Two Particle-in-Grid Realisations on Spacetrees (1508.02435v2)

Abstract: The present paper studies two particle management strategies for dynamically adaptive Cartesian grids at hands of a particle-in-cell code. One holds the particles within the grid cells, the other within the grid vertices. The fundamental challenge for the algorithmic strategies results from the fact that particles may run through the grid without velocity constraints. To facilitate this, we rely on multiscale grid representations. They allow us to lift and drop particles between different spatial resolutions. We call this cell-based strategy particle in tree (PIT). Our second approach assigns particles to vertices describing a dual grid (PIDT) and augments the lifts and drops with multiscale linked cells. Our experiments validate the two schemes at hands of an electrostatic particle-in-cell code by retrieving the dispersion relation of Langmuir waves in a thermal plasma. They reveal that different particle and grid characteristics favour different realisations. The possibility that particles can tunnel through an arbitrary number of grid cells implies that most data is exchanged between neighbouring ranks, while very few data is transferred non-locally. This constraints the scalability as the code potentially has to realise global communication. We show that the merger of an analysed tree grammar with PIDT allows us to predict particle movements among several levels and to skip parts of this global communication a priori. It is capable to outperform several established implementations based upon trees and/or space-filling curves.

• The paper introduces two innovative strategies—PIT and PIDT—that optimize particle tracking on adaptive spacetree grids.
• The methodologies leverage dynamic grid refinements to efficiently map particle movements in a flexible particle-in-cell framework.
• Experimental results validate distinct performance trade-offs between PIT and PIDT in managing varied particle dynamics.

Overview of "Two Particle-in-Grid Realisations on Spacetrees"

The paper "Two Particle-in-Grid Realisations on Spacetrees" by Weinzierl et al. investigates two methodologies for integrating particle management on dynamically adaptive Cartesian grids through a particle-in-cell (PIC) framework. This work is fundamentally motivated by the computational challenge posed by particles that can traverse these grids without velocity constraints, and thus, it introduces innovative strategies to address this issue. The methodologies developed—Particle in Tree (PIT) and Particle in Dual Tree (PIDT)—differ in their approaches to particle-storage resolutions, leveraging the robust structure of spacetrees.

Key Methodologies

1. Particle in Tree (PIT): This method assigns particles to the smallest cell that contains them within the spacetree grid. Particles are 'lifted' to a parent container when traversing multiple cells, facilitating an efficient mapping of particles moving through the grid.
2. Particle in Dual Tree (PIDT): Here, particles are assigned to grid vertices and thus utilize a dual grid structure that enables them to move through multiscale linked cells. This methodology integrates the advantages of linked-list strategies by allowing particles to transition smoothly between adjacent cells.

The flexibility of these methods shines through in their application to PIC codes, where they enable optimal particle sorting and grid synchronization in the context of multi-scale spatial resolutions. The authors validate these methods within a practical setup of an electrostatic PIC model, assessing performance through the handling of Langmuir waves in thermal plasma.

Experimental Validation and Performance Insights

Experiments conducted as part of this work reveal that each strategy is well-suited to particular characteristics of particle and grid dynamics. A notable insight from this research is the variable performance outcomes of the two strategies, which hinge on the adaptation level of the grid and the velocity distribution among particles:

• PIT generally offers superior performance when particles move less frequently across cell boundaries, making it suitable for cases with low-resolution dynamics. It shows robust scalability up to a threshold before network communication becomes a bottleneck.
• PIDT, while initially more computationally intensive due to its complex movement tracking, surpasses PIT in scenarios with higher particle velocities or grid steeper adaptations because it better manages tunneling particles.

The implementation within a distributed memory framework also highlights the methods' potential for reduced communication overhead, particularly for PIDT, which benefits from asynchronous exchange patterns.

Implications and Future Directions

The developments presented in this paper offer crucial implications for the future design of PIC codes and similar particle-grid interaction frameworks, where multiscale adaptive grids are essential. The innovative utilization of spacetrees for dynamic particle management offers a compelling solution to the inherent difficulties posed by non-constraint particle velocities and could significantly enhance the scalability and efficiency of computational models in physics and engineering.

Future research may expand on these findings by integrating these methodologies into applications requiring complex particle dynamics, such as those observed in gravitational models or plasma simulations with significant particle inhomogeneity. The authors also allude to potential advances in harnessing local particle time-stepping, considering the possible application of their methods with local particle time-stepping algorithms that adaptively choose time steps based on particle velocity.

In conclusion, the paper highlights valuable contributions within computational modeling, specifically focusing on expanding the capabilities and performance of particle-in-grid systems. The methodology and experimental results serve as a coherent foundation for further exploration into efficient, scalable, and adaptable computational frameworks.