>> ffs_sparse ( 'nodes6.txt', 'triangles6.txt' ) 26-Sep-2006 12:23:32 FFS_SPARSE (MATLAB version): A version of FREE_FEM_SPARSE using MATLAB's sparse matrix storage, factor and solve facilities. Finite element solution of the steady incompressible Stokes equations on a triangulated region in 2 dimensions. - nu * ( Uxx + Uyy ) + dPdx = F1(x,y) - nu * ( Vxx + Vyy ) + dPdy = F2(x,y) Ux + Vy = F3(x,y). Boundary conditions: U(x,y) = U_BC(x,y) V(x,y) = V_BC(x,y) P(x,y) = P_BC(x,y) The finite element method uses Taylor-Hood triangular elements which are linear for pressure and quadratic for velocity. Fluid viscosity NU = 1.000000: Node file is "nodes6.txt". Element file is "triangles6.txt". Number of nodes = 169 First 10 nodes Row: 1 2 Col 1 0.000000 0.000000 2 0.083300 0.000000 3 0.166700 0.000000 4 0.250000 0.000000 5 0.333300 0.000000 6 0.416700 0.000000 7 0.500000 0.000000 8 0.583300 0.000000 9 0.666700 0.000000 10 0.750000 0.000000 Element order = 6 Number of elements = 72 First 10 elements Row: 1 2 3 4 5 6 Col 1 1 27 3 14 15 2 2 29 3 27 16 15 28 3 3 29 5 16 17 4 4 31 5 29 18 17 30 5 5 31 7 18 19 6 6 33 7 31 20 19 32 7 7 33 9 20 21 8 8 35 9 33 22 21 34 9 9 35 11 22 23 10 10 37 11 35 24 23 36 Quadrature order = 3 Dirichlet boundary condition on pressure will be applied at node 1 Total number of variables is 387 Variable indices per node: Node U_index V_index P_index 1 1 2 3 2 4 5 -1 3 6 7 8 4 9 10 -1 5 11 12 13 6 14 15 -1 7 16 17 18 8 19 20 -1 9 21 22 23 10 24 25 -1 11 26 27 28 12 29 30 -1 13 31 32 33 14 34 35 -1 15 36 37 -1 16 38 39 -1 17 40 41 -1 18 42 43 -1 19 44 45 -1 20 46 47 -1 21 48 49 -1 22 50 51 -1 23 52 53 -1 24 54 55 -1 25 56 57 -1 26 58 59 -1 27 60 61 62 28 63 64 -1 29 65 66 67 30 68 69 -1 31 70 71 72 32 73 74 -1 33 75 76 77 34 78 79 -1 35 80 81 82 36 83 84 -1 37 85 86 87 38 88 89 -1 39 90 91 92 40 93 94 -1 41 95 96 -1 42 97 98 -1 43 99 100 -1 44 101 102 -1 45 103 104 -1 46 105 106 -1 47 107 108 -1 48 109 110 -1 49 111 112 -1 50 113 114 -1 51 115 116 -1 52 117 118 -1 53 119 120 121 54 122 123 -1 55 124 125 126 56 127 128 -1 57 129 130 131 58 132 133 -1 59 134 135 136 60 137 138 -1 61 139 140 141 62 142 143 -1 63 144 145 146 64 147 148 -1 65 149 150 151 66 152 153 -1 67 154 155 -1 68 156 157 -1 69 158 159 -1 70 160 161 -1 71 162 163 -1 72 164 165 -1 73 166 167 -1 74 168 169 -1 75 170 171 -1 76 172 173 -1 77 174 175 -1 78 176 177 -1 79 178 179 180 80 181 182 -1 81 183 184 185 82 186 187 -1 83 188 189 190 84 191 192 -1 85 193 194 195 86 196 197 -1 87 198 199 200 88 201 202 -1 89 203 204 205 90 206 207 -1 91 208 209 210 92 211 212 -1 93 213 214 -1 94 215 216 -1 95 217 218 -1 96 219 220 -1 97 221 222 -1 98 223 224 -1 99 225 226 -1 100 227 228 -1 101 229 230 -1 102 231 232 -1 103 233 234 -1 104 235 236 -1 105 237 238 239 106 240 241 -1 107 242 243 244 108 245 246 -1 109 247 248 249 110 250 251 -1 111 252 253 254 112 255 256 -1 113 257 258 259 114 260 261 -1 115 262 263 264 116 265 266 -1 117 267 268 269 118 270 271 -1 119 272 273 -1 120 274 275 -1 121 276 277 -1 122 278 279 -1 123 280 281 -1 124 282 283 -1 125 284 285 -1 126 286 287 -1 127 288 289 -1 128 290 291 -1 129 292 293 -1 130 294 295 -1 131 296 297 298 132 299 300 -1 133 301 302 303 134 304 305 -1 135 306 307 308 136 309 310 -1 137 311 312 313 138 314 315 -1 139 316 317 318 140 319 320 -1 