locuoco / coulomb_oscillators

N-body Coulomb oscillators

N-body Coulomb oscillators

This repository contains two folders:

• 'Simulation' contains a code that uses a Fast Multipole Method (FMM) in 2D cartesian coordinates and symplectic integrators for the simulation of a N-body system of charged particles with an external elastic potential (i.e. Coulomb oscillators). It is written in C++11 with multithreading and CUDA 8.0 GA2 (any later version can also be used). It also uses the CUDA UnBound (CUB) library 1.6.4 (again, a later version can be used as long as it is supported by the CUDA compiler). More info on usage later.
• 'Graphics' contains a code that graphically visualizes the evolution of the system. It takes the output of 'Simulation' as input. It is written in C++/OpenGL. It uses OpenGL Mathematics, FreeType, FreeImage, GLEW and GLFW.

The code is currently mainly developed by Alessandro Lo Cuoco. parasort is a parallel sorting algorithm by Amir Baserinia based on the C++ standard algorithm std::sort (modified by Alessandro Lo Cuoco and redistributed under the original GPL v3 license). This software contains source code provided by NVIDIA Corporation.

External download links:

• CUDA UnBound (for Simulation)
• GLFW (for Graphics)
• GLEW (for Graphics)
• FreeType (for Graphics)
• FreeImage (for Graphics)
• OpenGL Mathematics for Graphics)

Simulation

Compilation

nvcc main.cu -o nbco -O3 -std=c++11 -arch=sm_<xy> -I <includes>

<xy> is the compute capability of the GPU (usually given in the form x.y), for example sm_21 corresponds to a compute capability of 2.1. <includes> is the folder which contains the CUB library.

Note: some CUDA versions may require the C++14 standard or later.

The resulting program will be called nbco. A compatible C++ compilator must be available.

Usage

nbco [options] [input]

[input] is the path to a file that contains a state of the system. The format is that of a binary file that contains the positions of all particles and then their respective velocities in the same order. This state is used for initialising the system to be simulated. If not specified, the system will be initalised by sampling from a known distribution (KV or gaussian).

Other options:

• -h or -help Display this information.
• -o <output> Specify the folder where the output will be written. Default is './out'. This folder must already exist. The format of output files is the same as the input file format described before.
• -n <npart> Number of particles to simulate. Default is 30001. Will be ignored if [input] is specified.
• -ds <v> Time step. Default is 5e-4.
• -iters <n> Number of total simulation iterations. Default is 30000.
• -steps <n> Number of steps to simulate before saving to file. Default is 200.
• -integ <name> Set the symplectic integrator to be used instead of the default one (2nd order). <name> must be chosen from the list {eu, fr, pefrl}, respectively the semi-implicit Euler (1st order), Forest-Ruth (4th order) and PEFRL (4th order).
• -p <order> FMM expansion order. Default is 5.
• -r <radius> Interaction radius. Must be 1 or greater. Default is 1.
• -eps <v> Smoothing factor. Must be greater than 0. Default is 1e-9.
• -i <v> A factor so that max FMM level is round(log(n*i/p^(3/2))). Default is 1.
• -ncoll P2P pass will not be calculated, effectively ignoring collisional effects. Note however that the result will depend on the max FMM level, and the simulation may be highly unreliable at certain conditions.
• -cpu Use CPU with multithreading (default is GPU).
• -cpu-threads <n> Number of CPU threads. Must be 1 or greater (default is 8). Implies -cpu.
• -cacheline <n> CPU cache line size in bytes. Defaut is 64. Will be ignored if -cpu is NOT specified.
• -gpu <blocksize> Specify the number of threads in a GPU block. It must be chosen from the list {1, 32, 64, 128, 256, 512, 1024} (1024 threads is available for compute capability 2.0 and above). Default is 128. Will be ignored if -cpu is specified.
• -gridsize <n> Specify the maximum number of blocks in a GPU grid. Must be 1 or greater. Default is 128. Will be ignored if -cpu is specified.
• -test Show relative errors and execution times of a single iteration instead of doing the simulation.
• -ga Initialise the system with a gaussian distribution instead of a KV distribution (which is the default).
• -xi <v> Set the perveance.
• -omega0 <vx> <vy> Set the phase advances.
• -x <vx> <vy> Set the std.dev. of positions. Will be ignored if [input] is specified.
• -u <vx> <vy> Set the std.dev. of velocities. Will be ignored if [input] is specified.
• -A <vx> <vy> Set the system semi-axes. Will be ignored if [input] is specified.
• -omega <vx> <vy> Set the depressed phase advances. Will be ignored if [input] is specified.

Note: x = A / 2 and u = omega * A / 2.