08-Oct-2025 23:03:20 wathen_matrix_test(): MATLAB/Octave version 6.4.0. Test wathen_matrix(). wathen_test01(): Assemble, factor and solve a Wathen system defined by wathen_ge(). Elements in X direction NX = 4 Elements in Y direction NY = 4 Number of elements = 16 Number of nodes N = 65 Maximum solution error is 9.4369e-16 wathen_test02(): Assemble, factor and solve a Wathen system using wathen_gb(). Elements in X direction NX = 4 Elements in Y direction NY = 4 Number of elements = 16 Number of nodes N = 65 Lower bandwidth ML = 16 Lower bandwidth MU = 16 B: 1: -45.9914 2: 281.409 3: -339.082 4: 1546.84 5: -387.509 6: 1096.56 7: -380.593 8: 1261.52 9: -210.846 10: 427.672 11: 1384.65 12: 2704.43 13: 1826.43 14: 912.589 15: -568.127 16: 2127.49 17: -1400.67 18: 2436.82 19: -1593.38 20: 2603.12 21: -1291.04 22: 1417.16 23: -328.832 24: 1891.78 25: 3883.3 26: 4207.11 27: 2385.22 28: 724.197 29: -460.234 30: 1899.01 31: -1042.46 32: 2727.96 33: -1624.08 34: 4724.93 35: -1471.6 36: 678.403 37: -208.899 38: 59.6304 39: 716.31 40: 3237.63 41: 2359.31 42: 263.587 43: -85.3629 44: 336.71 45: -428.609 46: 1878.69 47: -1109.53 48: 1929.4 49: -1123.39 50: 1593.14 51: -429.002 52: 238.328 53: 1019.52 54: 1094.67 55: 1283.98 56: 1084.17 57: -36.4143 58: 225.774 59: -359.604 60: 970.195 61: -272.155 62: 60.2942 63: -353.239 64: 1266.09 65: -359.661 Maximum solution error is 8.77076e-15 wathen_test03(): Assemble, factor and solve a Wathen system defined by wathen_sparse(). Elements in X direction NX = 4 Elements in Y direction NY = 4 Number of elements = 16 Number of nodes N = 65 Maximum solution error is 9.99201e-16 wathen_test04() Assemble, factor and solve a Wathen system defined by wathen_davis(). Elements in X direction NX = 4 Elements in Y direction NY = 4 Number of elements = 16 Number of nodes N = 65 Maximum solution error is 9.99201e-16 wathen_test05() For various problem sizes and storage schemes, measure the storage used for the Wathen system. Predicted Observed GE Band Band Band Sparse NX Elements Nodes storage width width storage storage 1 1 8 64 15 15 176 64 2 4 21 441 21 21 651 221 4 16 65 4225 33 33 3185 817 8 64 225 50625 57 57 19125 3137 16 256 833 693889 105 105 130781 12289 32 1024 3201 10246401 201 201 963501 48641 wathen_test06(): For various problem sizes, time the assembly and factorization of a Wathen system using the wathen_ge() function. NX Elements Nodes Storage Assembly Factor Error 1 1 8 64 7.48e-04 2.88e-05 9.44e-16 2 4 21 441 2.54e-03 2.10e-05 1.11e-15 4 16 65 4225 9.85e-03 1.85e-04 1.67e-15 8 64 225 50625 6.08e-02 1.16e-03 1.11e-15 16 256 833 693889 2.09e-01 1.52e-02 1.44e-15 32 1024 3201 10246401 6.88e-01 3.00e-01 2.04e-15 wathen_test07(): For various problem sizes, time the assembly and factorization of a Wathen system using the wathen_gb() function. NX Elements Nodes Storage Assembly Factor Error 1 1 8 176 1.19e-03 3.19e-03 2.22e-16 2 4 21 651 4.20e-03 1.47e-02 3.33e-15 4 16 65 3185 1.63e-02 4.89e-02 5.47e-14 8 64 225 19125 4.02e-02 2.45e-01 3.44e-15 16 256 833 130781 1.62e-01 1.68e+00 9.33e-15 32 1024 3201 963501 6.45e-01 1.22e+01 1.32e-14 wathen_test08(): For various problem sizes, time the assembly and factorization of a Wathen system wathen_gb()/wathen_ge()/wathen_sparse()/wathen_davis(). NX