Skip to main content

Theory and Modern Applications

Table 7 The number of multigrid V-cycles and CPU time with two schemes and different relaxation methods with \(\pmb{32^{2}}\) for Example 2

From: Multigrid method based on transformation-free high-order scheme for solving 2D Helmholtz equation on nonuniform grids

Scheme

Grids

Line GS

Red-black GS

Natural GS

Iterations

CPU

Iterations

CPU

Iterations

CPU

CDS

\( 8^{2} \)

9

0.060

11

0.140

11

0.800

\(16^{2} \)

11

0.062

12

0.840

11

1.392

\(32^{2}\)

11

0.284

12

1.220

12

2.268

\(64^{2}\)

12

2.652

13

2.842

13

3.230

\(128^{2}\)

13

2.920

15

3.296

15

3.838

HOC

\( 8^{2} \)

8

0.070

8

0.532

12

0.720

\(16^{2} \)

8

0.073

8

0.660

12

0.960

\(32^{2}\)

9

0.210

9

0.977

12

1.862

\(64^{2} \)

9

2.510

10

1.322

13

2.890

\(128^{2} \)

11

2.872

12

2.260

18

3.713