>> ffs_sparse ( 'nodes6.txt', 'triangles6.txt' ) 27-Mar-2007 11:38:06 FFS_SPARSE: MATLAB version: A version of FREE_FEM_STOKES 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 may be of Dirichlet type: U(x,y) = U_BC(x,y) V(x,y) = V_BC(x,y) P(x,y) = P_BC(x,y) or of Neumann type with zero right hand side: dU/dn(x,y) = 0 dV/dn(x,y) = 0 dP/dn(x,y) = 0 The finite element method uses Taylor-Hood triangular elements which are linear for pressure and quadratic for velocity. Quadrature order = 7 Kinematic viscosity NU = 1.000000 Current status: * testing zero Neumann condition option. 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 Dirichlet boundary condition on pressure will be applied at node 1 Number of Neumann conditions added = Boundary conditions per node: Node U_cond V_cond P_cond 1 2 2 2 2 2 2 0 3 2 2 1 4 2 2 0 5 2 2 1 6 2 2 0 7 2 2 1 8 2 2 0 9 2 2 1 10 2 2 0 (SKIPPING ENTRIES) 159 2 2 1 160 2 2 0 161 2 2 1 162 2 2 0 163 2 2 1 164 2 2 0 165 2 2 1 166 2 2 0 167 2 2 1 168 2 2 0 169 2 2 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 (SKIPPING ENTRIES) 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 1.001442 0 0.000010 -0.666509 0 2 0 1.001442 0.000010 0 -0.666509 3 -0.027830 -0.027830 0 0.027837 -0.027810 4 -0.666509 0 -0.027810 2.664753 0 5 0 -0.666509 -0.027810 0 2.664753 6 0.166427 0 -0.000007 -0.665548 0 7 0 0.166427 -0.000007 0 -0.665548 8 -0.000027 -0.000027 0 -0.027703 -0.055513 9 0 0 0 0 0 10 0 0 0 0 0 Col: 6 7 8 9 10 Row 1 0.166427 0 -0.000010 0 0 2 0 0.166427 0 0 0 3 0.000010 0 0 0 0 4 -0.665548 0 0.027810 0 0 5 0 -0.665548 0 0 0 6 2.000723 0 0.000012 -0.666667 0 7 0 2.000723 0.000012 0 -0.666667 8 -0.000052 -0.055618 0 0.027803 -0.027787 9 -0.666667 0 -0.027803 2.666668 0 10 0 -0.666667 -0.027787 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 9 0.000000 10 0.000000 Matrix A after Dirichlet BC 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 -0.000027 -0.000027 0 -0.027703 -0.055513 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 -0.000052 -0.055618 0 0.027803 -0.027787 9 0 0 0 1 0 10 0 0 0 0 1 Part of right hand side after Dirichlet BC adjustments: 1 0.000000 2 0.000000 3 0.000000 4 0.000000 5 0.000000 6 0.000000 7 0.000000 8 0.000000 9 0.000000 10 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 -25.670570 9 0.000000 10 0.000000 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 -25.670570 4 0.000000 0.000000 5 0.000000 0.000000 -29.178870 6 0.000000 0.000000 7 0.000000 0.000000 -29.678398 8 0.000000 0.000000 9 0.000000 0.000000 -29.777977 10 0.000000 0.000000 (SKIPPING ENTRIES) 159 0.000000 0.000000 -29.225993 160 0.000000 0.000000 161 0.000000 0.000000 -28.869249 162 0.000000 0.000000 163 0.000000 0.000000 -28.968828 164 0.000000 0.000000 165 0.000000 0.000000 -29.468356 166 0.000000 0.000000 167 0.000000 0.000000 -32.976656 168 0.000000 0.000000 169 0.000000 0.000000 -58.647226 Pressure nodes written to "nodes3.txt". Pressure triangles written to "triangles3.txt". Pressures written to "pressure3.txt". FFS_SPARSE: Normal end of execution. 27-Mar-2007 11:38:16 >>