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Preconditioned NS Computation with FV Method on Colocated Grid. Daniel Lee 東海大學數學系 Dec. 21, 2002. Outline. Model Equation Test Cases The Discrete Geometry The Discrete Algebraic System Solution Procedure Numerical Results and Discussion. Model Equation. - PowerPoint PPT Presentation
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1
Preconditioned NS Computation with FV Method on Colo
cated GridDaniel Lee
東海大學數學系Dec. 21, 2002
2
Outline
Model Equation Test Cases The Discrete Geometry The Discrete Algebraic System Solution Procedure Numerical Results and Discussion
3
Model Equation
x-momentum equation y-momentum equation z-momentum equation continuity equation pressure-poisson equation ( PPE )
5
Test Cases
2D one-side-driven cavity flow two-side-driven cavity flow exact-solution cavity flow3D one-face-driven cavity flow air ventilation
7
Discretization of Geometry
boundary-fitted FV discretization cell-centered FV scheme ghost-cell boundary treatment colocated variables approach
9
Discretization of the PDE central finite differencing for PPE hybrid of UFD and CFD for momentum
eqs with appropriate B.C. treatment, resp
ectively
10
Preconditioned Linear System left-preconditioning with right-preconditioning with Split-preconditioning assume consider ie
bMAxM 11 IAM 1
buAM 1
buM 1
IAM 1
MLUA :bLUxAUL 111 )( bLuAUL 111
Uxu
11
基本測試
12
Possion 方程: ,運用 CG 迭代方法
preconditioner
nx, ny iter res r_res max err cpu ratio
None-CG 160 548 8.11e-05 9.30e-11 1.21e-09 9.907 1.000
Jacobi-CG 160 548 8.11e-05 9.30e-11 1.21e-09 9.178 0.926
SGS-CG 160 195 7.12e-05 8.16e-11 1.12e-09 5.914 0.596
SSOR-CG 160 58 6.57e-05 7.54e-11 5.61e-10 1.831 0.184
ILU(0)-CG 160 164 7.50e-05 8.60e-11 1.05e-09 4.564 0.460
MILU(0)-CG
160 57 6.17e-05 7.08e-11 1.64e-10 1.640 0.165
33 yxU
13
Possion 方程:,運用 CG 迭代方法
preconditioner
nx, ny iter res r_res max err cpu ratio
None-CG
160 546 2.28e-04 9.51e-11 1.43e-06 9.028 1.000
Jacobi-CG
160 546 2.28e-04 9.51e-11 1.43e-06 9.216 1.020
SGS-CG
160 194 2.19e-04 9.14e-11 1.42e-06 5.892 0.652
SSOR-CG
160 58 1.72e-04 7.19e-11 1.43e-06 1.837 0.203
ILU(0)-CG
160 163 2.36e-04 9.86e-11 1.42e-06 4.468 0.494
MILU(0)-CG
160 18 2.07e-04 8.64e-11 1.43e-06 0.571 0.062
yxeU
14
Possion 方程:,運用 BiCG 迭代方法
preconditioner
nx, ny iter res r_res max err cpu ratio
None-BiCG
160 548 8.11e-05 9.30e-11 1.21e-09 16.661 1.000
Jacobi-BiCG
160 548 8.11e-05 9.30e-11 1.21e-09 18.076 1.082
SGS-BiCG 160 195 7.12e-05 8.16e-11 1.12e-09 10.725 0643
