Distributed Meshes : Fracture

1
Distributed Meshes Fracture

• Matt Galloway
• Pembroke College

2
Mesh Data Structures

• Uses of 2D 3D Triangulations
• Computer Graphics
• Finite Element Analysis
• The requirements of such data structures
• Speed versus memory
• Ease of use (object oriented?)
• Current data structures
• Mainly written in C and can be clumsy
• Fracture Algorithm
• Why is it needed?

3
Application Layers
Physics Layer Displacements, Velocities,
Accelerations
Geometry Layer Location of nodes/elements,
connectivity
4
Specification of Project

• Design a data structure to store the connectivity
  information for the geometry layer
• Vertices, elements, cohesive elements
• Implement a function to fracture faces
• Should be as fast as possible
• Fracture should be done at run-time
• Analyse the ability of the data structure and
  algorithms to be distributed over multiple
  processes
• Good scalability is essential for large meshes

5
Components of the Data Structure

• Vertices, Edges, Faces and Tetrahedrons

Vertex
Edge
Face
Tetrahedron
6
Components of the Data Structure

• Final data structure implemented

Vertex
Edge
Face
Tetrahedron
7
Implementation of Data Structure

• Vertex class
• Stores co-ordinates of the point
• Element classes
• Tetra4, Tetra10, CohFace3, CohFace6
• Templated by vertex class
• Mesh class
• Holds the Vertex and Element lists
• Templated by traits class
• Use of the STL and Boost
• stdvector / stdmap (variable size arrays)
• boostarray (fixed size arrays)

8
Mesh Data Structure

• Traits technique employed (StdMeshTraits)
• Allows different element/vertex types
• Types defined from traits template parameter
• STL stdmap used for element and vertex lists
• stdmapltint, VertexHandlegt, stdmapltint,
  ElementHandlegt
• Iterators
• Helper functions to iterate over the stdmap
  variables
• Other functions
• Fracture
• Add vertices / elements
• Load file (using stdistream)

9
Fracture Algorithm Theory

• Faces are fractured by asking the mesh to
  fracture the ith face of a certain element
• Cohesive elements are inserted into the mesh
  between the fractured faces
• Cohesive elements enable the physics layer to
  store information about the faces it has
  fractured
• Calculating if an edge is boundary is an
  important algorithm
• Current work has been focused on implementing the
  boundary edge fracture algorithms

10
Boundary Edge Algorithm

• Important part of the fracture algorithm
• It will be called for each edge of a fractured
  face
• Animation showing how the implemented algorithm
  works

11
Fracture Algorithm

• Vertices are duplicated according to the scheme
  outlined below
• Call fracture function with node defining the
  face
• Cohesive element is returned and added to mesh
  data structure

12
Fracture Algorithm Demonstration

• OpenGL test program was implemented to show how
  the fracture algorithm works

13
Future Work

• Implement distributed code
• MPI Framework
• Benchmark the fracture algorithm against other
  data-structures
• Evaluate scalability
• Implement test programs showing how the
  data-structure and algorithms work

14
Any Questions?