迭代求解矩阵测试

最新推荐文章于 2023-12-29 01:48:39 发布

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本文通过测试发现CUDA实现的矩阵求解速度比CPU快417倍。针对Poisson问题，使用不同的预条件器进行迭代求解，如CG、GMRES和bicgstab。结果显示，bicgstab无法收敛，而采用AINV预条件器的求解效果较好，尤其是在调整参数后，能在较短时间内达到收敛。预条件器的效率对解决大型矩阵问题至关重要。

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code of cuda is 417 times faster than code of cpu

poisson5point(no preconditioner)

1000＊1000 cg: 1021 收敛

gmres(50) 261

gmres(100) 217

cg_m 1269 时间都差不多

bicgstab 无穷大，不收敛

smooth_aggregate: 2.9second

Preconditioner statistics
Number of Levels:5
Operator Complexity:1.32831745
Grid Complexity:1.148772
level unknownsnonzeros:
0 10000004996000[75.2832086%]
1 1401101512942[22.7980641%]
2 8289121945[1.83755222%]
3 3565218[0.0786284593%]
4 17169[0.00254660974%]

AINV

Successfully converged after 1269 iterations.
Solver converged to 1.000000e+00 tolerance after 1269 iterations (9.738784e-01 final residual)
In [no preconditer]:6.296808004e+00 seconds

Solving with scaled bridson preconditioner (drop tolerance .1)
Solver converged to 1.000000000e+00 tolerance after 656 iterations (9.973784685e-01 final residual)
In [ainv preconditer(drop .1)]:2.055588698e+01 seconds

Solving with scaled bridson preconditioner (10 nonzeroes per row)
Solver converged to 1.000000000e+00 tolerance after 370 iterations (9.866030216e-01 final residual)
In [ainv preconditer static]:5.647993302e+01 seconds

Solving with AINV preconditioner (Lin strategy, p=2)
Solver converged to 1.000000000e+00 tolerance after 603 iterations (9.798558950e-01 final residual)
In [ainv preconditer static]:4.361557293e+01 seconds

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