SSOR-BiCG
160 58 6.57e-05 7.54e-11 5.61e-10 3.050 0.183
ILU(0)- BiCG
160 164 7.50e-05 8.60e-11 1.05e-09 7.713 0.462
MILU(0)- BiCG
160 57 8.12e-05 9.31e-11 8.41e-10 2.767 0.166
33 yxU
15
Possion 方程:,運用 BiCG 迭代方法 precondit
ionernx, ny iter iter r_res r_res r_res r_res
None-BiCG
160 Res Res max err max err max err max err
Jacobi-BiCG
160 546 546 cpu cpu cpu cpu
SGS-BiCG 160 2.28e-04 2.28e-04 ratio ratio ratio ratio
SSOR-BiCG
160 546 546 9.51e-11 9.51e-11 9.51e-11 9.51e-11
ILU(0)- BiCG
160 2.28e-04 2.28e-04 1.43e-06 1.43e-06 1.43e-06 1.43e-06
MILU(0)- BiCG
160 194 194 17.096 17.096 17.096 17.096
yxeU
16
Possion 方程:,運用 CGS 迭代方法 precondition
ernx, ny iter res r_res max err cpu ratio
None-CGS 160 428 8.58e-05 9.84e-11 1.52e-11 13.109 1.000
Jacobi-CGS 160 428 8.58e-05 9.84e-11 1.52e-11 13.847 1.051
SGS-CGS 160 130 7.88e-05 9.04e-11 9.88e-09 6.993 0.533
SSOR-CGS 160 36 8.70e-05 9.98e-11 7.66e-09 1.959 0.149
ILU(0)- CGS 160 121 7.65e-05 8.78e-11 7.82e-11 5.866 0.447
MILU(0)- CGS
160 77 3.65e-05 4.19e-11 7.92e-11 3.859 0.294
33 yxU
17
Possion 方程:,運用 CGS 迭代方法
preconditioner
nx, ny iter Res r_res max err
cpu ratio
None-CGS
160 428 2.31e-04
9.63e-11
1.43e-06
13.090 1.000
Jacobi-CGS
160 428 2.31e-04
9.63e-11
1.43e-06
14.182 1.083
SGS-CGS
160 130 1.91e-04
7.99e-11
1.43e-06
6.902 0.521
SSOR-CGS
160 38 4.18e-04
1.75e-11
1.42e-06
2.168 0.165
ILU(0)- CGS
160 121 1.78e-04
7.43e-11
1.42e-06
5.799 0.442
MILU(0)- CGS
160 23 1.34e-04
5.61e-11
1.43e-06
1.203 0.091
yxeU
18
Possion 方程:,運用 BiCGs 迭代方法
preconditioner
nx, ny iter res r_res max err cpu ratio
None-BiCGs
160 389 7.98e-05 9.15e-11 1.47e-08 12.826 1.000
Jacobi-BiCGs
160 382 8.65e-05 9.92e-11 3.23e-08 12.630 0.984
GS-BiCGs 160 488 5.31e-05 6.09e-11 4.77e-09 20.532 1.600
SGS-BiCGs 160 141 7.99e-05 9.17e-11 2.37e-08 7.458 0.581
SOR-BiCGs 160 294 8.14e-05 9.33e-11 1.33e-08 12.532 0.980
SSOR-BiCGs
160 35 1.73e-05 1.98e-11 2.06e-09 1.900 0.148
ILU(0)- BiCGs
160 119 8.48e-05 9.73e-11 2.15e-08 5.834 0.454
MILU(0)- BiCGs
160 37 6.48e-05 7.43e-11 4.75e-10 1.861 0.145
33 yxU
19
Possion 方程:,運用 BiCGs 迭代方法
yxeU
preconditioner
nx, ny iter res r_res max err cpu ratio
None-BiCGs 160 381 2.07e-04 8.64e-11 1.42e-06 12.195 1.000
Jacobi-BiCGs 160 387 2.34e-04 9.75e-11 1.41e-06 13.047 1.069
GS-BiCGs 160 407 3.06e-05 1.28e-11 1.43e-06 17.238 1.413
SGS-BiCGs 160 136 1.98e-04 8.28e-11 1.38e-06 7.177 0.580
SOR-BiCGs 160 350 1.42e-04 5.91e-11 1.49e-06 14.737 1.208
SSOR-BiCGs 160 34 9.56e-05 3.99e-11 1.43e-06 1.833 0.150
