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7 July 2009. Beam Dynamic Calculation by NVIDIA® CUDA Technology. 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:
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7 July 2009 Beam Dynamic Calculation by NVIDIA® CUDA Technology 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
Injection line Dee ESD Magnet sectors Computer model of the cyclotron
Inflector Electric field G1 Magnetic field Axial channel Magnetic field Regions of the field maps
φRF = 15° φRF = 13° φRF = 10° φRF = 28° Central region optimization
S0 S1 S2 S3 S4 Optimization process
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 Multi-Processing ( Open MP )
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
Compute Unified Device Architecture ( 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
SC effect no SC Losses 24% SC Losses 94% I = 4 mA
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.