1 / 32

Beam Dynamic Calculation by NVIDIA® CUDA Technology

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:

dakota
Download Presentation

Beam Dynamic Calculation by NVIDIA® CUDA Technology

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 7 July 2009 Beam Dynamic Calculation by NVIDIA® CUDA Technology E. Perepelkin, V. Smirnov, and S. Vorozhtsov JINR, Dubna

  2. 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

  3. Injection line Dee ESD Magnet sectors Computer model of the cyclotron

  4. Inflector Electric field G1 Magnetic field Axial channel Magnetic field Regions of the field maps

  5. Axial injection line

  6. Cyclotron

  7. φRF = 15° φRF = 13° φRF = 10° φRF = 28° Central region optimization

  8. Particle losses

  9. Bunch acceleration

  10. S0 S1 S2 S3 S4 Optimization process

  11. Acceleration field map

  12. 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

  13. Open Multi-Processing ( Open MP )

  14. Spiral inflector

  15. Beam phase space projectionsat the inflector entrance

  16. Beam phase space projectionsat the inflector exit Blue points – PIC by FFT (Grid: 25 x 25 x 25 )Red points – PP

  17. Calculation time 10,000 particlesNo geometry losses

  18. Compute Unified Device Architecture ( CUDA )

  19. GeForce 8800 GTX ( price ~ $300 )

  20. GPU structure 128 SP ( Streaming Processors )

  21. 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

  22. 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 )

  23. __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;

  24. __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

  25. __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

  26. __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

  27. __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);

  28. __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 )

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

  30. Comparison

  31. SC effect no SC Losses 24% SC Losses 94% I = 4 mA

  32. 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.

More Related