Nomenclature

• Mesh - conforming discretization of a domain using simplices (triangles and tetrahedrons), hypercubes (quads and hexahedrons), pyramids and prisms
• Field - "describe the distribution of input and solution tensors over the mesh entities" [Beall 1999; Simmetrix Web 2015]
• Field Element - localization of the field values on the closure of a mesh entity (e.g., the vertices and edges bounding a mesh face) to support operations that require those values. For example, integration, evaluation of the field at a location within the entity.
• DOF - degree of freedom, exists at a dof holder, can be scalar, vector, matrix, etc.
• DOF holder
  • can contain a DOF
  • possible holders: mesh entities, quadrature points, element centroids, etc.
• Node - a location on a mesh entitiy that is a dof holder. Multiple nodes can exist per mesh entity. For example, a mesh edge could have multiple nodes for a high order shape function.

References and Related Work

• PUMI users guide: https://www.scorec.rpi.edu/pumi/PUMI.pdf
• PUMI TOMS paper: https://www.scorec.rpi.edu/REPORTS/2015-4.pdf
• PUMI apf source code
• PUMI doxygen: https://www.scorec.rpi.edu/pumi/doxygen/
  • with internal headers: https://www.scorec.rpi.edu/~cwsmith/SCOREC/pumiDocs/html/
• PUMI APF library documentation:
  • The APF Library: https://github.com/SCOREC/core/blob/bcfbd128b65a629241b629c90e3665b539e2e9ae/apf/apf.tex
  • The Cavity Operator: https://github.com/SCOREC/core/blob/8959c599cc05e21d0fb470f941d9f892da62aa02/apf/cavity.tex
  • Interface For Field Access: https://github.com/SCOREC/core/blob/8959c599cc05e21d0fb470f941d9f892da62aa02/apf/attach.tex
  • Hierarchic Shape Functions: https://github.com/SCOREC/core/blob/8959c599cc05e21d0fb470f941d9f892da62aa02/apf/hierarchic.tex
• Mark Beall's thesis, Chapter 8: https://scorec.rpi.edu/REPORTS/1999-6.pdf
  • An object-oriented field API used within the framework ('Trellis') of other objects described in the thesis (mesh, model, solution, etc.).
  • Designed to support p-adaptivity (i.e., non-uniform field order)