ILU(0)- BiCGs 160 115 2.05e-04 8.57e-11 1.39e-06 5.667 0.464
MILU(0)- BiCGs
160 13 1.81e-04 7.55e-11 1.43e-06 0.688 0.055
20
Possion 方程: ,運用
GMRES(80) 迭代方法測試不同 restart 值的結果 33 yxU
preconditioner
nx, ny iter res r_res max err cpu
GMRES 80 275 1.36e-05 8.72e-11 1.42e-06 10.986
GMRES(10)
80 2426 1.56e-05 9.95e-11 1.41e-06 12.932
GMRES(20)
80 1313 1.56e-05 9.98e-11 1.43e-06 8.472
GMRES(30)
80 968 1.55e-05 9.90e-11 1.38e-06 7.418
GMRES(50)
80 698 1.56e-05 9.98e-11 1.49e-06 6.993
GMRES(80)
80 470 1.49e-05 9.56e-11 1.43e-06 6.412
GMRES(100)
80 444 1.51e-05 9.67e-11 1.39e-06 7.073
21
Possion 方程:,運用 GMRES(80) 迭代方法
33 yxU
preconditioner nx, ny iter res r_res max err cpu ratio
None-GMRES 80 470 1.49e-05 9.56e-11 8.36e-09 6.412 1.000
Jacobi-GMRES 80 470 5.84e-05 9.56e-11 8.36e-09 6.501 1.013
GS-GMRES 80 415 7.73e-05 9.53e-11 5.76e-09 6.077 0.947
SGS-GMRES 80 107 9.82e-05 8.57e-11 1.95e-09 1.557 0.242
SOR-GMRES 80 333 2.31e-04 9.97e-11 1.90e-09 4.877 0.760
SSOR-GMRES 80 41 7.98e-05 6.61e-11 6.88e-10 0.478 0.074
ILU(0)- GMRES 80 85 1.46e-04 9.41e-11 6.11e-10 1.309 0.204
MILU(0)- GMRES 80 38 6.33e-04 9.23e-11 4.96e-10 0.415 0.064
22
Possion 方程:,運用 GMRES(80) 迭代方法
yxeU
preconditioner
nx, ny iter res r_res max err cpu ratio
None-GMRES
80 580 4.26e-05 9.95e-11 5.73e-06 7.945 1.000
Jacobi-GMRES
80 580 1.66e-05 9.95e-11 5.73e-06 7.983 1.004
GS-GMRES 80 437 2.21e-05 9.89e-11 5.76e-06 6.320 0.795
SGS-GMRES 80 106 2.92e-05 9.20e-11 5.77e-06 1.531 0.192
SOR-GMRES 80 325 7.29e-05 9.99e-11 5.77e-06 4.867 0.612
SSOR-GMRES
80 40 4.60e-05 8.83e-11 5.77e-06 0.462 0.058
ILU(0)- GMRES
80 85 3.54e-05 8.29e-11 5.77e-06 1.367 0.172
MILU(0)- GMRES
80 17 2.47e-04 9.66e-11 5.78e-06 0.165 0.020
23
Possion 方程:,運用 QMR 迭代方法
33 yxU
preconditioner
nx, ny iter res r_res max err cpu ratio
None-QMR
160 532 8.40e-05 9.63e-11 5.30e-09 21.260 1.000
Jacobi-QMR
160 532 8.40e-05 9.63e-11 5.30e-09 22.076 1.038
SGS-QMR
160 189 8.41e-05 9.65e-11 5.07e-09 11.600 0.545
SSOR-QMR
160 57 6.38e-05 7.32e-11 1.35e-09 3.816 0.179
ILU(0)- QMR
160 159 8.69e-05 9.96e-11 5.05e-09 8.982 0.422
MILU(0)- QMR
160 59 3.79e-05 4.35e-11 1.10e-10 3.518 0.165
24
Possion 方程:,運用 QMR 迭代方法
yxeU
preconditioner
nx, ny iter Res r_res max err
cpu Ratio
None-QMR
160 529 2.36e-04
9.86e-11
1.41e-06
21.173 1.000
Jacobi-QMR
160 529 2.36e-04
9.86e-11
1.41e-06
21.673 1.023
SGS-QMR
160 188 2.37e-04
9.88e-11
1.41e-06
11.581 0.546
SSOR-QMR
160 57 1.63e-04
6.79e-11
1.43e-06
3.619 0.170
ILU(0)- QMR
160 159 2.08e-04
8.67e-11
1.41e-06
9.088 0.429
