Thermo-elasticTopologyOptimization/ref/amgcl_time_test.md

0. 待测线性系统：规模为50w*50w，非零项nnz为1.7e7。来源：lattice晶格压缩工况的IPC仿真。

1. AMGCL：CPU backend (花费主要在solve上)

solver	Relaxation	Coarsening	Time cost (s)
CG	gauss_seidel	ruge_stuben	51.55
CG	gauss_seidel	aggregation	31.56
CG	gauss_seidel	smoothed_aggregation (eps_strong=0.0, block_size = 3)	38.48
CG	gauss_seidel	smoothed_aggr_emin (eps_strong=0.0, block_size = 3)	42.70
CG	spai0	aggregation	51.30
LGMRES	gauss_seidel	ruge_stuben	25.54
LGMRES	gauss_seidel	aggregation	17.86
LGMRES	gauss_seidel	smoothed_aggregation (eps_strong=0.0, block_size = 3)	30.30
LGMRES	gauss_seidel	smoothed_aggr_emin (eps_strong=0.0, block_size = 3)	34.64
LGMRES	spai0	aggregation	38.44

2. AMGCL：CUDA Backend (GPU: GeForce GTX 1080 Ti，花费主要在setup上)

solver	Relaxation	Coarsening	Time cost (s)
CG	spai0	ruge_stuben	7.35
CG	spai0	aggregation	4.30
CG	spai0	smoothed_aggregation (eps_strong=0.0, block_size = 3)	9.98
CG	spai0	smoothed_aggr_emin (eps_strong=0.0, block_size = 3)	14.78
BiCGStabL(L=2)	spai0	ruge_stuben	7.85
BiCGStabL(L=2)	spai0	aggregation	3.88
BiCGStabL(L=2)	spai0	smoothed_aggregation (eps_strong=0.0, block_size = 3)	10.10
BiCGStabL(L=2)	spai0	smoothed_aggr_emin (eps_strong=0.0, block_size = 3)	15.07
LGMRES	spai0	ruge_stuben	7.55
LGMRES	spai0	aggregation	4.22
LGMRES	spai0	smoothed_aggregation (eps_strong=0.0, block_size = 3)	10.06
LGMRES	spai0	smoothed_aggr_emin (eps_strong=0.0, block_size = 3)	14.44

3. 该系统分别用CHOLMOD和cuSolver求解所需要的时间

CHOLMOD	9.05s
cuSolver (GPU: GeForce GTX 1080 Ti, solver=chol, reorder=metis)	17.11s

4. 关于AMGCL中backend，solver，Preconditioner，relaxation，coarsening选取的总结（仅针对该线性系统，不适合所有情况）

backend：

• CUDA比CPU (builtin)快5-12倍左右

solver：

• CPU上，较快：FGMRES > LGMRES > CG；BiCGStab没测；IDR(s)和Richardson较慢
• CUDA上，CG, BiCGStab, LGMRES, FGMRES性能接近，较快；IDR(s)和Richardson较慢

Preconditioners：

• AMG较快，其他没测试，Composite preconditioner针对the solution of saddle point或者Stokes-like systems

Relaxation：

• CPU上，较快：Gauss-Seidel和SPAI0，较慢：Damped Jacobi, Chebyshev, ILU, SPAI1
• CUDA上，较快：SPAI0，较慢：Damped Jacobi, Chebyshev, ILU, SPAI1，不能使用：Gauss-Seidel

Coarsening：

• CPU和CUDA的结论一致，aggregation > ruge_stuben > smoothed aggregation > smoothed_aggr_emin