>> ffns_sparse ( 'nodes6.txt', 'triangles6.txt' ) 26-Sep-2006 15:09:05 FFNS_SPARSE (MATLAB version): This is a special version of FREE_FEM_NAVIER_STOKES which uses MATLAB sparse matrix storage, factorization, and solution methods, replacing the general banded approach. Finite element solution of the steady incompressible Navier Stokes equations on a triangulated region in 2 dimensions. - nu * ( Uxx + Uyy ) + UUx + VUy + dPdx = F1(x,y) - nu * ( Vxx + Vyy ) + UVx + VVy + 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. Maximum number of Newton iterations IT_MAX = 1: Fluid viscosity NU = 1.000000: Node file is "nodes6.txt". Element file is "triangles6.txt". Number of nodes = 8185 First 10 nodes Row: 1 2 Col 1 0.000000 0.000000 2 0.000000 1.000000 3 0.000000 0.500000 4 0.000000 0.143160 5 0.000000 0.856840 6 0.000000 0.233640 7 0.000000 0.766360 8 0.000000 0.063210 9 0.000000 0.936790 10 0.000000 0.299300 Element order = 6 Number of elements = 4000 First 10 elements Row: 1 2 3 4 5 6 Col 1 1 22 24 58 59 60 2 22 1 195 58 61 224 3 24 23 16 62 63 64 4 23 24 22 62 59 65 5 22 193 23 225 226 65 6 342 193 22 362 225 227 7 342 195 480 228 363 364 8 23 193 196 226 229 230 9 343 193 342 365 362 366 10 342 484 343 367 516 366 Quadrature order = 3 Dirichlet boundary condition on pressure will be applied at node 1 Total number of variables is 18463 Variable indices per node: Node U_index V_index P_index 1 1 2 3 2 4 5 6 3 7 8 9 4 10 11 12 5 13 14 15 6 16 17 18 7 19 20 21 8 22 23 24 9 25 26 27 10 28 29 30 (SKIPPING ENTRIES) 8175 18442 18443 -1 8176 18444 18445 -1 8177 18446 18447 -1 8178 18448 18449 -1 8179 18450 18451 -1 8180 18452 18453 -1 8181 18454 18455 -1 8182 18456 18457 -1 8183 18458 18459 -1 8184 18460 18461 -1 8185 18462 18463 -1 NS_ADJ_COUNT returns NZ_NUM = 539069 ASSEMBLE_STOKES_SPARSE: Setting up sparse Stokes matrix with NZ_NUM = 539069 ASSEMBLE_STOKES_SPARSE: Sparse Stokes matrix used NZ_NUM = 539069 Initial block of Stokes stiffness matrix A: Col: 1 2 3 4 5 Row 1 0.845997 0 0.000000 0 0 2 0 0.845997 0.000001 0 0 3 -0.002351 -0.002595 0 0 0 4 0 0 0 0.845997 0 5 0 0 0 0 0.845997 6 0 0 0 -0.002351 0.002595 7 0 0 0 0 0 8 0 0 0 0 0 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 0.000000 0 0 0 0 5 -0.000001 0 0 0 0 6 0 0 0 0 0 7 0 2.822633 0 -0.000006 0 8 0 0 2.822633 0.000000 0 9 0 -0.012510 0.000000 0 0 10 0 0 0 0 1.689724 Part of Stokes 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 ...... .............. 18463 0.000000 Stokes matrix 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 -0.002351 0.002595 7 0 0 0 0 0 8 0 0 0 0 0 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 0 0 0 0 0 7 0 1 0 0 0 8 0 0 1 0 0 9 0 -0.012510 0.000000 0 0 10 0 0 0 0 1 Part of adjusted Stokes right hand: 1 0.000000 2 0.000000 3 0.000000 4 1.000000 5 0.000000 6 0.000000 7 0.000000 8 0.000000 ...... .............. 18463 0.000000 Part of the solution vector: 1 0.000000 2 0.000000 3 0.000000 4 1.000000 5 0.000000 6 -354.993174 7 0.000000 8 0.000000 ...... .............. 18463 0.000000 Solution to the STOKES equations: Node U V P 1 0.000000 0.000000 0.000000 2 1.000000 0.000000 -354.993174 3 0.000000 0.000000 -2.914764 4 0.000000 0.000000 -2.497820 5 0.000000 0.000000 -13.707704 6 0.000000 0.000000 -2.374983 7 0.000000 0.000000 -7.696647 8 0.000000 0.000000 -2.640208 9 0.000000 0.000000 -32.282745 10 0.000000 0.000000 -2.354836 (SKIPPING ENTRIES) 8175 0.000000 0.000000 8176 0.000000 0.000000 8177 0.000000 0.000000 8178 0.000000 0.000000 8179 0.000000 0.000000 8180 0.000000 0.000000 8181 0.000000 0.000000 8182 0.000000 0.000000 8183 0.000000 0.000000 8184 0.000000 0.000000 8185 0.000000 0.000000 Pressure nodes written to "nodes3.txt". Pressure triangles written to "triangles3.txt". Pressures written to "stokes_pressure3.txt". Part of Navier-Stokes FEM residual: 1 -0.000966 2 -0.001077 3 0.000014 4 0.506479 5 -0.054415 6 -0.000000 7 0.000018 8 -0.021603 ...... .............. 18463 0.567309 l2-norm of FEM residual = 2.794485 Part of Navier-Stokes FEM residual adjusted for BC: 1 0.000000 2 0.000000 3 0.000000 4 0.000000 5 0.000000 6 -0.000000 7 0.000000 8 0.000000 ...... .............. 18463 0.000000 l2-norm of adjusted FEM residual = 0.003488 JACOBIAN_FEM_SPARSE: Setting up sparse Stokes matrix with NZ_NUM = 539069 JACOBIAN_FEM_SPARSE: Sparse Stokes matrix used NZ_NUM = 539069 Part of Newton correction vector: 1 0.000000 2 0.000000 3 0.000000 4 0.000000 5 0.000000 6 0.729062 7 0.000000 8 0.000000 ...... .............. 18463 0.000000 l2-norm of Newton correction = 8.849382 Part of Navier-Stokes FEM residual: 1 -0.000901 2 -0.001004 3 0.000013 4 0.506545 5 -0.054375 6 0.000000 7 0.000018 8 -0.021584 ...... .............. 18463 0.567798 l2-norm of FEM residual = 2.794431 Part of Navier-Stokes FEM residual adjusted for BC: 1 0.000000 2 0.000000 3 0.000000 4 0.000000 5 0.000000 6 0.000000 7 0.000000 8 0.000000 ...... .............. 18463 0.000000 l2-norm of adjusted FEM residual = 0.000000 Convergence. Navier Stokes Pressures written to "navier_stokes_pressure3.txt". Navier Stokes velocities written to "navier_stokes_velocity6.txt". FFNS_SPARSE: Normal end of execution. 26-Sep-2006 15:27:20 >>