Overview
Particle-in-Cell transfers particle properties to a grid, advances grid fields, and interpolates updates back to particles.
SpecializedSource checked
Particle-in-Cell
Combines moving particles with a grid used to solve field quantities.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Simulation
- Difficulty
- Advanced
- Family
- Hybrid Particle-Grid Simulation
- Tier
- Specialized
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 1
- Code example
- Ready
- Visualization
- Ready
Core Concepts
particle-grid transferfield solveinterpolationadvection
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(particles + grid)
Average
O(steps * (particles + grid))
Worst
O(steps * (particles + grid))
Space
O(particles + grid)
When to Use
- Use when physics simulation needs particle-grid transfer.
- Use when the input matches the assumptions behind hybrid Particle-Grid Simulation.
When Not to Use
- Avoid when the time step, forces, or constraints make the system unstable for the chosen method.
- Avoid when a simpler algorithm gives the required result with less setup.
What It Does
- Combines moving particles with a grid used to solve field quantities
- Uses particle-grid transfer and field solve to guide the work.
- Produces updated state.
Use Cases
- Physics simulation
- Animation
- Interactive systems
Inputs
- Current state
- Forces or constraints
- Time step
Outputs
- Updated state
- Constraint corrections
- Collision results
Key Formulas (1)
Particle-to-grid transfer
gridvalue = weightedsum(particlevalues)
grid_value = weighted_sum(particle_values)Deposits particle quantities onto nearby grid cells.
Pseudocode
- 1.Prepare the inputs and state needed for Particle-in-Cell.
- 2.Apply the particle-grid transfer step while the stopping condition has not been met.
- 3.Update intermediate state and discard invalid candidates.
- 4.Return updated state.
Canonical Example
- Input
- Particle-in-Cell input with a small representative case
- Output
- Updated state
- Explanation
- Particle-in-Cell applies particle-grid transfer to produce updated state.
Implementation Notes
- Use deterministic update ordering when reproducibility matters.
- Keep the particle-grid transfer step separate enough to test independently.
Common Pitfalls
- Changing the time step without retuning stiffness or damping can destabilize the simulation.
- Forgetting to check edge cases can make Particle-in-Cell look correct on only ideal inputs.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryShow state updates, constraints, and error correction over simulation steps.
Step 1 of 4: Prepare the inputs and state needed for Particle-in-Cell.
simulation-mechanismNotes
Particle-in-Cell should be used with the assumptions and tradeoffs of hybrid Particle-Grid Simulation in mind.
Sources (1)
What each reference supports for this entry.
Fluid Simulation for Computer Graphics
BookFluid-simulation reference for particle-in-cell transfer between particles and grids.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageAlternative toFinite Volume Fluid Simulation
Particle-in-cell and finite-volume methods couple different particle/grid representations for simulation.
Related Algorithms
Tags
SimulationParticlesFluid SimulationMesh Method