08-Jan-2022 11:04:59 wathen_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2. Test wathen(). 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 1.19349e-15 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: -14.353 2: 208.104 3: -59.2505 4: 183.561 5: -109.191 6: 346.997 7: -162.022 8: 394.787 9: -99.0463 10: 149.407 11: 255.758 12: 442.971 13: 772.95 14: 446.624 15: -242.719 16: 822.789 17: -206.488 18: 115.062 19: -185.18 20: 498.883 21: -341.719 22: 1464.52 23: -401.276 24: 534.639 25: 703.893 26: 239.649 27: 1805.25 28: 1294.47 29: -249.564 30: 1092.04 31: -357.872 32: 117.193 33: 104.54 34: 460.651 35: -241.503 36: 2149.8 37: -304.826 38: 446.266 39: 706.224 40: 135.007 41: 1481.58 42: 471.899 43: -191.104 44: 1189.84 45: -65.2016 46: 103.149 47: -62.2339 48: 313.986 49: -82.293 50: 1255.23 51: -204.121 52: 390.411 53: 486.895 54: 168.581 55: 484.24 56: 589.142 57: -94.4358 58: 407.807 59: -144.653 60: 122.795 61: 63.1933 62: 179.845 63: -80.9119 64: 441.314 65: -125.937 Maximum solution error is 8.88178e-16 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 8.88178e-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 1.44329e-15 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 1.94e-04 9.80e-05 1.11e-15 2 4 21 441 1.34e-04 8.90e-05 5.55e-16 4 16 65 4225 9.90e-05 1.32e-04 1.33e-15 8 64 225 50625 2.25e-04 8.15e-04 1.22e-15 16 256 833 693889 3.16e-03 9.11e-03 2.04e-15 32 1024 3201 10246401 8.12e-03 1.58e-01 2.45e-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 2.11e-03 4.58e-03 1.22e-15 2 4 21 651 3.94e-04 1.60e-03 1.44e-15 4 16 65 3185 1.36e-04 4.49e-03 1.78e-15 8 64 225 19125 1.20e-03 2.46e-02 2.16e-15 16 256 833 130781 4.94e-04 1.43e-01 4.00e-15 32 1024 3201 963501 5.86e-03 1.10e+00 6.64e-12 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 5.10e-05 5.20e-05 8.36e-16 WATHEN_GB 1 1 8 176 4.10e-05 1.26e-03 6.66e-16 WATHEN_SPARSE 1 1 8 64 1.50e-03 7.00e-05 7.38e-01 WATHEN_DAVIS 1 1 8 64 1.62e-03 2.10e-05 7.59e-01 WATHEN_GE 2 4 21 441 4.90e-05 3.40e-05 1.44e-15 WATHEN_GB 2 4 21 651 3.60e-05 8.34e-04 9.99e-16 WATHEN_SPARSE 2 4 21 221 7.78e-04 2.20e-05 7.28e-01 WATHEN_DAVIS 2 4 21 221 5.90e-04 2.20e-05 1.26e+01 WATHEN_GE 4 16 65 4225 4.50e-05 5.80e-05 1.44e-15 WATHEN_GB 4 16 65 3185 4.50e-05 3.36e-03 3.89e-15 WATHEN_SPARSE 4 16 65 817 2.01e-03 9.60e-05 1.49e+00 WATHEN_DAVIS 4 16 65 817 1.37e-04 8.20e-05 8.89e-01 WATHEN_GE 8 64 225 50625 9.10e-05 3.31e-04 1.78e-15 WATHEN_GB 8 64 225 19125 9.70e-05 1.99e-02 4.55e-15 WATHEN_SPARSE 8 64 225 3137 9.04e-03 2.61e-04 5.66e+01 WATHEN_DAVIS 8 64 225 3137 1.33e-03 2.56e-04 2.74e+01 WATHEN_GE 16 256 833 693889 7.25e-04 5.73e-03 1.67e-15 WATHEN_GB 16 256 833 130781 4.44e-04 1.52e-01 6.55e-15 WATHEN_SPARSE 16 256 833 12289 4.19e-02 1.43e-03 2.28e+01 WATHEN_DAVIS 16 256 833 12289 6.68e-04 1.08e-03 9.83e+00 WATHEN_GE 32 1024 3201 10246401 7.88e-03 1.64e-01 2.55e-15 WATHEN_GB 32 1024 3201 963501 3.79e-03 1.19e+00 1.11e-14 WATHEN_SPARSE 32 1024 3201 48641 3.45e-01 6.65e-03 2.52e+01 WATHEN_DAVIS 32 1024 3201 48641 3.12e-03 1.12e-02 1.56e+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 3.03e-01 3.89e-03 2.89e-15 WATHEN_DAVIS 32 1024 3201 48641 1.54e-03 3.88e-03 2.33e-15 WATHEN_SPARSE 64 4096 12545 193537 2.82e+00 1.68e-02 4.44e-15 WATHEN_DAVIS 64 4096 12545 193537 6.07e-03 1.53e-02 7.11e-15 WATHEN_SPARSE 128 16384 49665 772097 6.27e+01 7.94e-02 4.44e-15 WATHEN_DAVIS 128 16384 49665 772097 2.91e-02 6.87e-02 4.77e-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 5.38235e-07 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 1.44329e-15 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 1.43409e-05 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 5.55112e-16 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_test(): Normal end of execution. 08-Jan-2022 11:06:14