation/restriction functions                 "shadow" specification 
    alignments                                                    ghost cells 
    boundary types/updates                                interaction types 
    flux registers                                                 parent storage

Separation of Concerns => Hierarchical Abstractions