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Beam Dynamic Calculation by NVIDIA® CUDA TechnologyPowerPoint Presentation

Beam Dynamic Calculation by NVIDIA® CUDA Technology

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### Beam Dynamic Calculation by NVIDIA® CUDA Technology

### Open Multi-Processing

### Compute Unified Device Architecture

E. Perepelkin, V. Smirnov, and S. Vorozhtsov

JINR, Dubna

Introduction

- Cyclotron beam dynamic problems [1]:
- Losses on geometry
- Space Charge effects
- Optimization of the central region [2]

- CBDA [3] code calculations:
- OpenMP ( by CPU )
- CUDA ( by GPU )
__________________________________________________________________

[1] Beam injection and extraction of RIKEN AVF cyclotron, A. Goto, CNS-RIKEN Workshop on Upgrade of AVF Cyclotron, CNS Wako Campus, 3-4 March 2008

[2] SPIRAL INFLECTORS AND ELECTRODES IN THE CENTRAL REGION OF THE VINCY CYCLOTRON, E. Perepelkin, A. Vorozhtsov, S. Vorozhtsov, P. Beličev, V. Jocić, N. Nešković, etc., Cyclotrons and Their Applications 2007, Eighteenth International Conference

[3] CBDA - CYCLOTRON BEAM DYNAMICS ANALYSIS CODE, E. Perepelkin, S. Vorozhtsov, RuPAC 2008, Zvenigorod, Russia

Very time consuming problem

- About 5 different variants – minimum
- Many ion species – accelerated
- Very complicated structure
- Multi macro particle simulations for SC dominated beams

One run requires ~ several days of computer time

( Open MP )

Beam phase space projectionsat the inflector entrance

Beam phase space projectionsat the inflector exit

Blue points – PIC by FFT (Grid: 25 x 25 x 25 )Red points – PP

Calculation time

10,000 particlesNo geometry losses

( CUDA )

GPU structure

128 SP ( Streaming Processors )

Kernel functions

- __global__ void Track ( field maps, particles coordinates )
- Calculate particle motion in electromagnetic field maps

- __global__ void Losses ( geometry, particles coordinates )
- Calculate particle losses on the structure

- __global__ void Rho ( particles coordinates )
- Produce charge density for SC effects

Kernel functions

- __global__ FFT ( charge density )
- FFT method ( analysis / synthesis )

- __global__ PoissonSolver ( Fourie’s coefficients )
- Find solution of Poisson equation

- __global__ E_SC ( electric potential )
- Calculate electric field by E = -grad( U )

__global__ void Track ( )

- Function with many parameters. Use variable type __constant__:
- __device__ __constant__ float d_float[200];
- __device__ __constant__ int d_int[80];

- Particle number corresponds
- int n = threadIdx.x+blockIdx.x*blockDim.x;

- Number of “if, goto, for” should be decreased;

__global__ void Losses ( )

- Geometry structure consists from triangles. Triangles coordinates stored in __shared__ variables. This feature gave drastically increase performance
- int tid = threadIdx.x; - used for parallel copying data to shared memory

- Particle number corresponds to
- int n = threadIdx.x+blockIdx.x*blockDim.x;
- Check particles and triangle match

__global__ void Rho

- Calculate charge impact in the nodes of mesh from particle with number
int n = threadIdx.x+blockIdx.x*blockDim.x;

Cell 7

Cell 8

Node

Cell 6

Cell 5

Cell 3

Cell 2

Cell 1

__global__ FFT ( )

- Used real FFT for sin(πn/N) basis functions;
- 3D transform consist from three 1D FFT for each axis: X, Y, Z
- int n = threadIdx.x+blockIdx.x*blockDim.x;
k=(int)(n/(NY+1));

j=n-k*(NY+1);

m=j*(NX+1)+k*(NX+1)*(NY+1);

FFT_X[i+1]=Rho[i+m];

n = j + k*(NY+1)

NY

NZ

__global__ PoissonSolver ( )

- int n = threadIdx.x+blockIdx.x*blockDim.x;
- Uind(i,j,k) = Uind(i,j,k) / ( kxi2 + kyj2 + kzk2 )
ind(i,j,k)=i+j*(NX+1)+k*(NX+1)*(NY+1);

k=(int)(n/(NX+1)*(NY+1));

j=(int)(n-k*(NX+1)*(NY+1))/(NX+1);

i=n-j*(NX+1)-k*(NX+1)*(NY+1);

__global__ E_SC ( )

- int n = threadIdx.x+blockIdx.x*blockDim.x+st_ind

Un + ( NX + 1 )( NY + 1 )

Un + ( NX + 1 )

Un

Un - 1

Un - ( NX + 1 )

Un + 1

Un - ( NX + 1 )( NY + 1 )

Performance

* Mesh size: 25 x 25 x 25. Particles: 100,000. Triangles: 2054

Conclusions

- Very chipper technology
- Increasing of performance at power 1.5 gave chance to produce the complex cyclotron modeling
- Careful programming
- Expand this method for calculation of beam halo and etc.

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