The ITAPS Data Model

We use the information flow through a mesh-based simulation as the framework for developing interoperable geometry, mesh and solution field components. A simulation's information flow begins with a problem definition which consists of a description of the geometric and temporal domain annotated by attributes designating mathematical model details and parameters. The geometric domain is then often decomposed into a set of piecewise components, the mesh, and the continuous PDEs is then approximated on that mesh using, for example, finite difference or finite element techniques. Simulation automation and reliability often imply feedback of the PDE discretization information back to the domain discretization (i.e. in adaptive methods) or even modification of the physical domain or attributes (e.g., design optimization).

Based on this model of information flow, ITAPS researchers have defined an abstract data model that supports a wide array of supporting technologies and encompasses a broad spectrum of usage scenarios. The data model divides the data required by a simulation into three core data types: the geometric data, the mesh data, and the field data. These core data types are associated with each other through data relation managers. The data relation managers control the relationships among two or more of the core data types, resolve cross references between entities in different groups, and can provide additional functionality that depends on multiple core data types. The building blocks within these data models are the concepts of entities, entity sets, and tags.
As a particular example, consider the discrete representation of the computational domain, or the mesh. ITAPS mesh entities correspond to the individual pieces of the mesh, namely, vertices, edges, faces and regions. Specific examples include a hexahedron, edge, triangle or vertex. Mesh entities are classified by their entity type (topological dimension) and entity topology (shape). Higher-dimensional entities are defined by lower-dimensional entities with shape and orientation defined using canonical ordering relationships. To determine which adjacencies are supported by an underlying implementation, an adjacency table is defined which can be returned by a query through the interface. The implementation can report that adjacency information is always, sometimes, or never available; and to be available at a cost that is constant, logarithmic (i.e., tree search), or linear (i.e., search over all entities) in the size of the mesh. ITAPS mesh entity sets are extensively used to collect mesh entities together in meaningful ways, for example, to represent the set of all faces classified on a geometric face, or the set of regions in a domain decomposition for parallel computing.

To support many of the services that applications desire, such as adaptive mesh refinement, it is important that the data model include the concept of modification to allow changes to geometry, topology, or set structure. In the case of the mesh, capabilities include changing vertex coordinates and adding or deleting entities. Modification often requires interactions between the mesh, geometry and field data models and is one of the primary uses for the data relations manager. For example, when refining a mesh, it is often critical to associate or classify the mesh entity with one or more specific entities in the underlying geometric model to ensure accuracy, particlarly on curved or complex geometries.