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