For most simulation methods, the computation time is a big problem. In the case of particle methods, the higher spatial resolution leads to the larger number of particles. As a result, the amount of calculation increases and the computation time becomes longer. In most cases, the computation time of a particle simulation ranges from several minutes to several weeks. In this column, I would like to talk about the following two methods for reducing the computation time of particle simulations.

#### 5.1 Parallel computation

The parallel computation shortens the computation time by using multiple processing units in parallel. For example, if you have two operating units and need to execute 100 operations, by using the two operating units in parallel you can reduce the number of operations per unit by 50 %, compared to a case of a single operating unit. As a result, we can shorten the computation time. Nowadays, most CPUs have multiple CPU cores, which are the operating units. We can carry out parallel computations by using the CPU cores in parallel. We can also use Graphics Processing Units (GPUs) for parallel computation of particle simulation.

#### 5.2 Reduction of particles

The larger number of particles leads to the larger amount of calculation and the longer computation time. Therefore, it is very important to reduce the number of required particles. We can reduce the number of particles by using large particles. However, it is difficult to express flows in detail by the large particles because the spatial resolution is low. To solve the problem, techniques for handling non-uniform size particles have been developed. **Movie 1** shows the examples of non-uniform size particle simulation. In this case, the overlapping particle technique* 1)* , which is a multi-spatial resolution technique, was applied. The left simulation domain was simulated at a low spatial resolution with large particles, while the right simulation domain was simulated at a high spatial resolution with small particles.

**(a) Tsunami**

**(b) Liquid flowing through in a very narrow region**

**Movie 1 Examples of reduction of particles by non-uniform size particles.**

Ellipsoidal particles also can reduce the number of required particle as shown in **Movie 2**. In this case, the left simulation domain was simulated by ellipsoidal particles, whose horizontal length is longer than the vertical length, while the right simulation domain was simulated by spherical particles. We can find that particles in the left simulation domain were ellipsoid because the distance between particles in horizontal direction is longer than that in vertical direction. By using ellipsoidal particles, we can reduce the number of particles, keeping the spatial resolution in a certain direction. For the details of the techniques, see the reference papers* 1,2)* and book

*.*

**3)****Movie 2 Example of ellipsoidal particle simulation**

Reference:

*1)*

K. Shibata, S. Koshizuka, T. Matsunaga and I. Masaie, “The overlapping particle technique for multi-resolution simulation of particle methods”, Computer Methods in Applied Mechanics and Engineering. Vol. 325, pp.434-462 (2017)

https://doi.org/10.1016/j.cma.2017.06.030

*2)*

K. Shibata, S. Koshizuka, I. Masaie, “Cost reduction of particle simulations by an ellipsoidal particle model”, Computer Methods in Applied Mechanics and Engineering, Vol. 307, pp.411-450 (2016)

http://dx.doi.org/10.1016/j.cma.2016.04.026

*3)*

S. Koshizuka, K. Shibata, M. Kondo and T. Matsunaga, “Moving Particle Semi-implicit Method, A Meshfree Particle Method for Fluid Dynamics”, ISBN: 9780128127797, Academic Press (2018)

https://www.elsevier.com/books/moving-particle-semi-implicit-method/koshizuka/978-0-12-812779-7

#### TOC

**Introduction to the particle method**

**Introduction to the particle method**

#### About The Author

**Kazuya Shibata, Ph.D.**

Assistant Professor at Department of System Innovation, Graduate School of Engineering, The University of Tokyo.