Sponsor:
Advanced Scientific Computing Research (ASCR) under the U.S. Department of Energy Office of Science (Office of Science)
Project Team Members:
Northwestern University
The HDF Group
- Quincey Koziol
- Gerd Herber
Argonne National Laboratory
North Carolina State University
- Nagiza Samatova
- Sriram Lakshminarasimhan
Computational Fracture Mechanics (CFM) Use Case
To get a general feel for the kinds of problems people in CFM are trying to tackle have a look at the General CFM references below. For its entertainment value, I suggest you start with the two movies under CFG at DARPATECH 2007.
Topology / Geometry / Discretization
In CFM, there are three (or more) layers of entities to be dealt with. Not all layers are present explicitly in all kinds of simulations. For example, if the geometry is polyhedral (there are no curved surfaces), typically only a topological decomposition and one or more discretizations (mesh) will be specified.
Dimension | Topology | Geometry | Discretization |
0 | Vertex | Point | Node |
1 | Edge, Loop, Polygon | Curve | Edge, Front |
2 | Face | Patch | Surface, Interface, Facet |
3 | Region, Polyhedron | Volume | Region, Element |
For simplicity the more specific decomposition will respect the more general decomposition: A topological face will be covered by geometric patches that do not extend beyond its boundary. Curves do not run across topological faces, but follow their bounding edges, loops or polygons.
Below is an example of a topological decomposition. This is a model of a polycrystalline structure with surface particle inclusions. Each grain or crystal is represented as a polyhedron (region). Each polyhedron is bounded by polygon bodies (faces). Each polygon body is bounded by one or more polygons (curves). For this project we assume that each polygon body is bounded by exactly one polygon. (In general this can always be achieved through appropriate decompositions.) Subsequently the polycrystal is meshed (decomposed into tets, bricks etc.), material properties and boundary are conditions assigned, and a (non-linear) Finite Element Analysis (FEM) is performed. There are 3 screenshots polycrystal1,2,3.gif, the OpenDX .net file (elf.net), and a sample DX data file (elf.dx) under Attachments.
Popular Element Types and AMR
High-order p-methods are popular in some circles, but linear, quadratic and cubic elements will probably cover more than 80% of the market. The most popular shapes in 3D are tets, bricks (hexahedra), wedges (prisms), and pyramids, plus the odd-ball interface or cohesive elements. We might want to focus on conforming decompositions, i.e., meshes or grids where adjacent elements can share only entire faces, not parts. Arbitrary element connectivity, non-conforming grids are popular in certain fluid-mechanics simulations, see for example On the use of general elements in fluid dynamics simulations.
The three most common types of coarsening/refinement are h-refinement (element subdivision), p-refinement (increase of shape function order, more nodes per element), and r-refinement (changing node positions, but no connectivity change). For the purposes of Damsel we might want to focus on h-refinement and keep an eye on p-refinement. Hierarchical h-refinement, i.e., there are a few pre-defined patterns of how to subdivide elements of a given type (e.g., 1:2, 1:4, and 1:8 for tetrahedra), is popular and simplifies the book keeping. In order to prevent element quality deterioration it is sometimes necessary for elements targeted for refinement to consult with adjacent elements about which refinement or coarsening pattern to apply.
We might want to add a "surgical" capability to carve out regions (of elements) and replace them with a on the interface conforming sub-mesh. This is a fairly common procedure, for example, when inserting cracks into an existing (un-cracked) model.
References
General CFM
* Paul Wawrzynek et al. "Advances in Simulation of Arbitrary 3D Crack Growth using FRANC3D/NG"
Unstructured AMR
* De Cougny, H.L. and Shephard, M.S. "Parallel Refinement and Coarsening of Tetrahedral Meshes"
* Oliker, L. and Biswas, R. "Load Balancing Unstructured Adaptive Grids for CFD Problems"
* Oliker, L. et al. "Parallel Tetrahedral Mesh Adaptation with Dynamic Load Balancing"
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