MILU(0)- QMR
160 19 1.75e-04
7.29e-11
1.43e-06
1.262 0.050
25
Possion 方程: ,運用 BiCGs
迭代方法搭配預優化算子 SOR 測試不同 w 的結果 yxeU
preconditioner nx, ny iter res r_res max err cpu ratio
SOR-BiCGs(w=1.0) 160 407 3.06e-05 1.28e-11 1.43e-06 17.434 1.000
SOR-BiCGs(w=1.1) 160 390 1.59e-04 6.64e-11 6.64e-06 16.192 0.928
SOR-BiCGs(w=1.2) 160 421 1.83e-04 7.62e-11 7.62e-06 17.428 0.999
SOR-BiCGs(w=1.3) 160 489 2.16e-04 9.03e-11 9.03e-06 20.788 1.192
SOR-BiCGs(w=1.4) 160 378 9.59e-05 4.00e-11 4.00e-06 15.785 0.905
SOR-BiCGs(w=1.5) 160 421 2.20e-04 9.20e-11 9.20e-06 17.557 1.007
SOR-BiCGs(w=1.6) 160 389 6.84e-05 2.86e-11 2.86e-06 16.376 0.939
SOR-BiCGs(w=1.7) 160 343 1.92e-04 8.02e-11 8.02e-06 14.387 0.825
SOR-BiCGs(w=1.8) 160 347 2.32e-04 9.66e-11 9.66e-06 14.548 0.834
SOR-BiCGs(w=1.9) 160 350 1.42e-04 5.91e-11 5.91e-06 14.699 0.843
26
Possion 方程: ,運用 BiCGs
迭代方法搭配預優化算子 SSOR 測試不同 w 的結果 yxeU
preconditioner nx, ny iter res r_res max err cpu ratio
SSOR-BiCGs(w=1.0)
160 136 1.98e-04 8.28e-11 1.38e-06 7.200 1.000
SSOR-BiCGs(w=1.1)
160 125 2.02e-04 8.41e-11 1.36e-06 6.652 0.923
SSOR-BiCGs(w=1.2)
160 113 2.28e-04 9.53e-11 1.35e-06 5.991 0.832
SSOR-BiCGs(w=1.3)
160 102 1.43e-04 5.98e-11 1.48e-06 5.362 0.744
SSOR-BiCGs(w=1.4)
160 92 1.82e-04 7.61e-11 1.32e-06 4.968 0.690
SSOR-BiCGs(w=1.5)
160 84 8.86e-05 3.70e-11 1.38e-06 4.439 0.616
SSOR-BiCGs(w=1.6)
160 66 2.03e-04 8.47e-11 1.37e-06 3.605 0.500
SSOR-BiCGs(w=1.7)
160 56 1.30e-04 5.43e-11 1.49e-06 2.983 0.414
SSOR-BiCGs(w=1.8)
160 48 1.86e-04 7.78e-11 1.43e-06 2.594 0.360
SSOR-BiCGs(w=1.9)
160 34 9.56e-05 3.99e-11 1.43e-06 1.833 0.254
27
Possion 方程: ,運用
GMRES(80) 迭代方法測試左預優化和右預優化 yxeU
preconditioner nx, ny iter res r_res max err cpu
Jacobi-GMRES(L) 160 1546 2.32e-04 9.91e-11 1.31e-06 169.143
Jacobi-GMRES(R) 160 1546 2.37e-04 9.91e-11 1.31e-06 170.852
SGS- GMRES(L) 160 311 4.03e-04 9.03e-11 1.42e-06 36.671
SGS- GMRES(R) 160 304 2.09e-04 8.72e-11 1.40e-06 35.380
SSOR- GMRES(L) 160 57 6.39e-04 8.37e-11 1.43e-06 5.500
SSOR- GMRES(R) 160 55 2.21e-04 9.21e-11 1.42e-06 5.200
ILU(0)- GMRES(L) 160 247 5.86e-04 9.76e-11 1.42e-06 28.311
ILU(0)- GMRES(R) 160 238 2.34e-04 9.77e-11 1.42e-06 28.054
MILU(0)- GMRES(L)
160 21 4.75e-04 9.30e-11 1.43e-06 1.284
MILU(0)- GMRES(R)
160 18 1.74e-04 7.24e-11 1.44e-06 1.093
28
Possion 方程: ,運用
QMR(80) 迭代方法測試左預優化和右預優化 yxeU
preconditioner nx, ny iter res r_res max err cpu
Jacobi-QMR(L) 160 529 2.36e-04 9.86e-11 1.41e-06 21.712
Jacobi-QMR(R) 160 529 2.36e-04 9.86e-11 1.41e-06 22.068
