1 / 8

Optimizing Physical Simulation Paradigms for Parallel Discrete Event Simulations

Explore structured grids, particle solvers, sparse systems, and solvers for linear equations in physical simulations. Discuss the hindrance of sparse matrices and the effectiveness of parallel solvers. Examine examples like atoms, stars, and vortices. Delve into particle interactions and particle-mesh interactions, and the challenge of parallelizing hard algorithms.

micol
Download Presentation

Optimizing Physical Simulation Paradigms for Parallel Discrete Event Simulations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Application Paradigms: Parallel Discrete Event SimulationsCS433Spring 2001 Laxmikant Kale

  2. Physical Simulations: continued • Physical simulations: • Structured or unstructured grids, possibly with adaptive refinements • Equations/Solvers • Particles

  3. Solvers for Linear Equations • In many situations in physical simulations, you need to solve systems of linear equations • Arise naturally in discretizations of partial differential equations • Implicit time steps • Variables: • Are associated with points or regions in space • Typically, sparse systems: • because each equations connects “nearby” variables • Traditionally represented by Matrices • But, for sparse systems “physical” representations are better • Opinion: The “sparse matrix” data structure as an intermediate abstraction is unnecessary and a hindrance in some cases for effective parallelization

  4. Solvers • Direct: • parallel operations: broadcasting the pivot row • Iterative: • Communication needed between variables connected by an equation • Again, physical proximity: near-neighbor communication • Reductions for convergence • Complex iterative schemes: • Preconditioners • Multigrid solvers

  5. Particles • Examples: • atoms (molecular dynamics), stars (astrophysics), • Aluminum particles in burning gasses (Rocket) • Vortices (Fluid flow) • Typical decompositions: • Rectangular Cells • Quad/Oct trees, ORB cells • Interactions: • Particle-particle interactions • Within a cutoff distance • All to all (N-squared) • Special algorithms: Barnes-Hut, Multipole: O(N log N) • Harder to parallelize • Particle-mesh interactions: • PPPM

  6. Discrete event simulation • Physical simulations: • What we studied earlier: every part of the system advances uniformly in time, in synch • Not appropriate in many systems: • Events happen asynchronously, and components respond • Digital Circuits: Only need to attend to places where the signal changes, • The rest stay the same • Traffic in a city

  7. Discrete Event Simulation • Event Queue based simulation • Single event queue • Each event with a time-stamp • Queue prioritized by timestamps • Scheduler loop: • Select the event with earliest timestamp • process it (access objects, post new events) • Causality ensured

  8. PDES:Parallel Discrete Event Simulation • How to parallelize: • Queue is a sequential bottleneck (and not just the access time) • (1) process all events with the same timestamp • But there may not be enough • Process all that can be processed safely • Process events in approximate timestamp order • If some “object” notices it has processed events in non-causal order • Roll back

More Related