141 321 322 323 142 324 325 -1 143 326 327 328 144 329 330 -1 145 331 332 -1 146 333 334 -1 147 335 336 -1 148 337 338 -1 149 339 340 -1 150 341 342 -1 151 343 344 -1 152 345 346 -1 153 347 348 -1 154 349 350 -1 155 351 352 -1 156 353 354 -1 157 355 356 357 158 358 359 -1 159 360 361 362 160 363 364 -1 161 365 366 367 162 368 369 -1 163 370 371 372 164 373 374 -1 165 375 376 377 166 378 379 -1 167 380 381 382 168 383 384 -1 169 385 386 387 NS_ADJ_COUNT returns NZ_NUM = 10281 ASSEMBLE_STOKES_SPARSE: Setting up sparse Stokes matrix with NZ_NUM = 10281 ASSEMBLE_STOKES_SPARSE: Sparse Stokes matrix used NZ_NUM = 10281 Initial block of Stokes stiffness matrix A: Col: 1 2 3 4 5 Row 1 1.000802 0 0.000017 -0.665869 0 2 0 1.000802 0.000017 0 -0.665869 3 -0.027817 -0.027817 0 0.027817 -0.027817 4 -0.665869 0 -0.027817 2.663473 0 5 0 -0.665869 -0.027817 0 2.663473 6 0.166267 0 0 -0.665069 0 7 0 0.166267 0 0 -0.665069 8 -0.000033 -0.000033 0 -0.027683 -0.055500 9 0 0 0 0 0 10 0 0 0 0 0 Col: 6 7 8 9 10 Row 1 0.166267 0 -0.000017 0 0 2 0 0.166267 0 0 0 3 0.000017 0 0 0 0 4 -0.665069 0 0.027817 0 0 5 0 -0.665069 0 0 0 6 2.000403 0 0.000008 -0.666667 0 7 0 2.000403 0.000008 0 -0.666667 8 -0.000058 -0.055625 0 0.027800 -0.027783 9 -0.666667 0 -0.027800 2.666668 0 10 0 -0.666667 -0.027783 0 2.666668 Part of finite element right hand side vector: 1 0.000000 2 0.000000 3 0.000000 4 0.000000 5 0.000000 6 0.000000 7 0.000000 8 0.000000 ...... .............. 387 0.000000 Matrix A after boundary condition adjustments: Col: 1 2 3 4 5 Row 1 1 0 0 0 0 2 0 1 0 0 0 3 0 0 1 0 0 4 0 0 0 1 0 5 0 0 0 0 1 6 0 0 0 0 0 7 0 0 0 0 0 8 -0.000033 -0.000033 0 -0.027683 -0.055500 9 0 0 0 0 0 10 0 0 0 0 0 Col: 6 7 8 9 10 Row 1 0 0 0 0 0 2 0 0 0 0 0 3 0 0 0 0 0 4 0 0 0 0 0 5 0 0 0 0 0 6 1 0 0 0 0 7 0 1 0 0 0 8 -0.000058 -0.055625 0 0.027800 -0.027783 9 0 0 0 1 0 10 0 0 0 0 1 Part of right hand side vector: 1 0.000000 2 0.000000 3 0.000000 4 0.000000 5 0.000000 6 0.000000 7 0.000000 8 0.000000 ...... .............. 387 0.000000 Part of the solution vector: 1 0.000000 2 0.000000 3 0.000000 4 0.000000 5 0.000000 6 0.000000 7 0.000000 8 1.486817 ...... .............. 387 31.939483 Variable indices per node: Node U V P 1 0.000000 0.000000 0.000000 2 0.000000 0.000000 3 0.000000 0.000000 1.486817 4 0.000000 0.000000 5 0.000000 0.000000 1.408328 6 0.000000 0.000000 7 0.000000 0.000000 1.862209 8 0.000000 0.000000 9 0.000000 0.000000 2.349928 10 0.000000 0.000000 11 0.000000 0.000000 2.425984 12 0.000000 0.000000 13 0.000000 0.000000 2.260008 14 0.000000 0.000000 15 -0.009846 -0.005416 16 -0.011256 0.005764 17 -0.023003 0.007675 18 -0.035299 0.005506 19 -0.042983 0.003050 20 -0.045595 -0.000257 21 -0.042823 -0.003338 22 -0.033678 -0.005614 23 -0.022534 -0.006717 24 -0.011258 -0.005329 25 -0.002346 -0.002040 26 0.000000 0.000000 27 0.000000 0.000000 1.867016 28 -0.005920 0.010633 29 -0.022604 0.019165 1.446318 30 -0.044148 0.022347 31 -0.062940 0.018815 1.587907 32 -0.075667 0.010994 33 -0.080500 -0.000191 1.875591 34 -0.075412 -0.010647 35 -0.061536 -0.019326 2.184738 36 -0.042362 -0.023117 37 -0.022363 -0.020073 2.246636 38 -0.006300 -0.011564 39 0.000000 0.000000 2.021266 40 0.000000 0.000000 41 -0.008792 0.025670 42 -0.032873 0.041815 43 -0.062161 0.046121 44 -0.086943 0.038124 45 -0.104232 0.020944 