19 August 2018 05:19:10 PM
FEM2D_POISSON_SPARSE:
C++ version:
Compiled on Aug 19 2018 at 17:19:10.
A finite element method solver for the Poisson problem
in an arbitrary triangulated region in 2 dimensions,
using sparse storage and an iterative solver.
- 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
1 316.43 404.476
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 = 973
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 = 3809
ITR = 1 Residual = 7759.26
K = 1 Residual = 4032.12
K = 2 Residual = 2064.15
K = 3 Residual = 1043.02
K = 4 Residual = 590.701
K = 5 Residual = 322.888
K = 6 Residual = 216.479
K = 7 Residual = 135.269
K = 8 Residual = 86.7756
K = 9 Residual = 60.0495
K = 10 Residual = 41.0706
K = 11 Residual = 29.9242
K = 12 Residual = 24.3014
K = 13 Residual = 21.8875
K = 14 Residual = 20.799
K = 15 Residual = 20.2832
K = 16 Residual = 20.0608
K = 17 Residual = 19.8118
K = 18 Residual = 19.4362
K = 19 Residual = 18.4348
K = 20 Residual = 16.6214
ITR = 2 Residual = 16.6214
K = 1 Residual = 15.4254
K = 2 Residual = 14.6186
K = 3 Residual = 14.2974
K = 4 Residual = 14.0434
K = 5 Residual = 13.8703
K = 6 Residual = 13.6962
K = 7 Residual = 13.5309
K = 8 Residual = 13.0732
K = 9 Residual = 12.0107
K = 10 Residual = 10.759
K = 11 Residual = 9.32398
K = 12 Residual = 7.74327
K = 13 Residual = 5.52235
K = 14 Residual = 3.19957
K = 15 Residual = 1.89204
K = 16 Residual = 1.20179
K = 17 Residual = 0.757334
K = 18 Residual = 0.472641
K = 19 Residual = 0.280781
K = 20 Residual = 0.164021
ITR = 3 Residual = 0.164021
K = 1 Residual = 0.116865
K = 2 Residual = 0.0754133
K = 3 Residual = 0.045688
K = 4 Residual = 0.03016
K = 5 Residual = 0.0198329
K = 6 Residual = 0.0120077
K = 7 Residual = 0.00750916
K = 8 Residual = 0.00545619
K = 9 Residual = 0.00449566
K = 10 Residual = 0.00379011
K = 11 Residual = 0.00347831
K = 12 Residual = 0.00329433
K = 13 Residual = 0.0031818
K = 14 Residual = 0.00309904
K = 15 Residual = 0.00305887
K = 16 Residual = 0.0030335
K = 17 Residual = 0.00299789
K = 18 Residual = 0.00291357
K = 19 Residual = 0.00267515
K = 20 Residual = 0.0023612
ITR = 4 Residual = 0.0023612
K = 1 Residual = 0.00212853
K = 2 Residual = 0.00193195
K = 3 Residual = 0.00183494
K = 4 Residual = 0.0017952
K = 5 Residual = 0.00177621
K = 6 Residual = 0.00176246
K = 7 Residual = 0.00175323
K = 8 Residual = 0.00172536
K = 9 Residual = 0.00165591
K = 10 Residual = 0.00152236
K = 11 Residual = 0.00135436
K = 12 Residual = 0.00107715
K = 13 Residual = 0.000826228
K = 14 Residual = 0.000555383
K = 15 Residual = 0.000339122
K = 16 Residual = 0.000210543
K = 17 Residual = 0.000130116
K = 18 Residual = 8.25018e-05
K = 19 Residual = 5.20703e-05
K = 20 Residual = 3.54808e-05
ITR = 5 Residual = 3.54808e-05
K = 1 Residual = 2.5882e-05
K = 2 Residual = 1.67548e-05
K = 3 Residual = 1.07909e-05
K = 4 Residual = 6.98778e-06
K = 5 Residual = 4.69741e-06
K = 6 Residual = 3.25793e-06
K = 7 Residual = 2.61248e-06
K = 8 Residual = 2.33701e-06
K = 9 Residual = 2.16195e-06
K = 10 Residual = 2.09054e-06
K = 11 Residual = 2.04157e-06
K = 12 Residual = 2.01477e-06
K = 13 Residual = 1.98718e-06
K = 14 Residual = 1.95718e-06
K = 15 Residual = 1.91756e-06
K = 16 Residual = 1.85474e-06
K = 17 Residual = 1.72696e-06
K = 18 Residual = 1.45154e-06
K = 19 Residual = 1.08169e-06
K = 20 Residual = 8.18145e-07
MGMRES
Number of iterations = 100
Final residual = 8.18145e-07
Part of the solution vector vector U:
1 1.05491
2 0.981111
3 0.952925
4 0.88094
5 0.816493
6 0.783552
7 0.693623
8 0.530946
9 0.464421
10 0.409317
FEM2D_POISSON_SPARSE:
Wrote an ASCII file
"lake_values.txt".
of the form
U ( X(I), Y(I) )
which can be used for plotting.
FEM2D_POISSON_SPARSE:
Normal end of execution.
19 August 2018 05:19:10 PM