26 December 2010 10:43:12.284 AM FREE_FEM_POISSON FORTRAN90 version: 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. Current status: * Boundary conditions cannot be set easily. 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 The matrix half bandwidth is 581 The matrix bandwidth is 1163 The storage bandwidth is 1744 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 6 0.00000 0.00000 0.00000 0.00000 0.00000 7 0.00000 0.00000 0.00000 0.00000 0.00000 8 0.00000 0.00000 0.00000 0.00000 0.00000 9 0.00000 0.00000 0.00000 0.00000 0.00000 10 0.00000 0.00000 0.00000 0.00000 0.00000 Col: 6 7 8 9 10 Row --- 1 0.00000 0.00000 0.00000 0.00000 0.00000 2 0.00000 0.00000 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 0.00000 0.00000 5 0.00000 0.00000 0.00000 0.00000 0.00000 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 6 0.00000 0.00000 0.00000 0.00000 0.00000 7 0.00000 0.00000 0.00000 0.00000 0.00000 8 0.00000 0.00000 0.00000 0.00000 0.00000 9 0.00000 0.00000 0.00000 0.00000 0.00000 10 0.00000 0.00000 0.00000 0.00000 0.00000 Col: 6 7 8 9 10 Row --- 1 0.00000 0.00000 0.00000 0.00000 0.00000 2 0.00000 0.00000 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 0.00000 0.00000 5 0.00000 0.00000 0.00000 0.00000 0.00000 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 Part of the solution vector U: 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 Maximum absolute residual = 0.613230E-08 FREE_FEM_POISSON: Wrote an ASCII file "lake_solution.txt" of the form U ( X(I), Y(I) ) which can be used for plotting. FREE_FEM_POISSON: Normal end of execution. 26 December 2010 10:43:12.653 AM