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multigrid_poisson_1d_prb_output.txt
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26 July 2014 11:32:59 AM
MULTIGRID_POISSON_1D:
C++ version
Test the MULTIGRID_POISSON_1D library.
TEST01_MONO
MONOGRID_POISSON_1D solves a 1D Poisson BVP
using the Gauss-Seidel method.
-u''(x) = 1, for 0 < x < 1
u(0) = u(1) = 0.
Solution is u(x) = ( -x^2 + x ) / 2
Mesh index K = 5
Number of intervals N=2^K = 32
Number of nodes = 2^K+1 = 33
I X(I) U(I) U Exact(X(I))
0 0 0 0
1 0.03125 0.0150838 0.0151367
2 0.0625 0.029192 0.0292969
3 0.09375 0.0423251 0.0424805
4 0.125 0.0544837 0.0546875
5 0.15625 0.0656682 0.065918
6 0.1875 0.0758789 0.0761719
7 0.21875 0.0851163 0.0854492
8 0.25 0.0933807 0.09375
9 0.28125 0.100672 0.101074
10 0.3125 0.106992 0.107422
11 0.34375 0.112339 0.112793
12 0.375 0.116714 0.117188
13 0.40625 0.120118 0.120605
14 0.4375 0.122549 0.123047
15 0.46875 0.124009 0.124512
16 0.5 0.124497 0.125
17 0.53125 0.124014 0.124512
18 0.5625 0.122559 0.123047
19 0.59375 0.120131 0.120605
20 0.625 0.116732 0.117188
21 0.65625 0.11236 0.112793
22 0.6875 0.107016 0.107422
23 0.71875 0.100699 0.101074
24 0.75 0.0934081 0.09375
25 0.78125 0.085144 0.0854492
26 0.8125 0.0759058 0.0761719
27 0.84375 0.0656933 0.065918
28 0.875 0.054506 0.0546875
29 0.90625 0.0423435 0.0424805
30 0.9375 0.0292052 0.0292969
31 0.96875 0.0150909 0.0151367
32 1 0 0
Maximum error = 0.000502527
Number of iterations = 575
TEST01_MULTI
MULTIGRID_POISSON_1D solves a 1D Poisson BVP
using the multigrid method.
-u''(x) = 1, for 0 < x < 1
u(0) = u(1) = 0.
Solution is u(x) = ( -x^2 + x ) / 2
Mesh index K = 5
Number of intervals N=2^K = 32
Number of nodes = 2^K+1 = 33
I X(I) U(I) U Exact(X(I))
0 0 0 0
1 0.03125 0.0151174 0.0151367
2 0.0625 0.0292622 0.0292969
3 0.09375 0.0424323 0.0424805
4 0.125 0.0546305 0.0546875
5 0.15625 0.0658541 0.065918
6 0.1875 0.0761055 0.0761719
7 0.21875 0.0853817 0.0854492
8 0.25 0.093685 0.09375
9 0.28125 0.101013 0.101074
10 0.3125 0.107367 0.107422
11 0.34375 0.112744 0.112793
12 0.375 0.117148 0.117188
13 0.40625 0.120575 0.120605
14 0.4375 0.123028 0.123047
15 0.46875 0.124503 0.124512
16 0.5 0.125003 0.125
17 0.53125 0.124526 0.124512
18 0.5625 0.123072 0.123047
19 0.59375 0.120639 0.120605
20 0.625 0.11723 0.117188
21 0.65625 0.112841 0.112793
22 0.6875 0.107474 0.107422
23 0.71875 0.10113 0.101074
24 0.75 0.0938081 0.09375
25 0.78125 0.0855096 0.0854492
26 0.8125 0.0762335 0.0761719
27 0.84375 0.065978 0.065918
28 0.875 0.0547417 0.0546875
29 0.90625 0.0425244 0.0424805
30 0.9375 0.0293273 0.0292969
31 0.96875 0.0151519 0.0151367
32 1 0 0
Maximum error = 6.75166e-05
Number of iterations = 43
TEST02_MONO
MONOGRID_POISSON_1D solves a 1D Poisson BVP
using the Gauss-Seidel method.
