January 2 2011 1:14:50.326 PM FEM2D_POISSON_SPARSE FORTRAN90 version: A version of FEM2D_POISSON using sparse storage and an iterative solver. Solution of the Poisson equation in an arbitrary region in 2 dimensions. - DEL H(x,y) DEL U(x,y) + K(x,y) * U(x,y) = F(x,y) in the region U(x,y) = G(x,y) on the boundary. The finite element method is used, with triangular elements, which must be a 3 node linear triangle. Node file is "lake_nodes.txt". Element file is "lake_elements.txt". Number of nodes = 621 First 10 nodes Row 1 2 Col 1 316.430 404.476 2 291.049 400.709 3 265.165 409.779 4 241.468 402.403 5 216.551 396.521 6 163.285 411.371 7 142.818 391.164 8 111.954 346.703 9 100.035 325.727 10 103.987 302.516 Element order = 3 Number of elements = 974 First 10 elements Row 1 2 3 Col 1 619 618 39 2 620 619 39 3 125 126 7 4 125 132 126 5 143 135 150 6 143 150 154 7 481 69 482 8 454 68 464 9 460 472 473 10 460 450 472 Quadrature order = 3 Number of nonzero coefficients NZ_NUM = 3811 Part of Finite Element matrix A: Col: 1 2 3 4 5 Row --- 1 38.1432 0.00000 0.00000 0.00000 0.00000 2 0.00000 26.8833 0.00000 0.00000 0.00000 3 0.00000 0.00000 17.3269 0.00000 0.00000 4 0.00000 0.00000 0.00000 29.7398 0.00000 5 0.00000 0.00000 0.00000 0.00000 32.1393 Col: 6 7 8 9 10 Row --- 6 19.3873 0.00000 0.00000 0.00000 0.00000 7 0.00000 31.9242 0.00000 0.00000 0.00000 8 0.00000 0.00000 19.4226 0.00000 0.00000 9 0.00000 0.00000 0.00000 19.4323 0.00000 10 0.00000 0.00000 0.00000 0.00000 19.3334 Part of right hand side vector F: 1 75.722004 2 48.003598 3 29.483373 4 47.636355 5 48.041335 6 27.745294 7 41.648929 8 18.481132 9 16.373685 10 14.506157 Part of A after adjustment for Dirichlet condition: Col: 1 2 3 4 5 Row --- 1 1.00000 0.00000 0.00000 0.00000 0.00000 2 0.00000 1.00000 0.00000 0.00000 0.00000 3 0.00000 0.00000 1.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 1.00000 0.00000 5 0.00000 0.00000 0.00000 0.00000 1.00000 Col: 6 7 8 9 10 Row --- 6 1.00000 0.00000 0.00000 0.00000 0.00000 7 0.00000 1.00000 0.00000 0.00000 0.00000 8 0.00000 0.00000 1.00000 0.00000 0.00000 9 0.00000 0.00000 0.00000 1.00000 0.00000 10 0.00000 0.00000 0.00000 0.00000 1.00000 Part of F after adjustment for Dirichlet condition: 1 1.0549145 2 0.98111051 3 0.95292498 4 0.88094008 5 0.81649259 6 0.78355232 7 0.69362307 8 0.53094571 9 0.46442088 10 0.40931678 ITR = 1 Residual = 0.261618E+08 K = 1 Residual = 7759.88 K = 2 Residual = 4033.04 K = 3 Residual = 2064.68 K = 4 Residual = 1043.06 K = 5 Residual = 590.617 K = 6 Residual = 322.866 K = 7 Residual = 216.484 K = 8 Residual = 135.267 K = 9 Residual = 86.7598 K = 10 Residual = 60.0294 K = 11 Residual = 41.0438 K = 12 Residual = 29.8870 K = 13 Residual = 24.2582 K = 14 Residual = 21.8413 K = 15 Residual = 20.7500 K = 16 Residual = 20.2328 K = 17 Residual = 20.0105 K = 18 Residual = 19.7626 K = 19 Residual = 19.3900 K = 20 Residual = 18.3958 ITR = 2 Residual = 18.3958 K = 1 Residual = 18.3958 K = 2 Residual = 17.7722 K = 3 Residual = 17.4770 K = 4 Residual = 17.3160 K = 5 Residual = 17.1703 K = 6 Residual = 16.9056 K = 7 Residual = 16.5692 K = 8 Residual = 16.1985 K = 9 Residual = 14.9125 K = 10 Residual = 12.7793 K = 11 Residual = 10.9527 K = 12 Residual = 8.89099 K = 13 Residual = 6.86045 K = 14 Residual = 4.80118 K = 15 Residual = 2.83188 K = 16 Residual = 1.65976 K = 17 Residual = 0.981748 K = 18 Residual = 0.665924 K = 19 Residual = 0.420939 K = 20 Residual = 0.235930 ITR = 3 Residual = 0.235930 K = 1 Residual = 0.235929 K = 2 Residual = 0.164212 K = 3 Residual = 0.105276 K = 4 Residual = 0.733652E-01 K = 5 Residual = 0.472247E-01 K = 6 Residual = 0.279413E-01 K = 7 Residual = 0.168423E-01 K = 8 Residual = 0.112185E-01 K = 9 Residual = 0.814604E-02 K = 10 Residual = 0.584313E-02 K = 11 Residual = 0.452534E-02 K = 12 Residual = 0.354520E-02 K = 13 Residual = 0.314372E-02 K = 14 Residual = 0.288613E-02 K = 15 Residual = 0.271897E-02 K = 16 Residual = 0.265755E-02 K = 17 Residual = 0.263704E-02 K = 18 Residual = 0.262256E-02 K = 19 Residual = 0.260362E-02 K = 20 Residual = 0.254773E-02 ITR = 4 Residual = 0.254773E-02 K = 1 Residual = 0.254773E-02 K = 2 Residual = 0.249656E-02 K = 3 Residual = 0.245217E-02 K = 4 Residual = 0.239541E-02 K = 5 Residual = 0.235476E-02 K = 6 Residual = 0.231478E-02 K = 7 Residual = 0.226651E-02 K = 8 Residual = 0.217984E-02 K = 9 Residual = 0.188785E-02 K = 10 Residual = 0.138505E-02 K = 11 Residual = 0.891989E-03 K = 12 Residual = 0.600467E-03 K = 13 Residual = 0.445279E-03 K = 14 Residual = 0.323841E-03 K = 15 Residual = 0.218872E-03 K = 16 Residual = 0.137001E-03 K = 17 Residual = 0.727478E-04 K = 18 Residual = 0.413069E-04 K = 19 Residual = 0.239360E-04 K = 20 Residual = 0.158441E-04 ITR = 5 Residual = 0.158441E-04 K = 1 Residual = 0.158441E-04 K = 2 Residual = 0.121049E-04 K = 3 Residual = 0.739210E-05 K = 4 Residual = 0.448480E-05 K = 5 Residual = 0.285688E-05 K = 6 Residual = 0.185708E-05 K = 7 Residual = 0.145440E-05 K = 8 Residual = 0.117317E-05 K = 9 Residual = 0.102672E-05 K = 10 Residual = 0.915139E-06 MGMRES: Iterations = 90 Final Residual = 0.915139E-06 Part of the solution vector U: 1 1.0549145 2 0.98111051 3 0.95292499 4 0.88094010 5 0.81649261 6 0.78355235 7 0.69362308 8 0.53094573 9 0.46442090 10 0.40931677 FEM2D_POISSON_SPARSE: Wrote an ASCII file "lake_solution.txt" of the form U ( X(I), Y(I) ) which can be used for plotting. FEM2D_POISSON_SPARSE: Normal end of execution. January 2 2011 1:14:50.368 PM