46 -0.110129 -0.000986 47 -0.103879 -0.022511 48 -0.085897 -0.039675 49 -0.060432 -0.047478 50 -0.033209 -0.043151 51 -0.009928 -0.025866 52 0.000000 0.000000 53 0.000000 0.000000 1.755521 54 -0.012943 0.046560 55 -0.042750 0.073642 1.381935 56 -0.079112 0.079189 57 -0.109912 0.063272 1.507735 58 -0.129856 0.034709 59 -0.136914 -0.000818 1.909128 60 -0.129245 -0.035439 61 -0.108250 -0.064195 2.309657 62 -0.077001 -0.078083 63 -0.042819 -0.072615 2.404342 64 -0.013312 -0.045915 65 0.000000 0.000000 2.001749 66 0.000000 0.000000 67 -0.015884 0.073117 68 -0.051663 0.112338 69 -0.096448 0.115293 70 -0.130609 0.090503 71 -0.151729 0.048691 72 -0.158811 -0.001463 73 -0.151361 -0.051571 74 -0.128210 -0.093288 75 -0.092689 -0.115281 76 -0.052969 -0.110975 77 -0.017418 -0.072663 78 0.000000 0.000000 79 0.000000 0.000000 1.148425 80 -0.018823 0.104065 81 -0.060942 0.153409 0.569976 82 -0.109970 0.154517 83 -0.144199 0.119286 1.138889 84 -0.163023 0.063538 85 -0.170289 -0.001774 1.919025 86 -0.163008 -0.066350 87 -0.140927 -0.122815 2.770806 88 -0.104977 -0.155965 89 -0.061704 -0.156833 3.037835 90 -0.019396 -0.106617 91 0.000000 0.000000 2.672183 92 0.000000 0.000000 93 -0.022668 0.143340 94 -0.067786 0.200375 95 -0.114395 0.190743 96 -0.140740 0.142543 97 -0.153032 0.074642 98 -0.157487 -0.001749 99 -0.153628 -0.078300 100 -0.138422 -0.147503 101 -0.113288 -0.198285 102 -0.070386 -0.208103 103 -0.013788 -0.138057 104 0.000000 0.000000 105 0.000000 0.000000 -0.277326 106 -0.029862 0.207741 107 -0.075025 0.251625 -0.937195 108 -0.097538 0.220618 109 -0.105560 0.158347 0.484682 110 -0.103136 0.082303 111 -0.103471 0.001423 1.991189 112 -0.104376 -0.078846 113 -0.106851 -0.156245 3.598255 114 -0.100474 -0.219339 115 -0.067000 -0.249440 5.199316 116 -0.014640 -0.181723 117 0.000000 0.000000 3.204207 118 0.000000 0.000000 119 -0.049469 0.238565 120 -0.069426 0.259735 121 -0.036102 0.210976 122 -0.007650 0.143320 123 0.012016 0.072568 124 0.019052 0.002034 125 0.013185 -0.067657 126 -0.009802 -0.139227 127 -0.048153 -0.218754 128 -0.053194 -0.272788 129 -0.060920 -0.256306 130 0.000000 0.000000 131 0.000000 0.000000 -8.274715 132 -0.016833 0.262765 133 0.007939 0.223465 -3.687748 134 0.122651 0.138895 135 0.193126 0.083304 -0.670392 136 0.224548 0.036433 137 0.241086 -0.002488 1.887019 138 0.226496 -0.047037 139 0.181587 -0.094603 4.069819 140 0.100056 -0.161507 141 0.017609 -0.222141 8.672718 142 -0.054278 -0.221212 143 0.000000 0.000000 16.509194 144 0.000000 0.000000 145 0.165459 0.170105 146 0.267422 0.092574 147 0.451842 0.050214 148 0.526474 0.025918 149 0.559088 0.010328 150 0.571536 -0.001389 151 0.561680 -0.014136 152 0.516587 -0.031053 153 0.441663 -0.060579 154 0.339303 -0.096774 155 0.153200 -0.153799 156 0.000000 0.000000 157 1.000000 0.000000 -25.647229 158 1.000000 0.000000 159 1.000000 0.000000 -1.936478 160 1.000000 0.000000 161 1.000000 0.000000 0.289823 162 1.000000 0.000000 163 1.000000 0.000000 1.868645 164 1.000000 0.000000 165 1.000000 0.000000 2.992005 166 1.000000 0.000000 167 1.000000 0.000000 7.500136 168 1.000000 0.000000 169 1.000000 0.000000 31.939483 Pressure nodes written to "nodes3.txt". Pressure triangles written to "triangles3.txt". Pressures written to "pressure3.txt". FFS_SPARSE: Normal end of execution. 26-Sep-2006 12:23:43 >>