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