Parallel Decomposition-based Contact Response

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Parallel Decomposition-based Contact Response

• Fehmi Cirak
• California Institute of Technology

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Motivation

• Requirements to a contact library for the Virtual
  Test Facility
• Non-smooth geometries
• Modular software architecture for use with shell
  and solid solvers
• No problem dependent parameters
• Parallelization overhead in terms of
  implementation and performance should be minimum
• Some of the existing contact algorithms
• Explicit Methods
• Penalty methods
• Include problem dependent parameters
• Do not work for non-smooth geometries
• Explicit-implicit methods
• Very hard to parallelize and/or not efficient

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Discrete Variational Mechanics

• Discrete action integral
• with collision at time
• Equilibrium and collision equations
• Geometrically admissible configurations
• Constraint on the variations

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Inadmissible Configurations in 3D
Vertex-face collision
Edge-edge collision
Constraint function g is defined as the
tetrahedron volume
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Equilibrium and Collision Equations

• Equilibrium equations
• Collision equations
• Jumps in the momentum
• Jumps in the kinetic energy
• Collision events during explicit time-stepping of
  the equilibrium equations

Impact time tc
Impact time approximation as used in this work
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Momentum Decompositions

• Prior to solving the collision equations the
  momenta during the contact are decomposed into
  components
• Normal component
• Fix component does not lead to any relative
  motion

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Solving the Collision Equations

• Non-frictional case
• Closed form expressions for the momentum after
  the collision can be computed using the collision
  equations and momentum decompositions
• Frictional case
• Friction is modeled as an impulse in the slide
  direction
• Normal impulse same as in non-frictional case
• Coulomb model for friction

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DCR Algorithm (with Matt West)

• Update nodal positions and velocities using
  standard time stepping schemes, such as Newmark
• Search and remove inadmissible triangle-triangle
  intersections
• Remove face-node penetrations by projecting the
  penetrating node to the closest point on the
  triangles surface
• Remove edge-edge penetrations by projecting the
  penetrating edge to the closest point on the
  triangle edge
• Transfer momenta between colliding vertices and
  triangles using momentum decompositions
• Decompose the momenta prior to contact by
  computing , , , ,
  and
• Compute the normal impulse and the
  slide impulse
• Update momentum immediately after impact

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Spheres Impact

• Without Friction
• With Friction (? 0.5)

Time step 4000
Time step 500
Time step 2000
Time step 500
Time step 2000
Time step 4000
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Spheres Impact without Friction

• Radius 1.0 Neo-hookean material
  
• Thickness 0.05 Youngs modulus
  21000
• Poissons ratio 0.3
• Time step size 5.0e-6
  Density 0.0785

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Spheres Impact with Friction (?0.5)
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Cubes Impact
Neo-hookean material Youngs modulus 21000 Pois
sons ratio 0.3 Density 0.0785
Length 1.0 Thickness 0.2 Time
step size 5.0e-6
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Cubes Impact Energies and Momenta
Data for non-smooth impact of five cubes
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Parallel Contact Detection

• In large scale computations contact search takes
  up a significant amount of time
• There are basic differences in the communication
  patterns of contact search and element level
  computations
• Contact search is an inherently global problem
• Finite element computations are local for
  explicit dynamics
• For scalability different partitions for the
  solid and contact surface are necessary
• ll
• J
• L
• l

Contact partitioning with RCB algorithm
Solid partitioning with METIS
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Parallel Contact Algorithm

• Solid solver provides the entire surface mesh and
  the related vertex variables to all computational
  contact nodes
• Surface mesh is partitioned with recursive
  coordinate bisection using Zoltan
• An extended surface patch is assigned to each
  computational contact node
• Each computational node performs on its assigned
  partition
• Serial search for collisions
• Orthogonal range query with sparse buckets
• Local contact check for vertex-face and edge-edge
  penetrations
• Apply the serial DCR algorithm
• Collect all the modified vertex variables and
  return the surface mesh to the solid solver

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Scalabililty - Two Disk Impact

• Scalability runs performed on Frost by Sharon
  Brunett
• More tests for different examples in progress

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Integrated Simulation
Time step 1700
Time step 2700
Time step 3700
Time step 4700
5,2 M element solid mesh 1,3 M cell fluid mesh 4K
timesteps on 512 Frost procs.