28 October 2011 09:09:56 AM
POISSON_SERIAL:
C++ version
A program for solving the Poisson equation.
-DEL^2 U = F(X,Y)
on the rectangle 0 <= X <= 1, 0 <= Y <= 1.
F(X,Y) = pi^2 * ( x^2 + y^2 ) * sin ( pi * x * y )
The number of interior X grid points is 11
The number of interior Y grid points is 11
The X grid spacing is 0.1
The Y grid spacing is 0.1
RMS of F = 4.81514
RMS of exact solution = 0.600498
Step ||Unew|| ||Unew-U|| ||Unew-Exact||
0 0.28748 0.527212
1 0.298714 0.081152 0.479377
2 0.313895 0.0482049 0.444443
3 0.328591 0.0367994 0.415173
4 0.342452 0.0305623 0.389501
5 0.355491 0.0264622 0.366455
6 0.367769 0.023478 0.345474
7 0.379349 0.0211625 0.326193
8 0.390285 0.0192859 0.308357
9 0.400628 0.0177173 0.291774
10 0.410419 0.0163753 0.276297
11 0.419697 0.0152067 0.261808
12 0.428494 0.0141749 0.248209
13 0.436842 0.0132537 0.235421
14 0.444767 0.0124237 0.223376
15 0.452295 0.0116703 0.212012
16 0.459448 0.010982 0.201281
17 0.466248 0.0103498 0.191135
18 0.472715 0.00976654 0.181535
19 0.478865 0.00922625 0.172446
20 0.484717 0.00872406 0.163833
21 0.490286 0.00825588 0.155668
22 0.495586 0.00781826 0.147925
23 0.500632 0.00740828 0.140578
24 0.505435 0.00702342 0.133604
25 0.510009 0.00666152 0.126984
26 0.514365 0.00632069 0.120697
27 0.518513 0.00599928 0.114725
28 0.522464 0.00569583 0.109052
29 0.526227 0.00540904 0.103661
30 0.529811 0.00513778 0.0985389
31 0.533225 0.004881 0.0936705
32 0.536476 0.00463777 0.0890431
33 0.539574 0.00440725 0.0846444
34 0.542524 0.00418867 0.0804627
35 0.545335 0.00398131 0.0764873
36 0.548012 0.00378455 0.0727076
37 0.550561 0.00359776 0.0691138
38 0.55299 0.00342041 0.0656968
39 0.555303 0.00325197 0.0624476
40 0.557507 0.00309196 0.059358
41 0.559605 0.00293995 0.05642
42 0.561604 0.0027955 0.0536262
43 0.563507 0.00265822 0.0509694
44 0.565319 0.00252775 0.0484429
45 0.567045 0.00240373 0.0460402
46 0.568689 0.00228584 0.0437552
47 0.570254 0.00217376 0.0415822
48 0.571744 0.00206721 0.0395157
49 0.573163 0.0019659 0.0375504
50 0.574514 0.00186957 0.0356813
51 0.575801 0.00177798 0.0339038
52 0.577025 0.00169089 0.0322134
53 0.578191 0.00160807 0.0306057
54 0.579301 0.00152932 0.0290767
55 0.580358 0.00145443 0.0276226
56 0.581364 0.00138322 0.0262397
57 0.582321 0.00131549 0.0249245
58 0.583232 0.00125108 0.0236737
59 0.5841 0.00118984 0.0224841
60 0.584925 0.00113159 0.0213527
61 0.585711 0.00107619 0.0202768
62 0.586459 0.00102351 0.0192535
63 0.587171 0.000973408 0.0182803
64 0.587848 0.00092576 0.0173548
65 0.588493 0.000880445 0.0164746
66 0.589106 0.000837349 0.0156375
67 0.58969 0.000796363 0.0148414
68 0.590246 0.000757384 0.0140842
69 0.590775 0.000720313 0.0133641
70 0.591278 0.000685056 0.0126793
71 0.591756 0.000651526 0.0120281
72 0.592212 0.000619637 0.0114087
73 0.592645 0.000589308 0.0108197
74 0.593057 0.000560465 0.0102595
75 0.59345 0.000533033 0.00972673
76 0.593823 0.000506944 0.00922009
77 0.594178 0.000482132 0.00873828
78 0.594516 0.000458535 0.00828008
79 0.594837 0.000436092 0.00784434
80 0.595143 0.000414748 0.00742996
81 0.595434 0.000394448 0.0070359
82 0.595711 0.000375143 0.00666117
83 0.595974 0.000356782 0.00630482
84 0.596225 0.00033932 0.00596596
85 0.596463 0.000322712 0.00564373
86 0.59669 0.000306917 0.00533732
87 0.596906 0.000291896 0.00504597
88 0.597111 0.000277609 0.00476893
89 0.597306 0.000264022 0.00450552
90 0.597492 0.0002511 0.00425507
91 0.597668 0.00023881 0.00401695
92 0.597836 0.000227122 0.00379057
93 0.597996 0.000216006 0.00357535
94 0.598148 0.000205434 0.00337075
95 0.598293 0.000195379 0.00317627
96 0.59843 0.000185816 0.00299142
97 0.598561 0.000176722 0.00281573
98 0.598686 0.000168073 0.00264876
99 0.598804 0.000159846 0.00249011
100 0.598916 0.000152023 0.00233936
101 0.599024 0.000144582 0.00219616