SGS- QMR(L) 160 188 2.37e-04 9.88e-11 1.41e-06 11.696
SGS- QMR(R) 160 188 2.38e-04 9.95e-11 1.41e-06 11.678
SSOR- QMR(L) 160 57 1.63e-04 6.79e-11 1.43e-06 3.676
SSOR- QMR(R) 160 57 1.73e-04 7.24e-11 1.43e-06 3.653
ILU(0)- QMR(L) 160 159 2.08e-04 8.67e-11 1.41e-06 9.041
ILU(0)- QMR(R) 160 159 2.08e-04 8.67e-11 1.41e-06 9.099
MILU(0)- QMR(L) 160 19 1.75e-04 7.29e-11 1.43e-06 1.148
MILU(0)- QMR(R) 160 19 1.81e-04 7.57e-11 1.43e-06 1.198
29
應用測試2D
30
單邊驅動穴流:運用 CG 迭代方法測試 , nx=ny=80 preconditioner
t_steps iter cpu_total
final_res
diff_u Diff_v Diff_p ratio
None-CG
52 12513 33.88 1.2e-05 4.4e-03 2.6e-03 3.3e-03 1.000
Jacobi-CG
52 12394 33.73 1.1e-05 4.4e-03 2.6e-03 3.3e-03 0.995
SGS- CG
52 4931 24.46 3.4e-06 4.4e-03 2.6e-03 3.3e-03 0.721
SSOR- CG
52 2984 14.52 3.3e-06 4.4e-03 2.6e-03 3.3e-03 0.428
ILU(0)- CG
52 4354 20.85 2.8e-06 4.4e-03 2.6e-03 3.3e-03 0.615
MILU(0)-CG
52 3073 15.25 1.0e-07 4.4e-03 2.6e-03 3.3e-03 0.450
31
單邊驅動穴流:運用 BiCG 迭代方法測試 ,nx=ny=80 preconditioner
t_steps iter cpu_total
final_res
diff_u Diff_v Diff_p ratio
None-BiCG
52 12513 67.80 1.2e-05 4.4e-03 2.6e-03 3.3e-03 1.000
Jacobi-BiCG
52 12394 67.40 1.1e-05 4.4e-03 2.6e-03 3.3e-03 0.994
SGS- BiCG
52 4931 44.88 3.4e-06 4.4e-03 2.6e-03 3.3e-03 0.661
SSOR- BiCG
52 2984 27.86 3.3e-06 4.4e-03 2.6e-03 3.3e-03 0.410
ILU(0)- BiCG
52 4354 37.88 2.8e-06 4.4e-03 2.6e-03 3.3e-03 0.558
MILU(0)-BiCG
52 3073 26.93 1.0e-07 4.4e-03 2.6e-03 3.3e-03 0.397
32
單邊驅動穴流:運用 CGS 迭代方法測試 , nx=ny=80 preconditioner
t_steps iter cpu_total
final_res
diff_u Diff_v Diff_p ratio
None-CGS
52 9305 48.22 4.8e-04 4.4e-03 2.6e-03 3.3e-03 1.000
Jacobi-CGS
52 9284 48.28 1.1e-04 4.4e-03 2.6e-03 3.3e-03 1.001
SGS- CGS
52 3440 29.48 6.5e-07 4.4e-03 2.6e-03 3.3e-03 0.611
SSOR- CGS
52 2305 19.62 1.9e-06 4.4e-03 2.6e-03 3.3e-03 0.406
ILU(0)- CGS
52 2973 25.81 2.3e-06 4.4e-03 2.6e-03 3.3e-03 0.535
MILU(0)-CGS
52 2377 20.88 1.3e-07 4.4e-03 2.6e-03 3.3e-03 0.433
33
單邊驅動穴流:運用 BiCGs 迭代方法測試 , nx=ny=80 preconditio
nert_steps iter cpu_total final_res diff_u Diff_v Diff_p ratio
None-BiCGs 52 8686 46.79 5.6e-06 4.4e-03 2.6e-03 3.3e-03 1.000
Jacobi-BiCGs
52 8548 46.42 4.3e-06 4.4e-03 2.6e-03 3.3e-03 0.992
GS- BiCGs 52 7210 54.36 3.6e-05 4.4e-03 2.6e-03 3.3e-03 1.161
SGS- BiCGs 52 3521 29.72 1.9e-05 4.4e-03 2.6e-03 3.3e-03 0.635
SOR- BiCGs 52 7022 52.14 4.3e-07 4.4e-03 2.6e-03 3.3e-03 1.111
SSOR- BiCGs
52 2497 21.39 3.5e-07 4.4e-03 2.6e-03 3.3e-03 0.457
ILU(0)- BiCGs
52 3074 27.82 3.6e-06 4.4e-03 2.6e-03 3.3e-03 0.594
MILU(0)-BiCGs
52 2120 19.46 1.1e-07 4.4e-03 2.6e-03 3.3e-03 0.415
