1. Parallel Plasma Equilibrium Reconstruction Using GPU
Yao Huang1, Z.P.Luo1, Q.P.Yuan1, X.F.Pei1, X.N.Yue2,
B.J.Xiao1,2, L.Lao3 
1 Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China 
2 School of Nuclear Science & Technology, University of Science & Technology of China
3 General Atomics 1

2. Outline
Motivation
Introduction on GPU parallel computation and Parallel equilibrium reconstruction
Implementation
Future Plan 2

3. rt-EFIT / isoflux control
Magnetic measurement
12 PF currents
2 Plasma current
35 flux loops
38 magnetic probes
shape parameter,
control errors 3

4. rt-EFIT: fast loop reuses the data set from slow loop
RT-EFIT is divided into two portions to increase computation frequency
For EAST on 33*33 grids
fast loop: control errors (250 us)
slow loop: provides data set for fast loop
(~2 ms / 1 iteration)
Reusing the data set
Introduces error when plasma shape changes rapidly. 4

5. Outline
Motivation
Introduction on GPU parallel computation and Parallel equilibrium reconstruction
Implementation
Future Plan 5

6. GPU devotes more transistors for data process
GPU (Graphic Processing Unit) is a specialized coprocessor designed to rapidly manipulate and alter memory to accelerate the creation of images and output to a display.
GPU is specifically designed to allow vastly parallel computations, which devotes more transistors to data processing, CPU has many transistors on data cache and flow control.
ALU: Arthmetic Logical Unit, transistors for
data processing 6 6

7. GPU computation power compares favorably against CPU
GPU has evolved into a highly parallel, multithreaded, manycore processor with tremendous computational horsepower and very high memory bandwidth.
Theoretical GPU Theoretical CPU
GFLOP/S EAST GPU Server GB/S
Year Year
Floating-Point Operations per Second Memory Bandwidth
3000
1000 7 7

8. Parallelized reconstruction using GPU
P-EFIT is based on the EFIT but using massively parallel GPU cores to significantly accelerate the computation.
Response matrix calculation: Dividing the matrix into small parts, matrix multiplications, tens of us
Least square fitting: Making use of parallel matrix multiplication, the initial over-determined equation system is transformed into full rank system
Equilibrium solver or Poloidal flux refreshing (Δ* Inversion), : By eigenvalue decomposition, the block tri-diagonal matrix is transformed into independent block diagonal matrix which could be solved in parallel.
Boundary search, beta, li etc parallel algorithm.

9. Breakdown response matrix results in computation costs ~ tens of us
Breakdown the matrix manually to GPU cores,
Parallel multiplication and summation
Minimize the communication time
Time costive:
Elements multiplication & summation
Data access
Cost around 1ms
serially run on CPU
40μs on GPU
Calculating response matrix
74×1952 4×
1952 9 9

10. Δ* Inversion could be solved in parallel by eigenvalue decomposition
It solves the G-S equation directly with finite difference.
Discreteness
Eigenvalue decomposition 10 10

11. Δ* Inversion could be solved in parallel by eigenvalue decomposition
Block 0
Block 1 …
Block N-1
GPU hardware architecture
Experiments conduct on GPU with type Tesla k20, CPU Intel Xeon® E3-2400
65×65 grid ： 50μs
129×129 grid： 100μs
Modified prefix sum algorithm 11 11

12. Parallel Boundary Tracing, β, li …
Searching boundary in angular ray directions, the algorithm is designed to find the intersection point of plasma boundary and angular rays.
GPU searches 120 angular rays and boundary points in parallel, algorithm on GPU costs less than 15 us.
Parallel β, li etc, calculation
Integral and averaging can be parallelized on GPU. After knowing the plasma boundary location, β, li can be easily calculated in about 25us.

13. Outline
Motivation
Introduction on GPU parallel computation and Parallel equilibrium reconstruction
Implementation
Future Plan 13

14. PEFIT Flow Chart: Optimization of GPU/CPU Interactions
Receiving Diagnostic Data
P-EFIT grid: 65*65
time: 0.3ms
(RT-EFIT grid: 33*33
Fast loop: 0.25ms
Slow loop: 2ms)
Initializing Plasma Current
Response matrix calculation
Least square fitting
Δ* Inversion
Searching plasma boundary
Control errors, Betap,
li etc calculation
Parallel Computation Functions
RFM Switch
CPU
GPU
PCS
P-EFIT Data interface
with PCS
time: 0.03ms
Sending Control Error 14

15. P-EFIT implementation in PCS: RFM data transfer between GPU and PCS
EAST PCS is a linux cluster configured with 4 nodes.
RFM (reflective memory card) has been successfully applied in the system for data input and output.
GPU
Server 15

16. System Benchmark Test: Data interface using RFM can satisfy the needs of control and P-EFIT's result matches RT-EFIT result
Seg1
Seg3
Seg4
Seg6
Seg 8
Seg9
Experimental simulation tests showed that the data interface between PCS and GPU server works well and the P-EFIT's control error result matches RT-EFIT's. 16

17. Plasma Discharge Based on ISOFLUX/P-EFIT(shot:51044)17

18. P-EFIT results on DIII-D: P-EFIT magnetic equilibrium reconstruction results match EFIT results

19. P-EFIT Achieves 10 - 100 Acceleration Ratio in Reconstruction for A Whole shot.
257*257 grids
15 min
< 10 s.

20. Outline
Motivation
Introduction on GPU parallel computation and Parallel equilibrium reconstruction
Implementation
Future Plan 20

21. Meaning and Future Plan
Real-time reconstruction with more experimental measurements and physics constraints.
(2) Application in DIII-D, MAST and …
(3)Higher resolusion spatial grids in PCS 129*129 grid ms/iteration 21

22. Summary
P-EFIT could complete one iteration in 300 μs with 65×65 grid and 650μs with 129×129 grid at < 1/10 computation cost than EFIT, and comparable to RT-EFIT with coarser grid, satisfying the real-time control needs .
Benchmark test for EAST and DIII-D discharges on 65×65 and 129×129 spatial grids indicate that P-EFIT could accurately reproduce EFIT.
The implementation of P-EFIT into EAST PCS is realized by adding data interface and transferring data through RFM and we successfully apply
P-EFIT in PCS during the 2014 EAST experiment campaign.
This opens a way for more complicated equilibrium problem solver. We will continue work on more experimental measurements, physics constraints and higher resolution spatial grids.
Application to more device…DIII-D, MAST…not only on real-time control but also on data analysis. 22