Elements Nodes Storage Assembly Factor Error WATHEN_GE 1 1 8 64 7.17e-04 3.00e-05 4.44e-16 WATHEN_GB 1 1 8 176 7.39e-04 2.00e-03 5.55e-16 WATHEN_SPARSE 1 1 8 64 9.44e-04 4.39e-05 8.11e-01 WATHEN_DAVIS 1 1 8 64 7.53e-04 8.11e-06 2.86e-01 WATHEN_GE 2 4 21 441 2.45e-03 2.10e-05 1.44e-15 WATHEN_GB 2 4 21 651 2.59e-03 9.23e-03 1.78e-15 WATHEN_SPARSE 2 4 21 221 3.33e-03 1.60e-05 1.24e+01 WATHEN_DAVIS 2 4 21 221 2.57e-03 1.41e-05 6.52e-01 WATHEN_GE 4 16 65 4225 9.57e-03 1.66e-04 1.01e-15 WATHEN_GB 4 16 65 3185 1.65e-02 6.66e-02 2.36e-15 WATHEN_SPARSE 4 16 65 817 2.12e-02 1.35e-04 3.27e+00 WATHEN_DAVIS 4 16 65 817 1.68e-02 1.17e-04 8.64e-01 WATHEN_GE 8 64 225 50625 4.08e-02 6.81e-04 1.11e-15 WATHEN_GB 8 64 225 19125 6.52e-02 2.57e-01 4.33e-15 WATHEN_SPARSE 8 64 225 3137 5.55e-02 2.72e-04 3.09e+00 WATHEN_DAVIS 8 64 225 3137 3.96e-02 2.58e-04 2.56e+01 WATHEN_GE 16 256 833 693889 1.53e-01 1.02e-02 1.22e-15 WATHEN_GB 16 256 833 130781 2.17e-01 1.66e+00 5.78e-14 WATHEN_SPARSE 16 256 833 12289 2.66e-01 1.05e-03 9.99e+00 WATHEN_DAVIS 16 256 833 12289 1.59e-01 1.02e-03 4.41e+01 WATHEN_GE 32 1024 3201 10246401 6.38e-01 3.00e-01 1.85e-15 WATHEN_GB 32 1024 3201 963501 6.83e-01 1.18e+01 8.55e-15 WATHEN_SPARSE 32 1024 3201 48641 1.75e+00 9.35e-03 3.28e+01 WATHEN_DAVIS 32 1024 3201 48641 6.94e-01 1.13e-01 7.76e+01 wathen_test09(): For various problem sizes, time the assembly and factorization of a Wathen system using the wathen_sparse() and wathen_davis() functions. NX Elements Nodes Storage Assembly Factor Error WATHEN_SPARSE 32 1024 3201 48641 1.80e+00 6.78e-03 2.20e-15 WATHEN_DAVIS 32 1024 3201 48641 6.94e-01 1.03e-01 1.89e-15 WATHEN_SPARSE 64 4096 12545 193537 3.37e+01 2.48e-02 2.55e-15 WATHEN_DAVIS 64 4096 12545 193537 2.60e+00 2.44e-02 2.61e-15 WATHEN_SPARSE 128 16384 49665 772097 5.62e+02 5.67e-01 4.00e-15 WATHEN_DAVIS 128 16384 49665 772097 1.02e+01 1.93e+00 2.78e-15 wathen_test10() Assemble, factor and solve a Wathen system defined by wathen_ge() and cg_ge(). Elements in X direction NX = 2 Elements in Y direction NY = 2 Number of elements = 4 Number of nodes N = 21 Maximum solution error is 1.06793e-05 wathen_test11() Assemble, factor and solve a Wathen system defined by wathen_st() and cg_st(). Elements in X direction NX = 1 Elements in Y direction NY = 1 Number of elements = 1 Number of nodes N = 8 Number of nonzeros = 64 Maximum solution error is 6.10623e-16 wathen_test115() Assemble, factor and solve a Wathen system using wathen_gb() and cg_gb(). Elements in X direction NX = 2 Elements in Y direction NY = 2 Number of elements = 4 Number of nodes N = 21 Lower bandwidth ML = 10 Lower bandwidth MU = 10 Maximum solution error is 2.84818e-06 wathen_test12(): Assemble, factor and solve a Wathen system defined by wathen_davis() and cg_sparse(). Elements in X direction NX = 1 Elements in Y direction NY = 1 Number of elements = 1 Number of nodes N = 8 Maximum solution error is 1.88738e-15 wathen_spy_test Use spy() to display the sparsity of the Wathen matrix. Graphics file saved as "wathen_spy.png" wathen_xy_test(): wathen_xy() returns the (X,Y) coordinates of nodes. N was not supplied. N = 96 Graphics saved as "wathen_xy_test.png" wathen_matrix_test(): Normal end of execution. 08-Oct-2025 23:14:48