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Parallel algorithm design and optimization of geodynamic numerical simulation application on the Tianhe new-generation high-performance computer

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Abstract

CitcomCu is a numerical simulation software for mantle convection in the field of geodynamics, which can simulate thermo-chemical convection in a three-dimensional domain. Due to the increasing demand for high-precision simulations and larger application scales, larger-scale computing systems are needed to solve this problem. However, the parallel efficiency of CitcomCu on large-scale heterogeneous parallel computing systems is difficult to improve, especially it cannot adapt to the current mainstream heterogeneous high-performance computing architecture with CPUs and accelerators. In this paper, we propose an geodynamics numerical simulation parallel computing framework using heterogeneous computing architecture based on the Tianhe new-generation high-performance computer. Firstly, the data partitioning mode of CitcomCu was optimized based on the large-scale heterogeneous computing architecture to reduce the overall communication overhead. Secondly, the iterative solution algorithm of CitcomCu was improved to speed up the solution process. Finally, the NEON instruction set based on SIMD is used for the sparse matrix operations in the solution process to improve parallel efficiency. Based on our parallel computing framework, the optimized CitcomCu was deployed and tested on the Tianhe new-generation high-performance computer. Experimental data showed that the performance of the optimized program was 3.3975 times higher than that of the unoptimized program on a single node. Compared with 50,000 computational cores, the parallel efficiency of the unoptimized program on one million computational cores was 36.75%, while the parallel efficiency of the optimized program was improved by 16.22% and reached 42.71%. In addition, the optimized program can be executed on 40 million computational cores, with a parallel efficiency of 36.54%.

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Funding

The research was partially funded by Key-Area Research and Development Program of Guangdong Province (2021B0101190004), the National Key R &D Program of China (Grant Nos. 2021YFB0300800), The Key Program of National Natural Science Foundation of China (Grant Nos. U21A20461, 92055213), The National Natural Science Foundation of China (Grant No. 61872127), Research on High Precision Numerical Simulation and Parallel Computing Method for Ion Implanted Silicon Carbide Semiconductor Doping Process (U21A20461).

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Authors and Affiliations

  1. College of Information Science and Engineering, Hunan University, Changsha, 410082, Hunan, China

    Jin Yang, Wangdong Yang, Ruixuan Qi, Qinyun Tsai, Shengle Lin, Fengkun Dong, Kenli Li & Keqin Li

  2. Department of Computer Science, State University of New York, New Paltz, 12561, NY, USA

    Keqin Li

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  1. Jin Yang
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The paper properly credits the meaningful contributions of all authors. All authors have been personally and actively involved in substantial work leading to the paper and will take public responsibility for its content.

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Correspondence to Wangdong Yang.

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Appendix A: Appendix

Appendix A: Appendix

1.1 A.1. Noun introduction table

See Appendix Table 5.

Table 5 Noun introduction table
Full size table

1.2 A.2. Input File

# 1. Input and Output Files Information

datafile=“CASE2/caseA”

use_scratch="local"

oldfile=“CASE2/caseA”

restart=0

restart_timesteps=20000

stokes_flow_only=0

maxstep=1000

storage_spacing=50

# 2. Geometry, Ra numbers, Internal heating, Thermochemical/Purely thermal convection

Solver=multigrid node_assemble=1

rayleigh=10.97394e5

rayleigh_comp=1e6

composition=0

Q0=0

Q0_enriched=0

markers_per_ele=15

comp_depth=0.605

visc_heating=0

adi_heating=0

# 3. Grid And Multiprocessor Information

nprocx=16

nprocz=16

nprocy=8

nodex=33 nodez=33 nodey=33

mgunitx=32

mgunitz=32

mgunity=16

levels=3

# 4. Coordinate Information

Geometry=cart3d

dimenx=1.0

dimenz=1.0

dimeny=1.0

z_grid_layers=2

zz=0.0,1.0

nz=1,129

x_grid_layers=2

xx=0,1

nx=1,129

y_grid_layers=2

yy=0,1

ny=1,65

z_lmantle=0.76655052

z_410=0.857143

z_lith=0.9651568

# 5. Rheology

rheol=0

TDEPV=off

VISC_UPDATE=off

update_every_steps=2

num_mat=4

visc0=1.0e0,1.0e0,1.0e0,1.0e0

viscE=6.9077553,6.9077553,6.9077553,6.9077553

viscT=273,273,273,273

viscZ=5e-6,5e-6,5e-6,5e-6

SDEPV=off

sdepv_misfit=0.010

sdepv_expt=1,1,1,1

sdepv_trns=1.e0,1.e0,1.e0,1.e0

VMIN=on visc_min=5.0e-2

VMAX=on visc_max=2.0e04

visc_smooth_cycles=1

Viscosity=system

# 6. DIMENSIONAL INFORMATION and Depth-dependence

layerd=2870000.0

radius=6370000.0

ReferenceT=3800.0

refvisc=1.0e20

density=3300.0

thermdiff=1.0e-6

gravacc=9.8

thermexp=5e-5

cp=1250

wdensity=0.0

visc_factor=1.0

thermexp_factor=1.0

thermdiff_factor=1.00

dissipation_number=2.601

surf_temp=0.078947

# 7. phase changes: to turn off any of the phase changes, let Ra_XXX=0

Ra_410=0.0

Ra_670=0.0

clapeyron410=3.0e6

clapeyron670=-3.0e6

width410=3.5e4

width670=3.5e4

# 8. BOUNDARY CONDITIONS and Initial perturbations

topvbc=0

topvbxval=0.0

topvbyval=0.0

botvbc=0

botvbxval=0.0

botvbyval=0.0

toptbc=1 bottbc=1

toptbcval=0.0 bottbcval=1.0

periodicx=off

periodicy=off

flowthroughx=off

flowthroughy=off

num_perturbations=1

perturbmag=0.001

perturbk=1.0

perturbl=6.0

perturbm=0.0

# 9. SOLVER RELATED MATTERS

Problem=convection

aug_lagr=on

aug_number=1.0e3

precond=on

orthogonal=off

maxsub=1

viterations=2

mg_cycle=1

down_heavy=3

up_heavy=3

vlowstep=20

vhighstep=3

piterations=375

accuracy=1.0e-2

tole_compressibility=1e-7

# Tuning of energy equation

adv_sub_iterations=2

finetunedt=0.75

ll_max=20

nlong=180

nlati=90

# Data input and program debugging

DESCRIBE=off

BEGINNER=off

VERBOSE=off

verbose=off

COMPRESS=off

see_convergence=1

# vim:ts=8:sw=8

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Yang, J., Yang, W., Qi, R. et al. Parallel algorithm design and optimization of geodynamic numerical simulation application on the Tianhe new-generation high-performance computer. J Supercomput 80, 331–362 (2024). https://doi.org/10.1007/s11227-023-05469-9

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