102 0.599125 0.000137506 0.00206015
103 0.599222 0.000130776 0.00193099
104 0.599315 0.000124375 0.00180836
105 0.599402 0.000118288 0.00169198
106 0.599486 0.000112499 0.00158155
107 0.599565 0.000106993 0.00147681
108 0.59964 0.000101756 0.00137753
109 0.599712 9.67757e-05 0.00128346
110 0.59978 9.20391e-05 0.00119439
111 0.599845 8.75344e-05 0.00111014
112 0.599907 8.32502e-05 0.00103051
113 0.599966 7.91756e-05 0.000955361
114 0.600022 7.53005e-05 0.000884536
115 0.600075 7.1615e-05 0.000817919
116 0.600125 6.81099e-05 0.000755412
117 0.600173 6.47764e-05 0.000696939
118 0.600219 6.1606e-05 0.00064245
119 0.600262 5.85908e-05 0.000591924
120 0.600304 5.57232e-05 0.000545369
121 0.600343 5.29959e-05 0.000502827
122 0.60038 5.04021e-05 0.000464366
123 0.600416 4.79352e-05 0.000430082
124 0.60045 4.55891e-05 0.000400088
125 0.600482 4.33578e-05 0.000374492
126 0.600513 4.12357e-05 0.00035338
127 0.600542 3.92175e-05 0.000336776
128 0.600569 3.72981e-05 0.000324611
129 0.600596 3.54726e-05 0.000316706
130 0.600621 3.37364e-05 0.000312754
131 0.600645 3.20852e-05 0.000312349
132 0.600667 3.05149e-05 0.000315009
133 0.600689 2.90214e-05 0.000320228
134 0.600709 2.7601e-05 0.000327508
135 0.600729 2.62501e-05 0.000336392
136 0.600747 2.49653e-05 0.000346479
137 0.600765 2.37434e-05 0.000357429
138 0.600782 2.25813e-05 0.00036896
139 0.600798 2.14761e-05 0.000380847
140 0.600813 2.0425e-05 0.000392908
141 0.600827 1.94253e-05 0.000405001
142 0.600841 1.84746e-05 0.000417017
143 0.600854 1.75704e-05 0.000428871
144 0.600866 1.67104e-05 0.0004405
145 0.600878 1.58926e-05 0.000451855
146 0.600889 1.51147e-05 0.000462902
147 0.6009 1.4375e-05 0.000473617
148 0.60091 1.36714e-05 0.000483983
149 0.60092 1.30023e-05 0.000493992
150 0.600929 1.23659e-05 0.000503637
151 0.600938 1.17607e-05 0.000512919
152 0.600946 1.11851e-05 0.000521839
153 0.600954 1.06376e-05 0.000530402
154 0.600962 1.0117e-05 0.000538615
155 0.600969 9.62182e-06 0.000546485
156 0.600975 9.15089e-06 0.000554021
157 0.600982 8.70302e-06 0.000561233
158 0.600988 8.27706e-06 0.000568131
159 0.600994 7.87195e-06 0.000574724
160 0.600999 7.48667e-06 0.000581025
161 0.601005 7.12025e-06 0.000587043
162 0.60101 6.77176e-06 0.000592789
163 0.601015 6.44033e-06 0.000598274
164 0.601019 6.12511e-06 0.000603508
165 0.601023 5.82533e-06 0.000608501
166 0.601028 5.54022e-06 0.000613264
167 0.601031 5.26906e-06 0.000617805
168 0.601035 5.01117e-06 0.000622135
169 0.601039 4.76591e-06 0.000626262
170 0.601042 4.53265e-06 0.000630196
171 0.601045 4.31081e-06 0.000633945
172 0.601048 4.09982e-06 0.000637516
173 0.601051 3.89916e-06 0.000640919
174 0.601054 3.70832e-06 0.00064416
175 0.601057 3.52682e-06 0.000647248
176 0.601059 3.35421e-06 0.000650188
177 0.601061 3.19004e-06 0.000652988
178 0.601064 3.03391e-06 0.000655655
179 0.601066 2.88542e-06 0.000658194
180 0.601068 2.7442e-06 0.000660611
181 0.60107 2.60989e-06 0.000662912
182 0.601072 2.48215e-06 0.000665103
183 0.601073 2.36066e-06 0.000667189
184 0.601075 2.24513e-06 0.000669174
185 0.601077 2.13524e-06 0.000671063
186 0.601078 2.03074e-06 0.000672862
187 0.60108 1.93134e-06 0.000674573
188 0.601081 1.83682e-06 0.000676202
189 0.601082 1.74692e-06 0.000677752
190 0.601084 1.66142e-06 0.000679228
191 0.601085 1.5801e-06 0.000680631
192 0.601086 1.50277e-06 0.000681967
193 0.601087 1.42921e-06 0.000683238
194 0.601088 1.35926e-06 0.000684448
195 0.601089 1.29274e-06 0.000685598
196 0.60109 1.22947e-06 0.000686693
197 0.601091 1.16929e-06 0.000687735
198 0.601091 1.11206e-06 0.000688726
199 0.601092 1.05763e-06 0.000689669
200 0.601093 1.00587e-06 0.000690566
201 0.601094 9.56639e-07 0.00069142
The iteration has converged.
POISSON_SERIAL:
Normal end of execution.
28 October 2011 09:09:56 AM