CS 5220

Parallelism and locality

• Real world has parallelism and locality
  • Particles, people, etc function independently
  • Near interactions stronger than distant ones
  • Can often simplify dependence on distant objects
• More parallelism / locality through model
  • Limited dependency between adjacent time steps
  • Can neglect or approximate far-field effects
• Often get parallelism at multiple levels
  • Hierarchical circuit simulation
  • Interacting models for climate
  • Parallelizing trials/fevals in MC or optimization

Common ideas / issues

• Load balancing
  • Imbalance from lack of parallelism, poor distribution
  • Can be static or dynamic
• Locality
  • Want big blocks with low surface-to-volume ratio
  • Minimizes communication / computation ratio
  • Can generalize ideas to graph setting
• Tensions and tradeoffs
  • Irregular spatial decompositions for load balance at the cost of complexity, maybe extra communication

Basic styles of simulation

• Discrete event systems (continuous or discrete time)
• Particle systems
• Lumped parameter models (ODEs)
• Distributed parameter models (PDEs / integral equations)

Often more than one type of simulation appropriate.
Sometimes more than one at a time!

Basic styles of simulation

Discrete event systems

• Continuous or discrete time
• Game of life, logic-level circuit simulation
• Network simulation

Basic styles of simulation

Particle systems

• Billiards, electrons, galaxies, ...
• Ants, cars, ...?

Basic styles of simulation

Lumped parameter models

• Systems of Ordinary Differential Equations (ODEs)
• Circuits (SPICE), structures, chemical kinetics

Basic styles of simulation

Distributed parameter models

• PDEs / integral equations
• Heat, elasticity, electrostatics, ...

What next?

• T: Discrete event systems
• T: Particle systems
• R: Lumped parameter models
• R: Distributed parameter models