-u''(x) = - x * (x+3) * exp(x), for 0 < x < 1
u(0) = u(1) = 0.
Solution is u(x) = x * (x-1) * exp(x)
Mesh index K = 5
Number of intervals N=2^K = 32
Number of nodes = 2^K+1 = 33
I X(I) U(I) U Exact(X(I))
0 0 0 -0
1 0.03125 -0.0311615 -0.0312344
2 0.0625 -0.0622285 -0.0623727
3 0.09375 -0.0930982 -0.0933113
4 0.125 -0.123659 -0.123938
5 0.15625 -0.153789 -0.154132
6 0.1875 -0.18336 -0.183762
7 0.21875 -0.21223 -0.212687
8 0.25 -0.240247 -0.240755
9 0.28125 -0.26725 -0.267803
10 0.3125 -0.293063 -0.293657
11 0.34375 -0.317498 -0.318127
12 0.375 -0.340356 -0.341014
13 0.40625 -0.36142 -0.362101
14 0.4375 -0.38046 -0.381157
15 0.46875 -0.39723 -0.397938
16 0.5 -0.411467 -0.41218
17 0.53125 -0.422892 -0.423603
18 0.5625 -0.431206 -0.431908
19 0.59375 -0.436089 -0.436777
20 0.625 -0.437204 -0.43787
21 0.65625 -0.434189 -0.434828
22 0.6875 -0.426662 -0.427268
23 0.71875 -0.414214 -0.414782
24 0.75 -0.396415 -0.396938
25 0.78125 -0.372803 -0.373277
26 0.8125 -0.342894 -0.343312
27 0.84375 -0.306169 -0.306528
28 0.875 -0.262082 -0.262377
29 0.90625 -0.210054 -0.21028
30 0.9375 -0.14947 -0.149624
31 0.96875 -0.079681 -0.0797599
32 1 0 0
Maximum error = 0.000712828
Number of iterations = 702
TEST02_MULTI
MULTIGRID_POISSON_1D solves a 1D Poisson BVP
using the multigrid method.
-u''(x) = - x * (x+3) * exp(x), for 0 < x < 1
u(0) = u(1) = 0.
Solution is u(x) = x * (x-1) * exp(x)
Mesh index K = 5
Number of intervals N=2^K = 32
Number of nodes = 2^K+1 = 33
I X(I) U(I) U Exact(X(I))
0 0 0 -0
1 0.03125 -0.0312133 -0.0312344
2 0.0625 -0.062331 -0.0623727
3 0.09375 -0.0932499 -0.0933113
4 0.125 -0.123857 -0.123938
5 0.15625 -0.154033 -0.154132
6 0.1875 -0.183644 -0.183762
7 0.21875 -0.212552 -0.212687
8 0.25 -0.240603 -0.240755
9 0.28125 -0.267636 -0.267803
10 0.3125 -0.293473 -0.293657
11 0.34375 -0.317929 -0.318127
12 0.375 -0.340801 -0.341014
13 0.40625 -0.361875 -0.362101
14 0.4375 -0.38092 -0.381157
15 0.46875 -0.39769 -0.397938
16 0.5 -0.411922 -0.41218
17 0.53125 -0.423336 -0.423603
18 0.5625 -0.431634 -0.431908
19 0.59375 -0.436497 -0.436777
20 0.625 -0.437589 -0.43787
21 0.65625 -0.434551 -0.434828
22 0.6875 -0.427004 -0.427268
23 0.71875 -0.414543 -0.414782
24 0.75 -0.396734 -0.396938
25 0.78125 -0.373114 -0.373277
26 0.8125 -0.34319 -0.343312
27 0.84375 -0.306441 -0.306528
28 0.875 -0.262317 -0.262377
29 0.90625 -0.210239 -0.21028
30 0.9375 -0.149596 -0.149624
31 0.96875 -0.0797441 -0.0797599
32 1 0 0
Maximum error = 0.000281309
Number of iterations = 73
MULTIGRID_POISSON_1D:
Normal end of execution.
26 July 2014 11:32:59 AM