34
單邊驅動穴流:運用 GMRES(80) 迭代方法測試 ,nx=ny=80
preconditioner
t_steps iter cpu_total final_res diff_u Diff_v Diff_p ratio
Jacobi-GMRES
52 23187 298.21 6.3e-07 4.4e-03 2.6e-03 3.3e-03 1.000
SGS- GMRES
52 5428 73.29 4.4e-07 4.4e-03 2.6e-03 3.3e-03 0.245
SSOR- GMRES
52 3207 42.45 4.7e-06 4.4e-03 2.6e-03 3.3e-03 0.142
ILU(0)- GMRES
52 4793 67.73 8.4e-07 4.4e-03 2.6e-03 3.3e-03 0.227
MILU(0)-GMRES
52 2391 27.58 1.1e-07 4.4e-03 2.6e-03 3.3e-03 0.092
35
單邊驅動穴流:運用 QMR 迭代方法測試 , nx=ny=80 preconditio
nerT_steps iter cpu_total final_res diff_u Diff_v Diff_p ratio
None-QMR 52 14030 95.37 1.3e-07 4.4e-03 2.6e-03 3.3e-03 1.000
Jacobi-QMR
52 13870 95.20 1.3e-07 4.4e-03 2.6e-03 3.3e-03 0.998
SGS- QMR 52 5107 53.35 1.2e-07 4.4e-03 2.6e-03 3.3e-03 0.559
SSOR- QMR
52 3245 34.64 1.1e-07 4.4e-03 2.6e-03 3.3e-03 0.363
ILU(0)- QMR
52 4751 48.50 1.2e-07 4.4e-03 2.6e-03 3.3e-03 0.508
MILU(0)-QMR
52 3403 35.03 1.0e-07 4.4e-03 2.6e-03 3.3e-03 0.367
36
單邊驅動穴流:運用 CG 迭代方法測試 , nx=ny=160 preconditio
nerT_steps iter cpu_total final_res diff_u Diff_v Diff_p ratio
none-CG 205 89946 1311.69 2.9e-05 1.1e-03 6.6e-04 8.3e-04 1.000
Jacobi-CG 205 89735 1354.58 2.8e-05 1.1e-03 6.6e-04 8.3e-04 1.032
SGS- CG 205 33976 864.04 8.0e-06 1.1e-03 6.6e-04 8.3e-04 0.658
SSOR- CG 205 16240 417.24 5.2e-06 1.1e-03 6.6e-04 8.3e-04 0.318
ILU(0)- CG 205 29054 659.31 6.3e-06 1.1e-03 6.6e-04 8.3e-04 0.502
MILU(0)-CG
205 20511 480.99 4.2e-08 1.1e-03 6.6e-04 8.3e-04 0.365
37
單邊驅動穴流:運用 BiCGs 迭代方法測試 , nx=ny=160 precondit
ionerT_steps iter cpu_total final_res diff_u Diff_v Diff_p ratio
none-BiCGs
205 49880 1354.25 1.7e-04 1.1e-03 6.6e-04 8.3e-04 1.000
Jacobi-BiCGs
205 49760 1384.64 2.8e-04 1.1e-03 6.6e-04 8.3e-04 1.009
SGS- BiCGs
205 24046 1129.74 6.6e-06 1.1e-03 6.6e-04 8.3e-04 0.565
SSOR- BiCGs
205 10857 503.66 2.8e-06 1.1e-03 6.6e-04 8.3e-04 0.277
ILU(0)- BiCGs
205 20640 864.64 2.1e-05 1.1e-03 6.6e-04 8.3e-04 0.446
MILU(0)-BiCGs
205 13635 580.72 2.5e-08 1.1e-03 6.6e-04 8.3e-04 0.311
38
單邊驅動穴流:運用 QMR 迭代方法測試 , nx=ny=160 preconditio
nerT_steps iter cpu_total final_res diff_u Diff_v Diff_p ratio
none-QMR 205 109019 3778.75 4.2e-08 1.1e-03 6.6e-04 8.3e-04 1.000
Jacobi-QMR
205 108363 3814.11 4.3e-08 1.1e-03 6.6e-04 8.3e-04 1.022
SGS- QMR 205 38589 2136.44 4.0e-08 1.1e-03 6.6e-04 8.3e-04 0.834
SSOR- QMR
205 18865 1047.75 4.2e-08 1.1e-03 6.6e-04 8.3e-04 0.371
ILU(0)- QMR
205 32659 1685.48 4.2e-08 1.1e-03 6.6e-04 8.3e-04 0.638
MILU(0)-QMR
205 22603 1177.33 4.3e-08 1.1e-03 6.6e-04 8.3e-04 0.428
43
應用測試3D