Presentation Information
[PPS03-P13]Improvements on Gravitational Computation in Rubble-Pile Asteroid Formation Simulation
*Tokushige Ryo1, Naru Hirata1 (1.University of Aizu)
Keywords:
Asteroid,Rubble pile,Gravitational calculation,Simulation
Some asteroids are considered have formed from the gravitational reaccumulation of fragments formed by disruption of a parent body. These bodies, known as rubble-pile asteroids, exhibit a wide variety of shapes. However, the cause of this diversity in shape remains largely unknown. Our research group conducted computer simulations of rubble-pile asteroid formations to elucidate conditions to derive thier diverse shapes, but the high computational cost per trial limited the number of simulations they could perform. Therefore, this study aims to accelerate the simulation by improving the algorithm for gravitational interactions. We evaluate the reduction in computation time achieved by the new method, as well as the reproducibility of the resulting triaxial ratios and porosity compared to the previous results. The simulation code developed in the previous study employs the direct method for calculating gravitational interactions. This is a brute-force approach that computes interactions between every pair of fragments, resulting in a computational complexity of O (N2). Consequently, the computational load increases quadratically as the number of fragments, N increases. Our new calculation method is introduced focusing on the physical characteristics of the simulation. In this simulation, fragments already accumulate on the central and largest core fragment and remain substantially static relative to the core due to contact forces from surrounding fragments. The proposed method exploits this property to omit gravitational calculations between fragments that are static relative to the core.
The details of the proposed gravitational calculation algorithm are as follows: Evaluate the relative velocity of each particle to the core to determine whether it is stationary. For stationary fragments: Calculate interactions only with the core and with non-stationary fragments. For non-stationary fragments: Calculate interactions with all fragments. The computational complexity of this method is O(MN), where M represents the number of non-stationary fragments (active in calculation), and N denotes the total number of fragments.
We tested our code with two different cases: the monopolistic case and oligopolistic case, both of which were also used in the previous works. We made 70 runs for every case with two codes, totaling 280 runs. Calculation times and results (triaxial ratios and porosities) are evaluated.
The average times of gravitational calculations are 12.6 times faster for the monopolistic case, and 13.7 times faster for the monopolistic case, respectively. In some runs, the entire system exhibits significant rotation causing our acceleration strategy to fail. If we exclude those failure runs from the results, the acceleration rate reaches 25.0 times for both test cases. By referring to angular velocity around the core fragment instead of relative velocity, such failures can be avoided. We also discovered that collision detection and other processes account for a significant portion of the total simulation computation time, in addition to gravity calculations. We will investigate whether these processes can also be accelerated.
While triaxial ratios and porosities of outputs for the monopolistic case computed with our new code are briefly in agree with those with the previous code, those for the oligopolistic case show slight discrepancies. The average c/a ratio decrease from 0.82 to 0.78, and the average porosity increase from 34.3% to 36.2%. We will investigate whether these discrepancies are due to code modifications, and whether they are critical for discussion on rubble-pile formation process.
The details of the proposed gravitational calculation algorithm are as follows: Evaluate the relative velocity of each particle to the core to determine whether it is stationary. For stationary fragments: Calculate interactions only with the core and with non-stationary fragments. For non-stationary fragments: Calculate interactions with all fragments. The computational complexity of this method is O(MN), where M represents the number of non-stationary fragments (active in calculation), and N denotes the total number of fragments.
We tested our code with two different cases: the monopolistic case and oligopolistic case, both of which were also used in the previous works. We made 70 runs for every case with two codes, totaling 280 runs. Calculation times and results (triaxial ratios and porosities) are evaluated.
The average times of gravitational calculations are 12.6 times faster for the monopolistic case, and 13.7 times faster for the monopolistic case, respectively. In some runs, the entire system exhibits significant rotation causing our acceleration strategy to fail. If we exclude those failure runs from the results, the acceleration rate reaches 25.0 times for both test cases. By referring to angular velocity around the core fragment instead of relative velocity, such failures can be avoided. We also discovered that collision detection and other processes account for a significant portion of the total simulation computation time, in addition to gravity calculations. We will investigate whether these processes can also be accelerated.
While triaxial ratios and porosities of outputs for the monopolistic case computed with our new code are briefly in agree with those with the previous code, those for the oligopolistic case show slight discrepancies. The average c/a ratio decrease from 0.82 to 0.78, and the average porosity increase from 34.3% to 36.2%. We will investigate whether these discrepancies are due to code modifications, and whether they are critical for discussion on rubble-pile formation process.